text:
Extinction event

An extinction event (also known as a mass extinction or biotic crisis) is a widespread and rapid decrease in the biodiversity on Earth. Such an event is identified by a sharp fall in the diversity and abundance of multicellular organisms. It occurs when the rate of extinction increases with respect to the background extinction rate and the rate of speciation. Estimates of the number of major mass extinctions in the last 540 million years range from as few as five to more than twenty. These differences stem from disagreement as to what constitutes a "major" extinction event, and the data chosen to measure past diversity.

The "Big Five" mass extinctions
In a landmark paper published in 1982, Jack Sepkoski and David M. Raup identified five particular geological intervals with excessive diversity loss. They were originally identified as outliers on a general trend of decreasing extinction rates during the Phanerozoic, but as more stringent statistical tests have been applied to the accumulating data, it has been established that in the current, Phanerozoic Eon, multicellular animal life has experienced at least five major and many minor mass extinctions. The "Big Five" cannot be so clearly defined, but rather appear to represent the largest (or some of the largest) of a relatively smooth continuum of extinction events. All of the five in the Phanerozoic Eon were anciently preceded by the presumed far more extensive mass extinction of microbial life during the Oxygen Catastrophe early in the Proterozoic Eon. At the end of the Ediacaran and just before the Cambrian explosion, yet another Proterozoic extinction event (of unknown magnitude) is speculated to have ushered in the Phanerozoic.

Despite the common presentation focusing only on these five events, no measure of extinction shows any definite line separating them from the many other Phanerozoic extinction events that appear only slightly lesser catastrophies; further, using different methods of calculating an extinction's impact can lead to other events featuring in the top five.

Fossil records of older events are more difficult to interpret. This is because:
 * Older fossils are harder to find as they are usually buried at a considerable depth.
 * Dating of older fossils is more difficult.
 * Productive fossil beds are researched more than unproductive ones, therefore leaving certain periods unresearched.
 * Prehistoric environmental events can disturb the deposition process.
 * Marine fossils tend to be better preserved than their more sought-after land-based counterparts, but the deposition and preservation of fossils on land is more erratic.

It has been suggested that the apparent variations in marine biodiversity may actually be an artifact, with abundance estimates directly related to quantity of rock available for sampling from different time periods. However, statistical analysis shows that this can only account for 50% of the observed pattern, and other evidence such as fungal spikes (geologically rapid increase in fungal abundance) provides reassurance that most widely accepted extinction events are real. A quantification of the rock exposure of Western Europe indicates that many of the minor events for which a biological explanation has been sought are most readily explained by sampling bias.

Sixth mass extinction
Research completed after the seminal 1982 paper (Sepkoski and Raup) has concluded that a sixth mass extinction event is ongoing due to human activities:

Extinctions by severity
Extinction events can be tracked by several methods, including geological change, ecological impact, extinction vs. origination (speciation) rates, and most commonly diversity loss among taxonomic units. Most early papers used families as the unit of taxonomy, based on compendiums of marine animal families by Sepkoski (1982, 1992). Later papers by Sepkoski and other authors switched to genera, which are more precise than families and less prone to taxonomic bias or incomplete sampling relative to species. These are several major papers estimating loss or ecological impact from fifteen commonly-discussed extinction events. Different methods used by these papers are described in the following section. The "Big Five" mass extinctions are bolded. Graphed but not discussed by Sepkoski (1996), considered continuous with the Late Devonian mass extinction At the time considered continuous with the end-Permian mass extinction  Includes late Norian time slices  Diversity loss of both pulses calculated together  Pulses extend over adjacent time slices, calculated separately  Considered ecologically significant, but not analyzed directly  Excluded due to a lack of consensus on Late Triassic chronology

Breakthrough studies in the 1980s–1990s
For much of the 20th century, the study of mass extinctions was hampered by insufficient data. Mass extinctions, though acknowledged, were considered mysterious exceptions to the prevailing gradualistic view of prehistory, where slow evolutionary trends define faunal changes. The first breakthrough was published in 1980 by a team led by Luis Alvarez, who discovered trace metal evidence for an asteroid impact at the end of the Cretaceous period. The Alvarez hypothesis for the end-Cretaceous extinction gave mass extinctions, and catastrophic explanations, newfound popular and scientific attention. Another landmark study came in 1982, when a paper written by David M. Raup and Jack Sepkoski was published in the journal Science. This paper, originating from a compendium of extinct marine animal families developed by Sepkoski, identified five peaks of marine family extinctions which stand out among a backdrop of decreasing extinction rates through time. Four of these peaks were statistically significant: the Ashgillian (end-Ordovician), Late Permian, Norian (end-Triassic), and Maastrichtian (end-Cretaceous). The remaining peak was a broad interval of high extinction smeared over the later half of the Devonian, with its apex in the Frasnian stage.

Through the 1980s, Raup and Sepkoski continued to elaborate and build upon their extinction and origination data, defining a high-resolution biodiversity curve (the "Sepkoski curve") and successive evolutionary faunas with their own patterns of diversification and extinction. Though these interpretations formed a strong basis for subsequent studies of mass extinctions, Raup and Sepkoski also proposed a more controversial idea in 1984: a 26-million-year periodic pattern to mass extinctions. Two teams of astronomers linked this to a hypothetical brown dwarf in the distant reaches of the solar system, inventing the "Nemesis hypothesis" which has been strongly disputed by other astronomers.

Around the same time, Sepkoski began to devise a compendium of marine animal genera, which would allow researchers to explore extinction at a finer taxonomic resolution. He began to publish preliminary results of this in-progress study as early as 1986, in a paper which identified 29 extinction intervals of note. By 1992, he also updated his 1982 family compendium, finding minimal changes to the diversity curve despite a decade of new data. In 1996, Sepkoski published another paper which tracked marine genera extinction (in terms of net diversity loss) by stage, similar to his previous work on family extinctions. The paper filtered its sample in three ways: all genera (the entire unfiltered sample size), multiple-interval genera (only those found in more than one stage), and "well-preserved" genera (excluding those from groups with poor or understudied fossil records). Diversity trends in marine animal families were also revised based on his 1992 update.

Revived interest in mass extinctions led many other authors to re-evaluate geological events in the context of their effects on life. A 1995 paper by Michael Benton tracked extinction and origination rates among both marine and continental (freshwater & terrestrial) families, identifying 22 extinction intervals and no periodic pattern. Overview books by O.H. Walliser (1996) and A. Hallam and P.B. Wignall (1997) summarized the new extinction research of the previous two decades. One chapter in the former source lists over 60 geological events which could conceivably be considered global extinctions of varying sizes. These texts, and other widely circulated publications in the 1990s, helped to establish the popular image of mass extinctions as a "big five" alongside many smaller extinctions through prehistory.

New data on genera: Sepkoski's compendium
Though Sepkoski passed away in 1999, his marine genera compendium was formally published in 2002. This prompted a new wave of studies into the dynamics of mass extinctions. These papers utilized the compendium to track origination rates (the rate that new species appear or speciate) parallel to extinction rates in the context of geological stages or substages. A review and re-analysis of Sepkoski's data by Bambach (2006) identified 18 distinct mass extinction intervals, including 4 large extinctions in the Cambrian. These fit Sepkoski's definition of extinction, as short substages with large diversity loss and overall high extinction rates relative to their surroundings.

Bambach et al. (2004) considered each of the "Big Five" extinction intervals to have a different pattern in the relationship between origination and extinction trends. Moreover, background extinction rates were broadly variable and could be separated into more severe and less severe time intervals. Background extinctions were least severe relative to the origination rate in the middle Ordovician-early Silurian, late Carboniferous-Permian, and Jurassic-recent. This argues that the Late Ordovician, end-Permian, and end-Cretaceous extinctions were statistically significant outliers in biodiversity trends, while the Late Devonian and end-Triassic extinctions occurred in time periods which were already stressed by relatively high extinction and low origination.

Computer models run by Foote (2005) determined that abrupt pulses of extinction fit the pattern of prehistoric biodiversity much better than a gradual and continuous background extinction rate with smooth peaks and troughs. This strongly supports the utility of rapid, frequent mass extinctions as a major driver of diversity changes. Pulsed origination events are also supported, though to a lesser degree which is largely dependent on pulsed extinctions.

Similarly, Stanley (2007) used extinction and origination data to investigate turnover rates and extinction responses among different evolutionary faunas and taxonomic groups. In contrast to previous authors, his diversity simulations show support for an overall exponential rate of biodiversity growth through the entire Phanerozoic.

Tackling biases in the fossil record
As data continued to accumulate, some authors began to re-evaluate Sepkoski's sample using methods meant to account for sampling biases. As early as 1982, a paper by Phillip W. Signor and Jere H. Lipps noted that the true sharpness of extinctions was diluted by the incompleteness of the fossil record. This phenomenon, later called the Signor-Lipps effect, notes that a species' true extinction must occur after its last fossil, and that origination must occur before its first fossil. Thus, species which appear to die out just prior to an abrupt extinction event may instead be a victim of the event, despite an apparent gradual decline looking at the fossil record alone. A model by Foote (2007) found that many geological stages had artificially inflated extinction rates due to Signor-Lipps "backsmearing" from later stages with extinction events. Other biases include the difficulty in assessing taxa with high turnover rates or restricted occurrences, which cannot be directly assessed due to a lack of fine-scale temporal resolution. Many paleontologists opt to assess diversity trends by randomized sampling and rarefaction of fossil abundances rather than raw temporal range data, in order to account for all of these biases. But that solution is influenced by biases related to sample size. One major bias in particular is the "Pull of the recent", the fact that the fossil record (and thus known diversity) generally improves closer to the modern day. This means that biodiversity and abundance for older geological periods may be underestimated from raw data alone.

Alroy (2010) attempted to circumvent sample size-related biases in diversity estimates using a method he called "shareholder quorum subsampling" (SQS). In this method, fossils are sampled from a "collection" (such as a time interval) to assess the relative diversity of that collection. Every time a new species (or other taxon) enters the sample, it brings over all other fossils belonging to that species in the collection (its "share" of the collection). For example, a skewed collection with half its fossils from one species will immediately reach a sample share of 50% if that species is the first to be sampled. This continues, adding up the sample shares until a "coverage" or "quorum" is reached, referring to a pre-set desired sum of share percentages. At that point, the number of species in the sample are counted. A collection with more species is expected to reach a sample quorum with more species, thus accurately comparing the relative diversity change between two collections without relying on the biases inherent to sample size.

Alroy also elaborated on three-timer algorithms, which are meant to counteract biases in estimates of extinction and origination rates. A given taxon is a "three-timer" if it can be found before, after, and within a given time interval, and a "two-timer" if it overlaps with a time interval on one side. Counting "three-timers" and "two-timers" on either end of a time interval, and sampling time intervals in sequence, can together be combined into equations to predict extinction and origination with less bias. In subsequent papers, Alroy continued to refine his equations to improve lingering issues with precision and unusual samples.

McGhee et al. (2013), a paper which primarily focused on ecological effects of mass extinctions, also published new estimates of extinction severity based on Alroy's methods. Many extinctions were significantly more impactful under these new estimates, though some were less prominent.

Stanley (2016) was another paper which attempted to remove two common errors in previous estimates of extinction severity. The first error was the unjustified removal of "singletons", genera unique to only a single time slice. Their removal would mask the influence of groups with high turnover rates or lineages cut short early in their diversification. The second error was the difficulty in distinguishing background extinctions from brief mass extinction events within the same short time interval. To circumvent this issue, background rates of diversity change (extinction/origination) were estimated for stages or substages without mass extinctions, and then assumed to apply to subsequent stages with mass extinctions. For example, the Santonian and Campanian stages were each used to estimate diversity changes in the Maastrichtian prior to the K-Pg mass extinction. Subtracting background extinctions from extinction tallies had the effect of reducing the estimated severity of the six sampled mass extinction events. This effect was stronger for mass extinctions which occurred in periods with high rates of background extinction, like the Devonian.

Uncertainty in the Proterozoic and earlier eons
Because most diversity and biomass on Earth is microbial, and thus difficult to measure via fossils, extinction events placed on-record are those that affect the easily observed, biologically complex component of the biosphere rather than the total diversity and abundance of life. For this reason, well-documented extinction events are confined to the Phanerozoic eon – with the sole exception of the Oxygen Catastrophe in the Proterozoic – since before the Phanerozoic, all living organisms were either microbial, or if multicellular then soft-bodied. Perhaps due to the absence of a robust microbial fossil record, mass extinctions might only seem to be mainly a Phanerozoic phenomenon, with merely the observable extinction rates appearing low before large complex organisms with hard body parts arose.

Extinction occurs at an uneven rate. Based on the fossil record, the background rate of extinctions on Earth is about two to five taxonomic families of marine animals every million years.

The Oxygen Catastrophe, which occurred around 2.45 billion years ago in the Paleoproterozoic, is plausible as the first-ever major extinction event. It was perhaps also the worst-ever, in some sense, but with the Earth's ecology just before that time so poorly understood, and the concept of prokaryote genera so different from genera of complex life, that it would be difficult to meaningfully compare it to any of the "Big Five" even if Paleoproterozoic life were better known.

Since the Cambrian explosion, five further major mass extinctions have significantly exceeded the background extinction rate. The most recent and best-known, the Cretaceous–Paleogene extinction event, which occurred approximately Ma (million years ago), was a large-scale mass extinction of animal and plant species in a geologically short period of time. In addition to the five major Phanerozoic mass extinctions, there are numerous lesser ones, and the ongoing mass extinction caused by human activity is sometimes called the sixth mass extinction.

Evolutionary importance
Mass extinctions have sometimes accelerated the evolution of life on Earth. When dominance of particular ecological niches passes from one group of organisms to another, it is rarely because the newly dominant group is "superior" to the old but usually because an extinction event eliminates the old, dominant group and makes way for the new one, a process known as adaptive radiation.

For example, mammaliaformes ("almost mammals") and then mammals existed throughout the reign of the dinosaurs, but could not compete in the large terrestrial vertebrate niches that dinosaurs monopolized. The end-Cretaceous mass extinction removed the non-avian dinosaurs and made it possible for mammals to expand into the large terrestrial vertebrate niches. The dinosaurs themselves had been beneficiaries of a previous mass extinction, the end-Triassic, which eliminated most of their chief rivals, the crurotarsans. Similarly, within Synapsida, the replacement of taxa that originated in the earliest, Pennsylvanian and Cisuralian evolutionary radiation (often still called "pelycosaurs", though this is a paraphyletic group) by therapsids occurred around the Kungurian/Roadian transition, which is often called Olson's extinction  (which may be a slow decline over 20 Ma rather than a dramatic, brief event).

Another point of view put forward in the Escalation hypothesis predicts that species in ecological niches with more organism-to-organism conflict will be less likely to survive extinctions. This is because the very traits that keep a species numerous and viable under fairly static conditions become a burden once population levels fall among competing organisms during the dynamics of an extinction event.

Furthermore, many groups that survive mass extinctions do not recover in numbers or diversity, and many of these go into long-term decline, and these are often referred to as "Dead Clades Walking". However, clades that survive for a considerable period of time after a mass extinction, and which were reduced to only a few species, are likely to have experienced a rebound effect called the "push of the past".

Darwin was firmly of the opinion that biotic interactions, such as competition for food and space – the 'struggle for existence' – were of considerably greater importance in promoting evolution and extinction than changes in the physical environment. He expressed this in The Origin of Species:
 * "Species are produced and exterminated by slowly acting causes ... and the most import of all causes of organic change is one which is almost independent of altered ... physical conditions, namely the mutual relation of organism to organism – the improvement of one organism entailing the improvement or extermination of others".

Patterns in frequency
Various authors have suggested that extinction events occurred periodically, every 26 to 30 million years, or that diversity fluctuates episodically about every 62 million years. Various ideas, mostly regarding astronomical influences, attempt to explain the supposed pattern, including the presence of a hypothetical companion star to the Sun, oscillations in the galactic plane, or passage through the Milky Way's spiral arms. However, other authors have concluded that the data on marine mass extinctions do not fit with the idea that mass extinctions are periodic, or that ecosystems gradually build up to a point at which a mass extinction is inevitable. Many of the proposed correlations have been argued to be spurious or lacking statistical significance. Others have argued that there is strong evidence supporting periodicity in a variety of records, and additional evidence in the form of coincident periodic variation in nonbiological geochemical variables such as Strontium isotopes, flood basalts, anoxic events, orogenies, and evaporite deposition. One explanation for this proposed cycle is carbon storage and release by oceanic crust, which exchanges carbon between the atmosphere and mantle.

Mass extinctions are thought to result when a long-term stress is compounded by a short-term shock. Over the course of the Phanerozoic, individual taxa appear to have become less likely to suffer extinction, which may reflect more robust food webs, as well as fewer extinction-prone species, and other factors such as continental distribution. However, even after accounting for sampling bias, there does appear to be a gradual decrease in extinction and origination rates during the Phanerozoic. This may represent the fact that groups with higher turnover rates are more likely to become extinct by chance; or it may be an artefact of taxonomy: families tend to become more speciose, therefore less prone to extinction, over time; and larger taxonomic groups (by definition) appear earlier in geological time.

It has also been suggested that the oceans have gradually become more hospitable to life over the last 500 million years, and thus less vulnerable to mass extinctions, but susceptibility to extinction at a taxonomic level does not appear to make mass extinctions more or less probable.

Causes
There is still debate about the causes of all mass extinctions. In general, large extinctions may result when a biosphere under long-term stress undergoes a short-term shock. An underlying mechanism appears to be present in the correlation of extinction and origination rates to diversity. High diversity leads to a persistent increase in extinction rate; low diversity to a persistent increase in origination rate. These presumably ecologically controlled relationships likely amplify smaller perturbations (asteroid impacts, etc.) to produce the global effects observed.

Identifying causes of specific mass extinctions
A good theory for a particular mass extinction should:
 * explain all of the losses, not just focus on a few groups (such as dinosaurs);
 * explain why particular groups of organisms died out and why others survived;
 * provide mechanisms that are strong enough to cause a mass extinction but not a total extinction;
 * be based on events or processes that can be shown to have happened, not just inferred from the extinction.

It may be necessary to consider combinations of causes. For example, the marine aspect of the end-Cretaceous extinction appears to have been caused by several processes that partially overlapped in time and may have had different levels of significance in different parts of the world.

Arens and West (2006) proposed a "press / pulse" model in which mass extinctions generally require two types of cause: long-term pressure on the eco-system ("press") and a sudden catastrophe ("pulse") towards the end of the period of pressure. Their statistical analysis of marine extinction rates throughout the Phanerozoic suggested that neither long-term pressure alone nor a catastrophe alone was sufficient to cause a significant increase in the extinction rate.

Most widely supported explanations
MacLeod (2001) summarized the relationship between mass extinctions and events that are most often cited as causes of mass extinctions, using data from Courtillot, Jaeger & Yang et al. (1996), Hallam (1992) and Grieve & Pesonen (1992):
 * Flood basalt events (giant volcanic eruptions): 11 occurrences, all associated with significant extinctions But Wignall (2001) concluded that only five of the major extinctions coincided with flood basalt eruptions and that the main phase of extinctions started before the eruptions.
 * Sea-level falls: 12, of which seven were associated with significant extinctions.
 * Asteroid impacts: one large impact is associated with a mass extinction, that is, the Cretaceous–Paleogene extinction event; there have been many smaller impacts but they are not associated with significant extinctions, or cannot be dated precisely enough. The impact that created the Siljan Ring either was just before the Late Devonian Extinction or coincided with it.

The most commonly suggested causes of mass extinctions are listed below.

Flood basalt events
The formation of large igneous provinces by flood basalt events could have: Flood basalt events occur as pulses of activity punctuated by dormant periods. As a result, they are likely to cause the climate to oscillate between cooling and warming, but with an overall trend towards warming as the carbon dioxide they emit can stay in the atmosphere for hundreds of years.
 * produced dust and particulate aerosols, which inhibited photosynthesis and thus caused food chains to collapse both on land and at sea
 * emitted sulfur oxides that were precipitated as acid rain and poisoned many organisms, contributing further to the collapse of food chains
 * emitted carbon dioxide and thus possibly causing sustained global warming once the dust and particulate aerosols dissipated.

Flood basalt events have been implicated as the cause of many major extinction events. It is speculated that massive volcanism caused or contributed to the Kellwasser Event, the End-Guadalupian Extinction Event,  the End-Permian Extinction Event,   the Smithian-Spathian Extinction,  the Triassic-Jurassic Extinction Event, the Toarcian Oceanic Anoxic Event,  the Cenomanian-Turonian Oceanic Anoxic Event,   the Cretaceous-Palaeogene Extinction Event,  and the Palaeocene-Eocene Thermal Maximum. The correlation between gigantic volcanic events expressed in the large igneous provinces and mass extinctions was shown for the last 260 million years. Recently such possible correlation was extended across the whole Phanerozoic Eon.

Sea-level fall
These are often clearly marked by worldwide sequences of contemporaneous sediments that show all or part of a transition from sea-bed to tidal zone to beach to dry land – and where there is no evidence that the rocks in the relevant areas were raised by geological processes such as orogeny. Sea-level falls could reduce the continental shelf area (the most productive part of the oceans) sufficiently to cause a marine mass extinction, and could disrupt weather patterns enough to cause extinctions on land. But sea-level falls are very probably the result of other events, such as sustained global cooling or the sinking of the mid-ocean ridges.

Sea-level falls are associated with most of the mass extinctions, including all of the "Big Five"—End-Ordovician, Late Devonian, End-Permian, End-Triassic, and End-Cretaceous, along with the more recently recognised Capitanian mass extinction of comparable severity to the Big Five.

A 2008 study, published in the journal Nature, established a relationship between the speed of mass extinction events and changes in sea level and sediment. The study suggests changes in ocean environments related to sea level exert a driving influence on rates of extinction, and generally determine the composition of life in the oceans.

Impact events
The impact of a sufficiently large asteroid or comet could have caused food chains to collapse both on land and at sea by producing dust and particulate aerosols and thus inhibiting photosynthesis. Impacts on sulfur-rich rocks could have emitted sulfur oxides precipitating as poisonous acid rain, contributing further to the collapse of food chains. Such impacts could also have caused megatsunamis and/or global forest fires.

Most paleontologists now agree that an asteroid did hit the Earth about 66 Ma, but there is lingering dispute whether the impact was the sole cause of the Cretaceous–Paleogene extinction event. Nonetheless, in October 2019, researchers reported that the Cretaceous Chicxulub asteroid impact that resulted in the extinction of non-avian dinosaurs 66 Ma, also rapidly acidified the oceans, producing ecological collapse and long-lasting effects on the climate, and was a key reason for end-Cretaceous mass extinction.

The Permian-Triassic extinction event has also been hypothesised to have been caused by an asteroid impact that formed the Araguainha crater due to the estimated date of the crater's formation overlapping with the end-Permian extinction event. However, this hypothesis has been widely challenged, with the impact hypothesis being rejected by most researchers.

According to the Shiva hypothesis, the Earth is subject to increased asteroid impacts about once every 27 million years because of the Sun's passage through the plane of the Milky Way galaxy, thus causing extinction events at 27 million year intervals. Some evidence for this hypothesis has emerged in both marine and non-marine contexts. Alternatively, the Sun's passage through the higher density spiral arms of the galaxy could coincide with mass extinction on Earth, perhaps due to increased impact events. However, a reanalysis of the effects of the Sun's transit through the spiral structure based on maps of the spiral structure of the Milky Way in CO molecular line emission has failed to find a correlation.

A nearby nova, supernova or gamma ray burst
A nearby gamma-ray burst (less than 6000 light-years away) would be powerful enough to destroy the Earth's ozone layer, leaving organisms vulnerable to ultraviolet radiation from the Sun. Gamma ray bursts are fairly rare, occurring only a few times in a given galaxy per million years. It has been suggested that a gamma ray burst caused the End-Ordovician extinction, while a supernova has been proposed as the cause of the Hangenberg event. A supernova within 25 light-years would strip Earth of its atmosphere. Today there is in the Solar System's neighbourhood no critical star capable to produce a supernova dangerous to life on Earth.

Global cooling
Sustained and significant global cooling could kill many polar and temperate species and force others to migrate towards the equator; reduce the area available for tropical species; often make the Earth's climate more arid on average, mainly by locking up more of the planet's water in ice and snow. The glaciation cycles of the current ice age are believed to have had only a very mild impact on biodiversity, so the mere existence of a significant cooling is not sufficient on its own to explain a mass extinction.

It has been suggested that global cooling caused or contributed to the End-Ordovician, Permian–Triassic, Late Devonian extinctions, and possibly others. Sustained global cooling is distinguished from the temporary climatic effects of flood basalt events or impacts.

Global warming
This would have the opposite effects: expand the area available for tropical species; kill temperate species or force them to migrate towards the poles; possibly cause severe extinctions of polar species; often make the Earth's climate wetter on average, mainly by melting ice and snow and thus increasing the volume of the water cycle. It might also cause anoxic events in the oceans (see below).

Global warming as a cause of mass extinction is supported by several recent studies.

The most dramatic example of sustained warming is the Paleocene–Eocene Thermal Maximum, which was associated with one of the smaller mass extinctions. It has also been suggested to have caused the Triassic–Jurassic extinction event, during which 20% of all marine families became extinct. Furthermore, the Permian–Triassic extinction event has been suggested to have been caused by warming.

Clathrate gun hypothesis
Clathrates are composites in which a lattice of one substance forms a cage around another. Methane clathrates (in which water molecules are the cage) form on continental shelves. These clathrates are likely to break up rapidly and release the methane if the temperature rises quickly or the pressure on them drops quickly – for example in response to sudden global warming or a sudden drop in sea level or even earthquakes. Methane is a much more powerful greenhouse gas than carbon dioxide, so a methane eruption ("clathrate gun") could cause rapid global warming or make it much more severe if the eruption was itself caused by global warming.

The most likely signature of such a methane eruption would be a sudden decrease in the ratio of carbon-13 to carbon-12 in sediments, since methane clathrates are low in carbon-13; but the change would have to be very large, as other events can also reduce the percentage of carbon-13.

It has been suggested that "clathrate gun" methane eruptions were involved in the end-Permian extinction ("the Great Dying") and in the Paleocene–Eocene Thermal Maximum, which was associated with one of the smaller mass extinctions.

Anoxic events
Anoxic events are situations in which the middle and even the upper layers of the ocean become deficient or totally lacking in oxygen. Their causes are complex and controversial, but all known instances are associated with severe and sustained global warming, mostly caused by sustained massive volcanism.

It has been suggested that anoxic events caused or contributed to the Ordovician–Silurian, late Devonian,  Capitanian,  Permian–Triassic,  and Triassic–Jurassic extinctions, as well as a number of lesser extinctions (such as the Ireviken, Lundgreni, Mulde, Lau, Smithian-Spathian, Toarcian, and Cenomanian–Turonian events). On the other hand, there are widespread black shale beds from the mid-Cretaceous that indicate anoxic events but are not associated with mass extinctions.

The bio-availability of essential trace elements (in particular selenium) to potentially lethal lows has been shown to coincide with, and likely have contributed to, at least three mass extinction events in the oceans, that is, at the end of the Ordovician, during the Middle and Late Devonian, and at the end of the Triassic. During periods of low oxygen concentrations very soluble selenate (Se6+) is converted into much less soluble selenide (Se2-), elemental Se and organo-selenium complexes. Bio-availability of selenium during these extinction events dropped to about 1% of the current oceanic concentration, a level that has been proven lethal to many extant organisms.

British oceanologist and atmospheric scientist, Andrew Watson, explained that, while the Holocene epoch exhibits many processes reminiscent of those that have contributed to past anoxic events, full-scale ocean anoxia would take "thousands of years to develop".

Hydrogen sulfide emissions from the seas
Kump, Pavlov and Arthur (2005) have proposed that during the Permian–Triassic extinction event the warming also upset the oceanic balance between photosynthesising plankton and deep-water sulfate-reducing bacteria, causing massive emissions of hydrogen sulfide, which poisoned life on both land and sea and severely weakened the ozone layer, exposing much of the life that still remained to fatal levels of UV radiation.

Oceanic overturn
Oceanic overturn is a disruption of thermo-haline circulation that lets surface water (which is more saline than deep water because of evaporation) sink straight down, bringing anoxic deep water to the surface and therefore killing most of the oxygen-breathing organisms that inhabit the surface and middle depths. It may occur either at the beginning or the end of a glaciation, although an overturn at the start of a glaciation is more dangerous because the preceding warm period will have created a larger volume of anoxic water.

Unlike other oceanic catastrophes such as regressions (sea-level falls) and anoxic events, overturns do not leave easily identified "signatures" in rocks and are theoretical consequences of researchers' conclusions about other climatic and marine events.

It has been suggested that oceanic overturn caused or contributed to the late Devonian and Permian–Triassic extinctions.

Geomagnetic reversal
One theory is that periods of increased geomagnetic reversals will weaken Earth's magnetic field long enough to expose the atmosphere to the solar winds, causing oxygen ions to escape the atmosphere in a rate increased by 3–4 orders, resulting in a disastrous decrease in oxygen.

Plate tectonics
Movement of the continents into some configurations can cause or contribute to extinctions in several ways: by initiating or ending ice ages; by changing ocean and wind currents and thus altering climate; by opening seaways or land bridges that expose previously isolated species to competition for which they are poorly adapted (for example, the extinction of most of South America's native ungulates and all of its large metatherians after the creation of a land bridge between North and South America). Occasionally continental drift creates a super-continent that includes the vast majority of Earth's land area, which in addition to the effects listed above is likely to reduce the total area of continental shelf (the most species-rich part of the ocean) and produce a vast, arid continental interior that may have extreme seasonal variations.

Another theory is that the creation of the super-continent Pangaea contributed to the End-Permian mass extinction. Pangaea was almost fully formed at the transition from mid-Permian to late-Permian, and the "Marine genus diversity" diagram at the top of this article shows a level of extinction starting at that time, which might have qualified for inclusion in the "Big Five" if it were not overshadowed by the "Great Dying" at the end of the Permian.

Other hypotheses
Many other hypotheses have been proposed, such as the spread of a new disease, or simple out-competition following an especially successful biological innovation. But all have been rejected, usually for one of the following reasons: they require events or processes for which there is no evidence; they assume mechanisms that are contrary to the available evidence; they are based on other theories that have been rejected or superseded. Scientists have been concerned that human activities could cause more plants and animals to become extinct than any point in the past. Along with human-made changes in climate (see above), some of these extinctions could be caused by overhunting, overfishing, invasive species, or habitat loss. A study published in May 2017 in Proceedings of the National Academy of Sciences argued that a "biological annihilation" akin to a sixth mass extinction event is underway as a result of anthropogenic causes, such as over-population and over-consumption. The study suggested that as much as 50% of the number of animal individuals that once lived on Earth were already extinct, threatening the basis for human existence too.

Future biosphere extinction/sterilization
The eventual warming and expanding of the Sun, combined with the eventual decline of atmospheric carbon dioxide, could actually cause an even greater mass extinction, having the potential to wipe out even microbes (in other words, the Earth would be completely sterilized): rising global temperatures caused by the expanding Sun would gradually increase the rate of weathering, which would in turn remove more and more CO2 from the atmosphere. When CO2 levels get too low (perhaps at 50 ppm), most plant life will die out, although simpler plants like grasses and mosses can survive much longer, until levels drop to 10 ppm.

With all photosynthetic organisms gone, atmospheric oxygen can no longer be replenished, and it is eventually removed by chemical reactions in the atmosphere, perhaps from volcanic eruptions. Eventually the loss of oxygen will cause all remaining aerobic life to die out via asphyxiation, leaving behind only simple anaerobic prokaryotes. When the Sun becomes 10% brighter in about a billion years, Earth will suffer a moist greenhouse effect resulting in its oceans boiling away, while the Earth's liquid outer core cools due to the inner core's expansion and causes the Earth's magnetic field to shut down. In the absence of a magnetic field, charged particles from the Sun will deplete the atmosphere and further increase the Earth's temperature to an average of around 420 K (147 °C, 296 °F) in 2.8 billion years, causing the last remaining life on Earth to die out. This is the most extreme instance of a climate-caused extinction event. Since this will only happen late in the Sun's life, it would represent the final mass extinction in Earth's history (albeit a very long extinction event).

Effects and recovery
The effects of mass extinction events varied widely. After a major extinction event, usually only weedy species survive due to their ability to live in diverse habitats. Later, species diversify and occupy empty niches. Generally, it takes millions of years for biodiversity to recover after extinction events. In the most severe mass extinctions it may take 15 to 30 million years.

The worst Phanerozoic event, the Permian–Triassic extinction, devastated life on Earth, killing over 90% of species. Life seemed to recover quickly after the P-T extinction, but this was mostly in the form of disaster taxa, such as the hardy Lystrosaurus. The most recent research indicates that the specialized animals that formed complex ecosystems, with high biodiversity, complex food webs and a variety of niches, took much longer to recover. It is thought that this long recovery was due to successive waves of extinction that inhibited recovery, as well as prolonged environmental stress that continued into the Early Triassic. Recent research indicates that recovery did not begin until the start of the mid-Triassic, four to six million years after the extinction; and some writers estimate that the recovery was not complete until 30 million years after the P-T extinction, that is, in the late Triassic. Subsequent to the P-T extinction, there was an increase in provincialization, with species occupying smaller ranges – perhaps removing incumbents from niches and setting the stage for an eventual rediversification.

The effects of mass extinctions on plants are somewhat harder to quantify, given the biases inherent in the plant fossil record. Some mass extinctions (such as the end-Permian) were equally catastrophic for plants, whereas others, such as the end-Devonian, did not affect the flora.

In media
The term extinction level event (ELE) has been used in media. The 1998 film Deep Impact describes a potential comet strike of earth as an E.L.E.

title: Extinction event


text:
E. E. Smith

Edward Elmer Smith (May 2, 1890 – August 31, 1965) was an American food engineer (specializing in doughnut and pastry mixes) and science-fiction author, best known for the Lensman and Skylark series. He is sometimes called the father of space opera.

Family and education
Edward Elmer Smith was born in Sheboygan, Wisconsin, on May 2, 1890, to Fred Jay Smith and Caroline Mills Smith, both staunch Presbyterians of British ancestry. His mother was a teacher born in Michigan in February 1855; his father was a sailor, born in Maine in January 1855 to an English father. They moved to Spokane, Washington, the winter after Edward Elmer was born, where Mr. Smith was working as a contractor in 1900. In 1902, the family moved to Seneaquoteen, near the Pend Oreille River, in Kootenai County, Idaho. He had four siblings, Rachel M. born September 1882, Daniel M. born January 1884, Mary Elizabeth born February 1886 (all of whom were born in Michigan), and Walter E. born July 1891 in Washington. In 1910, Fred and Caroline Smith and their son Walter were living in the Markham Precinct of Bonner County, Idaho; Fred is listed in census records as a farmer.

Smith worked mainly as a manual laborer until he injured his wrist while fleeing from a fire at the age of 19. He attended the University of Idaho. (Many years later he would be installed in the 1984 Class of the University of Idaho Alumni Hall of Fame. ) He entered its prep school in 1907, and graduated with two degrees in chemical engineering in 1914. He was president of the Chemistry Club, the Chess Club, and the Mandolin and Guitar Club, and captain of the Drill and Rifle Team; he also sang the bass lead in Gilbert and Sullivan operettas. His undergraduate thesis was Some Clays of Idaho, co-written with classmate Chester Fowler Smith, who died in California of tuberculosis the following year, after taking a teaching fellowship at Berkeley. Whether the two were related is not known.

On October 5, 1915, in Boise, Idaho he married Jeanne Craig MacDougall, the sister of his college roommate, Allen Scott (Scotty) MacDougall. (Her sister was named Clarissa MacLean MacDougall; the heroine of the Lensman novels would later be named Clarissa MacDougall.) Jeanne MacDougall was born in Glasgow, Scotland; her parents were Donald Scott MacDougall, a violinist, and Jessica Craig MacLean. Her father had moved to Boise when the children were young, and later sent for his family; he died while they were en route in 1905. Jeanne's mother, who remarried businessman and retired politician John F. Kessler in 1914 worked at, and later owned, a boarding house on Ridenbaugh Street.

The Smiths had three children:
 * Roderick N., born June 3, 1918, in the District of Columbia, was employed as a design engineer at Lockheed Aircraft.
 * Verna Jean (later Verna Smith Trestrail), born August 25, 1920, in Michigan, was his literary executor until her death in 1994. (Her son Kim Trestrail is now the executor. ) Robert A. Heinlein in part dedicated his 1982 novel Friday to Verna.
 * Clarissa M. (later Clarissa Wilcox), was born December 13, 1921, in Michigan.

Early chemical career and the beginning of Skylark
After college, Smith was a junior chemist for the National Bureau of Standards in Washington, D.C., developing standards for butter and for oysters, while studying food chemistry at George Washington University. During World War I, he "wanted to fly a Jenny, but chemists were too scarce. (Or were Jennies too valuable?)" He ended up being sent to the Commission for Relief in Belgium headed by Herbert Hoover. His draft card, partly illegible, seems to show that Smith requested exemption from military service, based on his wife's dependence and on his contribution to the war effort as a civilian chemist.

One evening in 1915, the Smiths were visiting a former classmate from the University of Idaho, Dr. Carl Garby (1890–1928) who had also moved to Washington, D.C. He lived nearby in the Seaton Place Apartments with his wife, Lee Hawkins Garby. A long discussion about journeys into outer space ensued, and it was suggested that Smith should write down his ideas and speculations as a story about interstellar travel. Although he was interested, Smith believed after some thought that some romantic elements would be required and he was uncomfortable with that.

Lee Garby offered to take care of the love interest and the romantic dialogue, and Smith decided to give it a try. The sources of inspirations for the main characters in the novel were themselves; the "Seatons" and "Cranes" were based on the Smiths and Garbys, respectively. About one third of The Skylark of Space was completed by the end of 1916, when Smith and Garby gradually abandoned work on it.

Smith earned his master's degree in chemistry from the George Washington University in 1917, studying under Dr. Charles E. Munroe, whom Smith called "probably the greatest high-explosives man yet to live". Smith completed his PhD in chemical engineering in 1918, with a food engineering focus. His dissertation, The effect of bleaching with oxides of nitrogen upon the baking quality and commercial value of wheat flour, was published in 1919.

Writing Skylark
In 1919, Smith was hired as chief chemist for F. W. Stock & Sons of Hillsdale, Michigan, at one time the largest family-owned mill east of the Mississippi, working on doughnut mixes.

One evening late in 1919, after moving to Michigan, Smith was baby-sitting (presumably for Roderick) while his wife attended a movie. He resumed work on The Skylark of Space, finishing it in the spring of 1920. He submitted it to many book publishers and magazines, spending more in postage than he would eventually receive for its publication. Bob Davis, editor of Argosy, sent an encouraging rejection letter in 1922, saying that he liked the novel personally, but that it was too far out for his readers. Finally, upon seeing the April 1927 issue of Amazing Stories, he submitted it to that magazine. It was accepted, initially for $75, later raised to $125. It was published as a three-part serial in the August to October 1928 issues and it was such a success that associate editor Sloane requested a sequel before the second installment had been published. (According to Warner, but no other source, Smith began work on the sequel, Skylark Three, before the first book was accepted. )

Garby, whose husband died in 1928, was not interested in further collaboration, so Smith began work on Skylark Three alone. It was published as another three-part serial, in the August to October 1930 issues of Amazing, introduced as the cover story for August. This was as far as he had planned to take the Skylark series. It was praised in Amazings letter column, and he was paid ¾¢ per word, surpassing Amazings previous record of half a cent.

The early 1930s: between Skylark and Lensman
Smith then began work on what he intended as a new series, starting with Spacehounds of IPC, which he finished in the autumn of 1930. In this novel, he took pains to avoid the scientific impossibilities which had bothered some readers of the Skylark novels. Even in 1938, after he had written Galactic Patrol, Smith considered it his finest work. He later said of it, "This was really scientific fiction; not, like the Skylarks, pseudo-science". Even at the end of his career, he considered it his only work of true science fiction. It was published in the July through September 1931 issues of Amazing, with Sloane making unauthorized changes. Fan letters in the magazine complained about the novel's containment within the Solar System, and Sloane sided with the readers. So when Harry Bates, editor of Astounding Stories, offered Smith 2¢/word—payable on publication—for his next story, he agreed. This meant that it could not be a sequel to Spacehounds.

This book would be Triplanetary, "in which scientific detail would not be bothered about, and in which his imagination would run riot." Indeed, characters within the story point out its psychological and scientific implausibilities, and sometimes even seem to suggest self-parody. At other times, they are conspicuously silent about obvious implausibilities. The January 1933 issue of Astounding announced that Triplanetary would appear in the March issue, and that issue's cover illustrated a scene from the story, but Astounding's financial difficulties prevented the story from appearing. Smith then submitted the manuscript to Wonder Stories, whose new editor, 17-year-old Charles D. Hornig, rejected it, later boasting about the rejection in a fanzine. He finally submitted it to Amazing, which published it beginning in January 1934, but for only half a cent a word. Shortly after it was accepted, F. Orlin Tremaine, the new editor of the revived Astounding, offered one cent a word for Triplanetary. When he learned that he was too late, he suggested a third Skylark novel instead.

In the winter of 1933–34, Smith worked on The Skylark of Valeron, but he felt that the story was getting out of control. He sent his first draft to Tremaine, with a distraught note asking for suggestions. Tremaine accepted the rough draft for $850, and announced it in the June 1934 issue, with a full-page editorial and a three-quarter-page advertisement. The novel was published in the August 1934 through February 1935 issues. Astounding's circulation rose by 10,000 for the first issue, and its two main competitors, Amazing and Wonder Stories, fell into financial difficulties, both skipping issues within a year.

The Lensman series
In January 1936, a time period where he was already an established science-fiction writer, he took a job for salary plus profit-sharing, as production manager at Dawn Donut Co. of Jackson, Michigan. This initially entailed almost a year's worth of 18-hour days and seven-day workweeks. Individuals who knew Smith confirmed that he had a role in developing mixes for doughnuts and other pastries, but the contention that he developed the first process for making powdered sugar adhere to doughnuts cannot be substantiated. Smith was reportedly dislocated from his job at Dawn Donuts by prewar rationing in early 1940.

Smith had been contemplating writing a "space-police novel" since early 1927; once he had "the Lensmen's universe fairly well set up", he reviewed his science-fiction collection for "cops-and-robbers" stories. He cites Clinton Constantinescue's "War of the Universe" as a negative example, and Starzl and Williamson as positive ones. Tremaine responded extremely positively to a brief description of the idea.

Once Dawn Donuts became profitable in late 1936, Smith wrote an 85-page outline for what became the four core Lensman novels. In early 1937, Tremaine committed to buying them. Segmenting the story into four novels required considerable effort to avoid dangling loose ends. Smith cited Edgar Rice Burroughs as a negative example. After the outline was complete, he wrote a more detailed outline of Galactic Patrol, plus a detailed graph of its structure, with "peaks of emotional intensity and the valleys of characterization and background material." He notes, however, that he was never able to follow any of his outlines at all closely, as the "characters get away from me and do exactly as they damn please." After completing the rough draft of Galactic Patrol, he wrote the concluding chapter of the last book in the series, Children of the Lens. Galactic Patrol was published in the September 1937 through February 1938 issues of Astounding. Unlike the revised book edition, it was not set in the same universe as Triplanetary.

Gray Lensman, the fourth book in the series, appeared in Astounding's October 1939 through January 1940 issues. Gray Lensman was extremely well received, as was its cover illustration. Campbell's editorial in the December issue suggested that the October issue was the best issue of Astounding ever, and Gray Lensman was first place in the Analytical Laboratory statistics "by a lightyear", with three runners-up in a distant tie for second place. The cover was also praised by readers in Brass Tacks, and Campbell noted, "We got a letter from E. E. Smith saying he and [cover artist] Hubert Rogers agreed on how Kinnison looked."

Smith was the guest of honor at Chicon I, the second World Science Fiction Convention, held in Chicago over Labor Day weekend 1940, giving a speech on the importance of science fiction fandom entitled "What Does This Convention Mean?" He attended the convention's masquerade as C. L. Moore's Northwest Smith, and met fans living near him in Michigan, who would later form the Galactic Roamers, which previewed and advised him on his future work.

After Pearl Harbor, Smith discovered he "was one year over age for reinstatement" into the US Army. Instead he worked on high explosives at the Kingsbury Ordnance Plant in La Port, Indiana, at first as a chemical engineer, but gradually worked his way up to chief. In late 1943 he became head of the Inspection Division, and was fired in early 1944. An extended segment in the novel version of Triplanetary, set during World War II, suggests intimate familiarity with explosives and munitions manufacturing. Some biographers cite as fact that, just as Smith's protagonist in this segment lost his job over failure to approve substandard munitions, Smith did as well.

Smith spent the next few years working on "light farm machinery and heavy tanks for Allis-Chalmers," after which he was hired as manager of the Cereal Mix Division of J. W. Allen & Co., where he worked until his professional retirement in 1957.

Retirement and late writing
After Smith retired, he and his wife lived in Clearwater, Florida in the fall and winter, driving the smaller of their two trailers to Seaside, Oregon, each April, often stopping at science fiction conventions on the way. (Smith did not like to fly. ) In 1963, he was presented the inaugural First Fandom Hall of Fame award at the 21st World Science Fiction Convention in Washington, D.C. Some of his biography is captured in an essay by Robert A. Heinlein, which was reprinted in the collection Expanded Universe in 1980. A more detailed, although allegedly error-ridden biography is in Sam Moskowitz's Seekers of Tomorrow.

Robert Heinlein and Smith were friends. (Heinlein dedicated his 1958 novel Methuselah's Children "To Edward E. Smith, PhD". ) Heinlein reported that E. E. Smith perhaps took his "unrealistic" heroes from life, citing as an example the extreme competence of the hero of Spacehounds of IPC. He reported that E. E. Smith was a large, blond, athletic, very intelligent, very gallant man, married to a remarkably beautiful, intelligent, red-haired woman named MacDougal (thus perhaps the prototypes of 'Kimball Kinnison' and 'Clarissa MacDougal'). In Heinlein's essay, he reports that he began to suspect Smith might be a sort of "superman" when he asked Smith for help in purchasing a car. Smith tested the car by driving it on a back road at illegally high speeds with their heads pressed tightly against the roof columns to listen for chassis squeaks by bone conduction—a process apparently improvised on the spot.

In his nonseries novels written after his professional retirement, Galaxy Primes, Subspace Explorers, and Subspace Encounter, E. E. Smith explores themes of telepathy and other mental abilities collectively called "psionics", and of the conflict between libertarian and socialistic/communistic influences in the colonization of other planets. Galaxy Primes was written after critics such as Groff Conklin and P. Schuyler Miller in the early '50s accused his fiction of being passé, and he made an attempt to do something more in line with the concepts about which Astounding editor John W. Campbell encouraged his writers to make stories. Despite this, it was rejected by Campbell, and it was eventually published by Amazing Stories in 1959. His late story "The Imperial Stars" (1964), featuring a troupe of circus performers involved in sabotage in a galactic empire, recaptured some of the atmosphere from his earlier works and was intended as the first in a new series, with outlines of later parts rumored to still exist. In fact, the Imperial Stars characters and concepts were continued by author Stephen Goldin as the "Family D'Alembert series". While the book covers indicate the series was written by Smith and Goldin together, Goldin only ever had Smith's original novella to expand upon.

The fourth Skylark novel, Skylark DuQuesne, ran in the June to October 1965 issues of If, beginning once again as the cover story. Editor Frederik Pohl introduced it with a one-page summary of the previous stories, which were all at least 30 years old.

Lord Tedric
Smith published two novelettes entitled "Tedric" in Other Worlds Science Fiction Stories (1953) and "Lord Tedric" in Universe Science Fiction (1954). These were almost completely forgotten until after Smith's death. In 1975, a compendium of Smith's works was published, entitled The Best of E. E. "Doc" Smith, containing these two short stories, excerpts from several of his major works, and another short story first published in Worlds of If in 1964 entitled "The Imperial Stars".

In Smith's original short stories, Tedric was a smith (both blacksmith and whitesmith) residing in a small town near a castle in a situation roughly equivalent to England of the 1200s. He received instruction in advanced metallurgy from a time-traveler who wanted to change the situation in his own time by modifying certain events of the past. From this instruction, he was able to build better suits of armor and help defeat the villains of the piece. Unlike Eklund's later novels based on these short stories, the original Tedric never left his own time or planet, and fought purely local enemies of his own time period.

A few years later and 13 years after Smith's death, Verna Smith arranged with Gordon Eklund to publish another novel of the same name about the same fictional character, introducing it as "a new series conceived by E. E. 'Doc' Smith". Eklund later went on to publish the other novels in the series, one or two under the pseudonym "E. E. 'Doc' Smith" or "E. E. Smith". The protagonist possesses heroic qualities similar to those of the heroes in Smith's original novels and can communicate with an extra-dimensional race of beings known as the Scientists, whose archenemy is Fra Villion, a mysterious character described as a dark knight, skilled in whip-sword combat, and evil genius behind the creation of a planetoid-sized "iron sphere" armed with a weapon capable of destroying planets. As a result, Smith is believed by many to be the unacknowledged progenitor of themes that would appear in Star Wars. In fact, however, these appear in the sequels written by others after Smith's death.

Critical opinion
Smith's novels are generally considered to be classic space operas, and he is sometimes called the first of the three "novas" of 20th-century science fiction (with Stanley G. Weinbaum and Robert A. Heinlein as the second and third novas).

Heinlein credited him for being his main influence:

"I have learned from many writers—from Verne and Wells and Campbell and Sinclair Lewis, et al.—but I have learned more from you than from any of the others and perhaps more than for all the others put together..."

Smith expressed a preference for inventing fictional technologies that were not strictly impossible (so far as the science of the day was aware) but highly unlikely: "the more highly improbable a concept is—short of being contrary to mathematics whose fundamental operations involve no neglect of infinitesimals—the better I like it" was his phrase.

Lensman was one of five finalists when the 1966 World Science Fiction Convention judged Isaac Asimov's Foundation the Best All-Time Series.

The Science Fiction and Fantasy Hall of Fame inducted Smith in 2004.

Extending the Lensman universe
Vortex Blasters (also known as Masters of the Vortex) is set in the same universe as the Lensman novels. It is an extension to the main storyline which takes place between Galactic Patrol and Children of the Lens, and introduces a different type of psionics from that used by the Lensmen. Spacehounds of IPC is not a part of the series, despite occasional erroneous statements to the contrary. (It is listed as a novel in the series in some paperback editions of the 1970s.)

Influence on science and the military
Smith was widely read by scientists and engineers from the 1930s into the 1970s. Literary precursors of ideas which arguably entered the military-scientific complex include SDI (Triplanetary), stealth (Gray Lensman), the OODA loop, C3-based warfare, and the AWACS (Gray Lensman).

An inarguable influence was described in a June 11, 1947, letter to Smith from John W. Campbell (the editor of Astounding, where much of the Lensman series was originally published). In it, Campbell relayed Captain Cal Laning's acknowledgment that he had used Smith's ideas for displaying the battlespace situation (called the "tank" in the stories) in the design of the United States Navy's ships' Combat Information Centers. "The entire set-up was taken specifically, directly, and consciously from the Directrix. In your story, you reached the situation the Navy was in—more communication channels than integration techniques to handle it. You proposed such an integrating technique and proved how advantageous it could be. You, sir, were 100% right. As the Japanese Navy—not the hypothetical Boskonian fleet—learned at an appalling cost."

One underlying theme of the later Lensman novels was the difficulty in maintaining military secrecy—as advanced capabilities are revealed, the opposing side can often duplicate them. This point was also discussed extensively by John Campbell in his letter to Smith. Also in the later Lensman novels, and particular after the "Battle of Klovia" broke the Boskonian's power base at the end of Second Stage Lensmen, the Boskonian forces and particularly Kandron of Onlo reverted to terroristic tactics to attempt to demoralize Civilization, thus providing an early literary glimpse into this modern problem of both law enforcement and military response. The use of "Vee-two" gas by the pirates attacking the Hyperion in Triplanetary (in both magazine and book appearances) also suggests anticipation of the terrorist uses of poison gases. However, Smith lived through WWI, when the use of poison gas on troops was well known to the populace; extending the assumption that pirates might use it if they could obtain it was no great extension of the present-day knowledge.

The beginning of the story Skylark of Space describes in relative detail the protagonist's research into separation of platinum group residues, subsequent experiments involving electrolysis, and the discovery of a process evocative of cold fusion (over 50 years before Stanley Pons and Martin Fleischmann). He describes a nuclear process yielding large amounts of energy and producing only negligible radioactive waste—which then goes on to form the basis of the adventures in the Skylark books. Smith's general description of the process of discovery is highly evocative of Röntgen's descriptions of his discovery of the X-ray.

Another theme of the Skylark novels involves precursors of modern information technology. The humanoid aliens encountered in the first novel have developed a primitive technology called the "mechanical educator", which allows direct conversion of brain waves into intelligible thought for transmission to others or for electrical storage. By the third novel in the series, Skylark of Valeron, this technology has grown into an "Electronic Brain" which is capable of computation on all "bands" of energy—electromagnetism, gravity, and "tachyonic" energy and radiation bands included. This is itself derived from a discussion of reductionist atomic theory in the second novel, Skylark Three, which brings to mind modern quark and sub-quark theories of elementary particle physics.

Literary influences
In his 1947 essay "The Epic of Space", Smith listed (by last name only) authors he enjoyed reading: John W. Campbell, L. Sprague de Camp, Robert A. Heinlein, Murray Leinster, H. P. Lovecraft, and A. Merritt (specifically The Ship of Ishtar, The Moon Pool, The Snake Mother, and Dwellers in the Mirage, as well as the character John Kenton), C. L. Moore (specifically "Jirel of Joiry"), Roman Frederick Starzl, John Taine, A. E. van Vogt, Stanley G. Weinbaum (specifically "Tweerl" ), and Jack Williamson. In a passage on his preparation for writing the Lensman novels, he notes that Clinton Constantinescu's "War of the Universe" was not a masterpiece, but says that Starzl and Williamson were masters; this suggests that Starzl's Interplanetary Flying Patrol may have been an influence on Smith's Triplanetary Patrol, later the Galactic Patrol. The feeding of the Overlords of Delgon upon the life-force of their victims at the end of chapter five of Galactic Patrol seems a clear allusion to chapter 29 of The Moon Pool, Merritt's account of the Taithu and the power of love in chapters 29 and 34 also bear some resemblance to the end of Children of the Lens. Smith also mentions Edgar Rice Burroughs, complaining about loose ends at the end of one of his novels.

Smith acknowledges the help of the Galactic Roamers writers' workshop, plus E. Everett Evans, Ed Counts, an unnamed aeronautical engineer, Dr. James Enright, and Dr. Richard W. Dodson. Smith's daughter, Verna, lists the following authors as visitors to the Smith household in her youth: Lloyd Arthur Eshbach, Heinlein, Dave Kyle, Bob Tucker, Williamson, Pohl, Merritt, and the Galactic Roamers. Smith cites Bigelow's Theoretical Chemistry–Fundamentals as a justification for the possibility of the inertialess drive. Also, an extended reference is made to Rudyard Kipling's "Ballad of Boh Da Thone " in Gray Lensman (chapter 22, "Regeneration", in a conversation between Kinnison and MacDougall). Again in Gray Lensman, Smith quotes from Merritt's Dwellers in the Mirage, even name-checking the author:

"He could not even pray, with immortal Merritt's Dwayanu, 'Luka - turn your wheel so that I need not slay this woman!'"

Sam Moskowitz's biographical essay on Smith in Seekers of Tomorrow states that he regularly read Argosy magazine, and everything by H. G. Wells, Jules Verne, H. Rider Haggard, Edgar Allan Poe, and Edgar Rice Burroughs. Moskowitz also notes that Smith's "reading enthusiasms included poetry, philosophy, ancient and medieval history, and all of English literature". (Smith's grandson notes that he spoke, and sang, German. ) The influence of these is not readily apparent, except in the Roman section of Triplanetary, and in the impeccable but convoluted grammar of Smith's narration. Some influence of 19th-century philosophy of language may be detectable in the account in Galactic Patrol of the Lens of Arisia as a universal translator, which is reminiscent of Frege's strong realism about Sinn, that is, thought or sense.

Both Moskowitz and Smith's daughter Verna Smith Trestrail report that Smith had a troubled relationship with John Campbell, the editor of Astounding. Smith's most successful works were published under Campbell, but the degree of influence is uncertain. The original outline for the Lensman series had been accepted by F. Orlin Tremaine, and Smith angered Campbell by showing loyalty to Tremaine at his new magazine, Comet, when he sold him "The Vortex Blaster" in 1941. Campbell's announcement of Children of the Lens, in 1947, was less than enthusiastic. Campbell later said that he published it only reluctantly, though he praised it privately, and bought little from Smith thereafter.

Derivative works and influence on popular culture

 * Randall Garrett wrote a parody entitled Backstage Lensman which Smith reportedly enjoyed. Harry Harrison also parodied Smith's work in the novel Star Smashers of the Galaxy Rangers and the short story "Space Rats of the CCC".
 * Sir Arthur C. Clarke's space battle in Earthlight was based on the attack on the Mardonalian fortress in chapter seven of Skylark Three.
 * Steve 'Slug' Russell wrote one of the first computer games, Spacewar!, with inspiration from the space battles from the Lensman series.
 * The Japanese Lensman anime is more an imitation of Star Wars than a translation of the Lensman novels. Efforts to print translations of the associated manga in the United States in the early 1990s without payment of royalties to the Smith family were successfully blocked in court by Verna Smith Trestrail with the help of several California science-fiction authors and fans.
 * In his biography, George Lucas reveals that the Lensman novels were a major influence on his youth. J. Michael Straczynski, creator of the science-fiction television series Babylon 5, also has acknowledged the influence of the Lensman books.
 * Superman creator Jerry Siegel was impressed, at an early age, with the optimistic vision of the future presented in Skylark of Space.
 * An attempt to create a feature film based on the Lensman series by Ron Howard's Imagine Entertainment and Universal Studios began in 2008 with J. Michael Straczynski, the creator of Babylon 5, as writer, but in 2014 the project was scrapped because of budget limitations.
 * In her short Pliocene Companion book, author Julian May explained that a major character in her Exile series written in the early 1980s, Marc Remillard, was strongly influenced by Smith's villain character from Skylark DuQuesne, Marc DuQuesne. This was somewhat of a tribute to Smith. May had written an early science fiction short story called "Dune Roller" in 1950, and had attended several science fiction conventions in the early '50s, where she met and came to know Smith personally.
 * The 2019 album All Aboard the Skylark by Hawkwind is named after the stories.

Fictional appearances
Smith himself appears as a character in the 2006 novel The Chinatown Death Cloud Peril by Paul Malmont. The novel describes friendship and rivalry among pulp writers of the 1930s. He also appears as "Lensman Ted Smith" in the 1980 novel The Number of the Beast and as "Commander Ted Smith" in the 1985 novel The Cat Who Walks Through Walls, both by Robert A. Heinlein. It is also suggested that he was one of the inspirations for Heinlein's character Lazarus Long. Christopher Nuttall incorporates a fictional quote from “Edward E. Smith, Professor of Sociology” in his military science fiction book, “No Worse Enemy”.

Lensman

 * 1) Triplanetary (1948)
 * 2) First Lensman (1950)
 * 3) Galactic Patrol (1950)
 * 4) Gray Lensman (1951)
 * 5) Second Stage Lensmen (1953)
 * 6) The Vortex Blaster (1960)
 * 7) Children of the Lens (1954)

Skylark

 * 1) The Skylark of Space (1946)
 * 2) Skylark Three (1948)
 * 3) Skylark of Valeron (1949)
 * 4) Skylark DuQuesne (1966)

Subspace

 * 1) Subspace Explorers (1965)
 * 2) Subspace Encounter (1983)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: E. E. Smith


text:
Évariste Galois

Évariste Galois (25 October 1811 – 31 May 1832) was a French mathematician and political activist. While still in his teens, he was able to determine a necessary and sufficient condition for a polynomial to be solvable by radicals, thereby solving a problem that had been open for 350 years. His work laid the foundations for Galois theory and group theory, two major branches of abstract algebra.

Galois was a staunch republican and was heavily involved in the political turmoil that surrounded the French Revolution of 1830. As a result of his political activism, he was arrested repeatedly, serving one jail sentence of several months. For reasons that remain obscure, shortly after his release from prison, Galois fought in a duel and died of the wounds he suffered.

Early life
Galois was born on 25 October 1811 to Nicolas-Gabriel Galois and Adélaïde-Marie (née Demante). His father was a Republican and was head of Bourg-la-Reine's liberal party. His father became mayor of the village after Louis XVIII returned to the throne in 1814. His mother, the daughter of a jurist, was a fluent reader of Latin and classical literature and was responsible for her son's education for his first twelve years.

In October 1823, he entered the Lycée Louis-le-Grand where his teacher Louis Paul Émile Richard recognized his brilliance. At the age of 14, he began to take a serious interest in mathematics.

Galois found a copy of Adrien-Marie Legendre's Éléments de Géométrie, which, it is said, he read "like a novel" and mastered at the first reading. At 15, he was reading the original papers of Joseph-Louis Lagrange, such as the Réflexions sur la résolution algébrique des équations which likely motivated his later work on equation theory, and Leçons sur le calcul des fonctions, work intended for professional mathematicians, yet his classwork remained uninspired and his teachers accused him of putting on the airs of a genius.

Budding mathematician
In 1828, Galois attempted the entrance examination for the École Polytechnique, the most prestigious institution for mathematics in France at the time, without the usual preparation in mathematics, and failed for lack of explanations on the oral examination. In that same year, he entered the École Normale (then known as l'École préparatoire), a far inferior institution for mathematical studies at that time, where he found some professors sympathetic to him.

In the following year Galois's first paper, on continued fractions, was published. It was at around the same time that he began making fundamental discoveries in the theory of polynomial equations. He submitted two papers on this topic to the Academy of Sciences. Augustin-Louis Cauchy refereed these papers, but refused to accept them for publication for reasons that still remain unclear. However, in spite of many claims to the contrary, it is widely held that Cauchy recognized the importance of Galois's work, and that he merely suggested combining the two papers into one in order to enter it in the competition for the academy's Grand Prize in Mathematics. Cauchy, an eminent mathematician of the time though with political views that were diametrically opposed to those of Galois, considered Galois's work to be a likely winner.

On 28 July 1829, Galois's father died by suicide after a bitter political dispute with the village priest. A couple of days later, Galois made his second and last attempt to enter the Polytechnique and failed yet again. It is undisputed that Galois was more than qualified; accounts differ on why he failed. More plausible accounts state that Galois made too many logical leaps and baffled the incompetent examiner, which enraged Galois. The recent death of his father may have also influenced his behavior.

Having been denied admission to the École polytechnique, Galois took the Baccalaureate examinations in order to enter the École normale. He passed, receiving his degree on 29 December 1829. His examiner in mathematics reported, "This pupil is sometimes obscure in expressing his ideas, but he is intelligent and shows a remarkable spirit of research."

Galois submitted his memoir on equation theory several times, but it was never published in his lifetime. Though his first attempt was refused by Cauchy, in February 1830 following Cauchy's suggestion he submitted it to the academy's secretary Joseph Fourier, to be considered for the Grand Prix of the academy. Unfortunately, Fourier died soon after, and the memoir was lost. The prize would be awarded that year to Niels Henrik Abel posthumously and also to Carl Gustav Jacob Jacobi. Despite the lost memoir, Galois published three papers that year. One laid the foundations for Galois theory. The second was about the numerical resolution of equations (root finding in modern terminology). The third was an important one in number theory, in which the concept of a finite field was first articulated.

Political firebrand
Galois lived during a time of political turmoil in France. Charles X had succeeded Louis XVIII in 1824, but in 1827 his party suffered a major electoral setback and by 1830 the opposition liberal party became the majority. Charles, faced with political opposition from the chambers, staged a coup d'état, and issued his notorious July Ordinances, touching off the July Revolution which ended with Louis Philippe becoming king. While their counterparts at the Polytechnique were making history in the streets, Galois, at the École Normale, was locked in by the school's director. Galois was incensed and wrote a blistering letter criticizing the director, which he submitted to the Gazette des Écoles, signing the letter with his full name. Although the Gazette's editor omitted the signature for publication, Galois was expelled.

Although his expulsion would have formally taken effect on 4 January 1831, Galois quit school immediately and joined the staunchly Republican artillery unit of the National Guard. He divided his time between his mathematical work and his political affiliations. Due to controversy surrounding the unit, soon after Galois became a member, on 31 December 1830, the artillery of the National Guard was disbanded out of fear that they might destabilize the government. At around the same time, nineteen officers of Galois's former unit were arrested and charged with conspiracy to overthrow the government.

In April 1831, the officers were acquitted of all charges, and on 9 May 1831, a banquet was held in their honor, with many illustrious people present, such as Alexandre Dumas. The proceedings grew riotous. At some point, Galois stood and proposed a toast in which he said, "To Louis Philippe," with a dagger above his cup. The republicans at the banquet interpreted Galois's toast as a threat against the king's life and cheered. He was arrested the following day at his mother's house and held in detention at Sainte-Pélagie prison until 15 June 1831, when he had his trial. Galois's defense lawyer cleverly claimed that Galois actually said, "To Louis-Philippe, if he betrays," but that the qualifier was drowned out in the cheers. The prosecutor asked a few more questions, and perhaps influenced by Galois's youth, the jury acquitted him that same day.

On the following Bastille Day (14 July 1831), Galois was at the head of a protest, wearing the uniform of the disbanded artillery, and came heavily armed with several pistols, a loaded rifle, and a dagger. He was again arrested. During his stay in prison, Galois at one point drank alcohol for the first time at the goading of his fellow inmates. One of these inmates, François-Vincent Raspail, recorded what Galois said while drunk in a letter from 25 July. Excerpted from the letter:

"And I tell you, I will die in a duel on the occasion of some coquette de bas étage . Why? Because she will invite me to avenge her honor which another has compromised. Do you know what I lack, my friend? I can confide it only to you: it is someone whom I can love and love only in spirit. I've lost my father and no one has ever replaced him, do you hear me...?"

Raspail continues that Galois, still in a delirium, attempted suicide, and that he would have succeeded if his fellow inmates had not forcibly stopped him. Months later, when Galois's trial occurred on 23 October, he was sentenced to six months in prison for illegally wearing a uniform. While in prison, he continued to develop his mathematical ideas. He was released on 29 April 1832.

Final days
Galois returned to mathematics after his expulsion from the École Normale, although he continued to spend time in political activities. After his expulsion became official in January 1831, he attempted to start a private class in advanced algebra which attracted some interest, but this waned, as it seemed that his political activism had priority. Siméon Denis Poisson asked him to submit his work on the theory of equations, which he did on 17 January 1831. Around 4 July 1831, Poisson declared Galois's work "incomprehensible", declaring that "[Galois's] argument is neither sufficiently clear nor sufficiently developed to allow us to judge its rigor"; however, the rejection report ends on an encouraging note: "We would then suggest that the author should publish the whole of his work in order to form a definitive opinion." While Poisson's report was made before Galois's 14 July arrest, it took until October to reach Galois in prison. It is unsurprising, in the light of his character and situation at the time, that Galois reacted violently to the rejection letter, and decided to abandon publishing his papers through the academy and instead publish them privately through his friend Auguste Chevalier. Apparently, however, Galois did not ignore Poisson's advice, as he began collecting all his mathematical manuscripts while still in prison, and continued polishing his ideas until his release on 29 April 1832, after which he was somehow talked into a duel.

Galois's fatal duel took place on 30 May. The true motives behind the duel are obscure. There has been much speculation about them. What is known is that, five days before his death, he wrote a letter to Chevalier which clearly alludes to a broken love affair.

Some archival investigation on the original letters suggests that the woman of romantic interest was Stéphanie-Félicie Poterin du Motel, the daughter of the physician at the hostel where Galois stayed during the last months of his life. Fragments of letters from her, copied by Galois himself (with many portions, such as her name, either obliterated or deliberately omitted), are available. The letters hint that Poterin du Motel had confided some of her troubles to Galois, and this might have prompted him to provoke the duel himself on her behalf. This conjecture is also supported by other letters Galois later wrote to his friends the night before he died. Galois's cousin, Gabriel Demante, when asked if he knew the cause of the duel, mentioned that Galois "found himself in the presence of a supposed uncle and a supposed fiancé, each of whom provoked the duel." Galois himself exclaimed: "I am the victim of an infamous coquette and her two dupes."

As to his opponent in the duel, Alexandre Dumas names Pescheux d'Herbinville, who was actually one of the nineteen artillery officers whose acquittal was celebrated at the banquet that occasioned Galois's first arrest. However, Dumas is alone in this assertion, and if he were correct it is unclear why d'Herbinville would have been involved. It has been speculated that he was Poterin du Motel's "supposed fiancé" at the time (she ultimately married someone else), but no clear evidence has been found supporting this conjecture. On the other hand, extant newspaper clippings from only a few days after the duel give a description of his opponent (identified by the initials "L.D.") that appear to more accurately apply to one of Galois's Republican friends, most probably Ernest Duchatelet, who was imprisoned with Galois on the same charges. Given the conflicting information available, the true identity of his killer may well be lost to history.

Whatever the reasons behind the duel, Galois was so convinced of his impending death that he stayed up all night writing letters to his Republican friends and composing what would become his mathematical testament, the famous letter to Auguste Chevalier outlining his ideas, and three attached manuscripts. Mathematician Hermann Weyl said of this testament, "This letter, if judged by the novelty and profundity of ideas it contains, is perhaps the most substantial piece of writing in the whole literature of mankind." However, the legend of Galois pouring his mathematical thoughts onto paper the night before he died seems to have been exaggerated. In these final papers, he outlined the rough edges of some work he had been doing in analysis and annotated a copy of the manuscript submitted to the academy and other papers.

Early in the morning of 30 May 1832, he was shot in the abdomen, was abandoned by his opponents and his own seconds, and was found by a passing farmer. He died the following morning at ten o'clock in the Hôpital Cochin (probably of peritonitis), after refusing the offices of a priest. His funeral ended in riots. There were plans to initiate an uprising during his funeral, but during the same time the leaders heard of General Jean Maximilien Lamarque's death and the rising was postponed without any uprising occurring until 5 June. Only Galois's younger brother was notified of the events prior to Galois's death. Galois was 20 years old. His last words to his younger brother Alfred were: "'Ne pleure pas, Alfred ! J'ai besoin de tout mon courage pour mourir à vingt ans !' (Don't weep, Alfred! I need all my courage to die at twenty!)"

On 2 June, Évariste Galois was buried in a common grave of the Montparnasse Cemetery whose exact location is unknown. In the cemetery of his native town – Bourg-la-Reine – a cenotaph in his honour was erected beside the graves of his relatives.

Évariste Galois died in 1832. Joseph Liouville began studying Galois's unpublished papers in 1842 and acknowledged their value in 1843. It is not clear what happened in the 10 years between 1832 and 1842 nor what eventually inspired Joseph Liouville to begin reading Galois's papers. Jesper Lützen explores this subject at some length in Chapter XIV Galois Theory of his book about Joseph Liouville without reaching any definitive conclusions.

It is certainly possible that mathematicians (including Liouville) did not want to publicize Galois's papers because Galois was a republican political activist who died 5 days before the June Rebellion, an unsuccessful anti-monarchist insurrection of Parisian republicans. In Galois's obituary, his friend Auguste Chevalier almost accused academicians at the École Polytechnique of having killed Galois since, if they had not rejected his work, he would have become a mathematician and would not have devoted himself to the republican political activism for which some believed he was killed.

Given that France was still living in the shadow of the Reign of Terror and the Napoleonic era, Liouville might have waited until the June Rebellion's political turmoil subsided before turning his attention to Galois's papers.

Liouville finally published Galois's manuscripts in the October–November 1846 issue of the Journal de Mathématiques Pures et Appliquées. Galois's most famous contribution was a novel proof that there is no quintic formula – that is, that fifth and higher degree equations are not generally solvable by radicals. Although Niels Henrik Abel had already proved the impossibility of a "quintic formula" by radicals in 1824 and Paolo Ruffini had published a solution in 1799 that turned out to be flawed, Galois's methods led to deeper research into what is now called Galois Theory, which can be used to determine, for any polynomial equation, whether it has a solution by radicals.

Contributions to mathematics

From the closing lines of a letter from Galois to his friend Auguste Chevalier, dated 29 May 1832, two days before Galois's death:

"Tu prieras publiquement Jacobi ou Gauss de donner leur avis, non sur la vérité, mais sur l'importance des théorèmes.

Après cela, il y aura, j'espère, des gens qui trouveront leur profit à déchiffrer tout ce gâchis.

(Ask Jacobi or Gauss publicly to give their opinion, not as to the truth, but as to the importance of these theorems. Later there will be, I hope, some people who will find it to their advantage to decipher all this mess.)"

Within the 60 or so pages of Galois's collected works are many important ideas that have had far-reaching consequences for nearly all branches of mathematics. His work has been compared to that of Niels Henrik Abel (1802–1829), a contemporary mathematician who also died at a very young age, and much of their work had significant overlap.

Algebra
While many mathematicians before Galois gave consideration to what are now known as groups, it was Galois who was the first to use the word group (in French groupe) in a sense close to the technical sense that is understood today, making him among the founders of the branch of algebra known as group theory. He called the decomposition of a group into its left and right cosets a proper decomposition if the left and right cosets coincide, which is what today is known as a normal subgroup. He also introduced the concept of a finite field (also known as a Galois field in his honor) in essentially the same form as it is understood today.

In his last letter to Chevalier and attached manuscripts, the second of three, he made basic studies of linear groups over finite fields:
 * He constructed the general linear group over a prime field, GL(ν, p) and computed its order, in studying the Galois group of the general equation of degree pν.
 * He constructed the projective special linear group PSL(2,p). Galois constructed them as fractional linear transforms, and observed that they were simple except if p was 2 or 3. These were the second family of finite simple groups, after the alternating groups.
 * He noted the exceptional fact that PSL(2,p) is simple and acts on p points if and only if p is 5, 7, or 11.

Galois theory
Galois's most significant contribution to mathematics is his development of Galois theory. He realized that the algebraic solution to a polynomial equation is related to the structure of a group of permutations associated with the roots of the polynomial, the Galois group of the polynomial. He found that an equation could be solved in radicals if one can find a series of subgroups of its Galois group, each one normal in its successor with abelian quotient, that is, its Galois group is solvable. This proved to be a fertile approach, which later mathematicians adapted to many other fields of mathematics besides the theory of equations to which Galois originally applied it.

Analysis
Galois also made some contributions to the theory of Abelian integrals and continued fractions.

As written in his last letter, Galois passed from the study of elliptic functions to consideration of the integrals of the most general algebraic differentials, today called Abelian integrals. He classified these integrals into three categories.

Continued fractions
In his first paper in 1828, Galois proved that the regular continued fraction which represents a quadratic surd ζ is purely periodic if and only if ζ is a reduced surd, that is, $$\zeta > 1$$ and its conjugate $$\eta$$ satisfies $$-1 < \eta < 0$$.

In fact, Galois showed more than this. He also proved that if ζ is a reduced quadratic surd and η is its conjugate, then the continued fractions for ζ and for (−1/η) are both purely periodic, and the repeating block in one of those continued fractions is the mirror image of the repeating block in the other. In symbols we have

\begin{align} \zeta& = [\,\overline{a_0;a_1,a_2,\dots,a_{m-1}}\,]\\[3pt] \frac{-1}{\eta}& = [\,\overline{a_{m-1};a_{m-2},a_{m-3},\dots,a_0}\,]\, \end{align} $$

where ζ is any reduced quadratic surd, and η is its conjugate.

From these two theorems of Galois a result already known to Lagrange can be deduced. If r > 1 is a rational number that is not a perfect square, then

\sqrt{r} = \left[\,a_0;\overline{a_1,a_2,\dots,a_2,a_1,2a_0}\,\right]. $$

In particular, if n is any non-square positive integer, the regular continued fraction expansion of √n contains a repeating block of length m, in which the first m − 1 partial denominators form a palindromic string.

title: Évariste Galois