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Carbon monoxide

Carbon monoxide (chemical formula CO) is a poisonous, flammable gas that is colorless, odorless, tasteless, and slightly less dense than air. Carbon monoxide consists of one carbon atom and one oxygen atom connected by a triple bond. It is the simplest carbon oxide. In coordination complexes, the carbon monoxide ligand is called carbonyl. It is a key ingredient in many processes in industrial chemistry.

The most common source of carbon monoxide is the partial combustion of carbon-containing compounds. Numerous environmental and biological sources generate carbon monoxide. In industry, carbon monoxide is important in the production of many compounds, including drugs, fragrances, and fuels. Upon emission into the atmosphere, carbon monoxide affects several processes that contribute to climate change.

Indoors CO is one of the most acutely toxic contaminants affecting indoor air quality. CO may be emitted from tobacco smoke and generated from malfunctioning fuel burning stoves (wood, kerosene, natural gas, propane) and fuel burning heating systems (wood, oil, natural gas) and from blocked flues connected to these appliances. Carbon monoxide poisoning is the most common type of fatal air poisoning in many countries.

Carbon monoxide has important biological roles across phylogenetic kingdoms. It is produced by many organisms, including humans. In mammalian physiology, carbon monoxide is a classical example of hormesis where low concentrations serve as an endogenous neurotransmitter (gasotransmitter) and high concentrations are toxic resulting in carbon monoxide poisoning. It is isoelectronic with both cyanide anion CN− and molecular nitrogen N2.

Physical and chemical properties
Carbon monoxide is the simplest oxocarbon and is isoelectronic with other triply-bonded diatomic species possessing 10 valence electrons, including the cyanide anion, the nitrosonium cation, boron monofluoride and molecular nitrogen. It has a molar mass of 28.0, which, according to the ideal gas law, makes it slightly less dense than air, whose average molar mass is 28.8.

The carbon and oxygen are connected by a triple bond that consists of a net two pi bonds and one sigma bond. The bond length between the carbon atom and the oxygen atom is 112.8 pm. This bond length is consistent with a triple bond, as in molecular nitrogen (N2), which has a similar bond length (109.76 pm) and nearly the same molecular mass. Carbon–oxygen double bonds are significantly longer, 120.8 pm in formaldehyde, for example. The boiling point (82 K) and melting point (68 K) are very similar to those of N2 (77 K and 63 K, respectively). The bond-dissociation energy of 1072 kJ/mol is stronger than that of N2 (942 kJ/mol) and represents the strongest chemical bond known.

The ground electronic state of carbon monoxide is a singlet state since there are no unpaired electrons.

Bonding and dipole moment
Carbon and oxygen together have a total of 10 electrons in the valence shell. Following the octet rule for both carbon and oxygen, the two atoms form a triple bond, with six shared electrons in three bonding molecular orbitals, rather than the usual double bond found in organic carbonyl compounds. Since four of the shared electrons come from the oxygen atom and only two from carbon, one bonding orbital is occupied by two electrons from oxygen, forming a dative or dipolar bond. This causes a C←O polarization of the molecule, with a small negative charge on carbon and a small positive charge on oxygen. The other two bonding orbitals are each occupied by one electron from carbon and one from oxygen, forming (polar) covalent bonds with a reverse C→O polarization since oxygen is more electronegative than carbon. In the free carbon monoxide molecule, a net negative charge δ– remains at the carbon end and the molecule has a small dipole moment of 0.122 D.

The molecule is therefore asymmetric: oxygen has more electron density than carbon and is also slightly positively charged compared to carbon being negative. By contrast, the isoelectronic dinitrogen molecule has no dipole moment. Carbon monoxide has a computed fractional bond order of 2.6, indicating that the "third" bond is important but constitutes somewhat less than a full bond. Thus, in valence bond terms, –C≡O+ is the most important structure, while :C=O is non-octet, but has a neutral formal charge on each atom and represents the second most important resonance contributor. Because of the lone pair and divalence of carbon in this resonance structure, carbon monoxide is often considered to be an extraordinarily stabilized carbene. Isocyanides are compounds in which the O is replaced by an NR (R = alkyl or aryl) group and have a similar bonding scheme.

If carbon monoxide acts as a ligand, the polarity of the dipole may reverse with a net negative charge on the oxygen end, depending on the structure of the coordination complex. See also the section "Coordination chemistry" below.

Bond polarity and oxidation state
Theoretical and experimental studies show that, despite the greater electronegativity of oxygen, the dipole moment points from the more-negative carbon end to the more-positive oxygen end. The three bonds are in fact polar covalent bonds that are strongly polarized. The calculated polarization toward the oxygen atom is 71% for the σ-bond and 77% for both π-bonds.

The oxidation state of carbon in carbon monoxide is +2 in each of these structures. It is calculated by counting all the bonding electrons as belonging to the more electronegative oxygen. Only the two non-bonding electrons on carbon are assigned to carbon. In this count, carbon then has only two valence electrons in the molecule compared to four in the free atom.

Occurrence
Carbon monoxide occurs in various natural and artificial environments. Photochemical degradation of plant matter for example generates an estimated 60 million tons/year. Typical concentrations in parts per million are as follows:

Atmospheric presence

Carbon monoxide (CO) is present in small amounts (about 80 ppb) in the Earth's atmosphere. Most of the rest comes from chemical reactions with organic compounds emitted by human activities and natural origins due to photochemical reactions in the troposphere that generate about 5 × 1012 kilograms per year. Other natural sources of CO include volcanoes, forest and bushfires, and other miscellaneous forms of combustion such as fossil fuels. Small amounts are also emitted from the ocean, and from geological activity because carbon monoxide occurs dissolved in molten volcanic rock at high pressures in the Earth's mantle. Because natural sources of carbon monoxide vary from year to year, it is difficult to accurately measure natural emissions of the gas.

Carbon monoxide has an indirect effect on radiative forcing by elevating concentrations of direct greenhouse gases, including methane and tropospheric ozone. CO can react chemically with other atmospheric constituents (primarily the hydroxyl radical, •OH) that would otherwise destroy methane. Through natural processes in the atmosphere, it is oxidized to carbon dioxide and ozone. Carbon monoxide is short-lived in the atmosphere (with an average lifetime of about one to two months), and spatially variable in concentration.

Due to its long lifetime in the mid-troposphere, carbon monoxide is also used as a tracer for pollutant plumes.

Astronomy
Beyond Earth, carbon monoxide is the second-most common diatomic molecule in the interstellar medium, after molecular hydrogen. Because of its asymmetry, this polar molecule produces far brighter spectral lines than the hydrogen molecule, making CO much easier to detect. Interstellar CO was first detected with radio telescopes in 1970. It is now the most commonly used tracer of molecular gas in general in the interstellar medium of galaxies, as molecular hydrogen can only be detected using ultraviolet light, which requires space telescopes. Carbon monoxide observations provide much of the information about the molecular clouds in which most stars form.

Beta Pictoris, the second brightest star in the constellation Pictor, shows an excess of infrared emission compared to normal stars of its type, which is caused by large quantities of dust and gas (including carbon monoxide) near the star.

In the atmosphere of Venus carbon monoxide occurs as a result of the photodissociation of carbon dioxide by electromagnetic radiation of wavelengths shorter than 169 nm. It has also been identified spectroscopically on the surface of Neptune's moon Triton.

Solid carbon monoxide is a component of comets. The volatile or "ice" component of Halley's Comet is about 15% CO. At room temperature and at atmospheric pressure, carbon monoxide is actually only metastable (see Boudouard reaction) and the same is true at low temperatures where CO and are solid, but nevertheless it can exist for billions of years in comets. There is very little CO in the atmosphere of Pluto, which seems to have been formed from comets. This may be because there is (or was) liquid water inside Pluto.

Carbon monoxide can react with water to form carbon dioxide and hydrogen:

 * CO + H2O → +

This is called the water-gas shift reaction when occurring in the gas phase, but it can also take place (very slowly) in an aqueous solution. If the hydrogen partial pressure is high enough (for instance in an underground sea), formic acid will be formed:

 * CO + H2O → HCOOH

These reactions can take place in a few million years even at temperatures such as found on Pluto.

Urban pollution
Carbon monoxide is a temporary atmospheric pollutant in some urban areas, chiefly from the exhaust of internal combustion engines (including vehicles, portable and back-up generators, lawnmowers, power washers, etc.), but also from incomplete combustion of various other fuels (including wood, coal, charcoal, oil, paraffin, propane, natural gas, and trash).

Large CO pollution events can be observed from space over cities.

Role in ground level ozone formation
Carbon monoxide is, along with aldehydes, part of the series of cycles of chemical reactions that form photochemical smog. It reacts with hydroxyl radical (•OH) to produce a radical intermediate •HOCO, which transfers rapidly its radical hydrogen to O2 to form peroxy radical (HO2•) and carbon dioxide. Peroxy radical subsequently reacts with nitrogen oxide (NO) to form nitrogen dioxide (NO2) and hydroxyl radical. NO2 gives O(3P) via photolysis, thereby forming O3 following reaction with O2. Since hydroxyl radical is formed during the formation of NO2, the balance of the sequence of chemical reactions starting with carbon monoxide and leading to the formation of ozone is:
 * CO + 2O2 + hν → + O3

(where hν refers to the photon of light absorbed by the NO2 molecule in the sequence)

Although the creation of NO2 is the critical step leading to low level ozone formation, it also increases this ozone in another, somewhat mutually exclusive way, by reducing the quantity of NO that is available to react with ozone.

Indoor air pollution
Carbon monoxide is one of the most acutely toxic indoor air contaminants. Carbon monoxide may be emitted from tobacco smoke and generated from malfunctioning fuel burning stoves (wood, kerosene, natural gas, propane) and fuel burning heating systems (wood, oil, natural gas) and from blocked flues connected to these appliances. In developed countries the main sources of indoor CO emission come from cooking and heating devices that burn fossil fuels and are faulty, incorrectly installed or poorly maintained. Appliance malfunction may be due to faulty installation or lack of maintenance and proper use. In low- and middle-income countries the most common sources of CO in homes are burning biomass fuels and cigarette smoke.

Mining
Miners refer to carbon monoxide as "whitedamp" or the "silent killer". It can be found in confined areas of poor ventilation in both surface mines and underground mines. The most common sources of carbon monoxide in mining operations are the internal combustion engine and explosives; however, in coal mines, carbon monoxide can also be found due to the low-temperature oxidation of coal. The idiom "Canary in the coal mine" pertained to an early warning of a carbon monoxide presence.

Health effects
Carbon monoxide poisoning is the most common type of fatal air poisoning in many countries. Acute exposure can also lead to long-term neurological effects such as cognitive and behavioural changes. Severe CO poisoning may lead to unconsciousness, coma and death. Chronic exposure to low concentrations of carbon monoxide may lead to lethargy, headaches, nausea, flu-like symptoms and neuropsychological and cardiovascular issues.

Chemistry
Carbon monoxide has a wide range of functions across all disciplines of chemistry. The four premier categories of reactivity involve metal-carbonyl catalysis, radical chemistry, cation and anion chemistries.

Coordination chemistry

Most metals form coordination complexes containing covalently attached carbon monoxide. Only metals in lower oxidation states will complex with carbon monoxide ligands. This is because there must be sufficient electron density to facilitate back-donation from the metal dxz-orbital, to the π* molecular orbital from CO. The lone pair on the carbon atom in CO also donates electron density to the dx2−y2 on the metal to form a sigma bond. This electron donation is also exhibited with the cis effect, or the labilization of CO ligands in the cis position. Nickel carbonyl, for example, forms by the direct combination of carbon monoxide and nickel metal:
 * Ni + 4 CO → Ni(CO)4 (1 bar, 55 °C)

For this reason, nickel in any tubing or part must not come into prolonged contact with carbon monoxide. Nickel carbonyl decomposes readily back to Ni and CO upon contact with hot surfaces, and this method is used for the industrial purification of nickel in the Mond process.

In nickel carbonyl and other carbonyls, the electron pair on the carbon interacts with the metal; the carbon monoxide donates the electron pair to the metal. In these situations, carbon monoxide is called the carbonyl ligand. One of the most important metal carbonyls is iron pentacarbonyl, Fe(CO)5:

Many metal–CO complexes are prepared by decarbonylation of organic solvents, not from CO. For instance, iridium trichloride and triphenylphosphine react in boiling 2-methoxyethanol or DMF to afford IrCl(CO)(PPh3)2.

Metal carbonyls in coordination chemistry are usually studied using infrared spectroscopy.

Organic and main group chemistry
In the presence of strong acids and water, carbon monoxide reacts with alkenes to form carboxylic acids in a process known as the Koch–Haaf reaction. In the Gattermann–Koch reaction, arenes are converted to benzaldehyde derivatives in the presence of CO, AlCl3 and HCl. Organolithium compounds (e.g. butyl lithium) react with carbon monoxide, but these reactions have little scientific use.

Although CO reacts with carbocations and carbanions, it is relatively nonreactive toward organic compounds without the intervention of metal catalysts.

With main group reagents, CO undergoes several noteworthy reactions. Chlorination of CO is the industrial route to the important compound phosgene. With borane CO forms the adduct H3BCO, which is isoelectronic with the acetylium cation [H3CCO]+. CO reacts with sodium to give products resulting from C−C coupling such as sodium acetylenediolate 2·. It reacts with molten potassium to give a mixture of an organometallic compound, potassium acetylenediolate 2·, potassium benzenehexolate 6, and potassium rhodizonate 2·.

The compounds cyclohexanehexone or triquinoyl (C6O6) and cyclopentanepentone or leuconic acid (C5O5), which so far have been obtained only in trace amounts, can be regarded as polymers of carbon monoxide. At pressures exceeding 5 GPa, carbon monoxide converts to polycarbonyl, a solid polymer that is metastable at atmospheric pressure but is explosive.

Laboratory preparation
Carbon monoxide is conveniently produced in the laboratory by the dehydration of formic acid or oxalic acid, for example with concentrated sulfuric acid. Another method is heating an intimate mixture of powdered zinc metal and calcium carbonate, which releases CO and leaves behind zinc oxide and calcium oxide:

 * Zn + CaCO3 → ZnO + CaO + CO

Silver nitrate and iodoform also afford carbon monoxide:

 * CHI3 + 3AgNO3 + H2O → 3HNO3 + CO + 3AgI

Finally, metal oxalate salts release CO upon heating, leaving a carbonate as byproduct:

Production
Thermal combustion is the most common source for carbon monoxide. Carbon monoxide is produced from the partial oxidation of carbon-containing compounds; it forms when there is not enough oxygen to produce carbon dioxide, such as when operating a stove or an internal combustion engine in an enclosed space.

A large quantity of CO byproduct is formed during the oxidative processes for the production of chemicals. For this reason, the process off-gases have to be purified.

Many methods have been developed for carbon monoxide production.

Industrial production
A major industrial source of CO is producer gas, a mixture containing mostly carbon monoxide and nitrogen, formed by combustion of carbon in air at high temperature when there is an excess of carbon. In an oven, air is passed through a bed of coke. The initially produced equilibrates with the remaining hot carbon to give CO. The reaction of  with carbon to give CO is described as the Boudouard reaction. Above 800 °C, CO is the predominant product:

 * (g) + C (s) → 2 CO (g) (ΔHr = 170 kJ/mol)

Another source is "water gas", a mixture of hydrogen and carbon monoxide produced via the endothermic reaction of steam and carbon:

 * H2O (g) + C (s) → H2 (g) + CO (g) (ΔHr = 131 kJ/mol)

Other similar "synthesis gases" can be obtained from natural gas and other fuels.

Carbon monoxide can also be produced by high-temperature electrolysis of carbon dioxide with solid oxide electrolyzer cells. One method developed at DTU Energy uses a cerium oxide catalyst and does not have any issues of fouling of the catalyst.

 * 2 → 2 CO + O2

Carbon monoxide is also a byproduct of the reduction of metal oxide ores with carbon, shown in a simplified form as follows:

 * MO + C → M + CO

Carbon monoxide is also produced by the direct oxidation of carbon in a limited supply of oxygen or air.

 * 2 C + O2 → 2 CO

Since CO is a gas, the reduction process can be driven by heating, exploiting the positive (favorable) entropy of reaction. The Ellingham diagram shows that CO formation is favored over in high temperatures.

Chemical industry
Carbon monoxide is an industrial gas that has many applications in bulk chemicals manufacturing. Large quantities of aldehydes are produced by the hydroformylation reaction of alkenes, carbon monoxide, and H2. Hydroformylation is coupled to the Shell higher olefin process to give precursors to detergents.

Phosgene, useful for preparing isocyanates, polycarbonates, and polyurethanes, is produced by passing purified carbon monoxide and chlorine gas through a bed of porous activated carbon, which serves as a catalyst. World production of this compound was estimated to be 2.74 million tonnes in 1989.
 * CO + Cl2 → COCl2

Methanol is produced by the hydrogenation of carbon monoxide. In a related reaction, the hydrogenation of carbon monoxide is coupled to C−C bond formation, as in the Fischer–Tropsch process where carbon monoxide is hydrogenated to liquid hydrocarbon fuels. This technology allows coal or biomass to be converted to diesel.

In the Cativa process, carbon monoxide and methanol react in the presence of a homogeneous iridium catalyst and hydroiodic acid to give acetic acid. This process is responsible for most of the industrial production of acetic acid.

Metallurgy
Carbon monoxide is a strong reductive agent and has been used in pyrometallurgy to reduce metals from ores since ancient times. Carbon monoxide strips oxygen off metal oxides, reducing them to pure metal in high temperatures, forming carbon dioxide in the process. Carbon monoxide is not usually supplied as is, in the gaseous phase, in the reactor, but rather it is formed in high temperature in presence of oxygen-carrying ore, or a carboniferous agent such as coke, and high temperature. The blast furnace process is a typical example of a process of reduction of metal from ore with carbon monoxide.

Likewise, blast furnace gas collected at the top of blast furnace, still contains some 10% to 30% of carbon monoxide, and is used as fuel on Cowper stoves and on Siemens-Martin furnaces on open hearth steelmaking.

Lasers
Carbon monoxide has also been used as a lasing medium in high-powered infrared lasers.

Proposed use as a rocket fuel
Carbon monoxide has been proposed for use as a fuel on Mars by NASA researcher Geoffrey Landis. Carbon monoxide/oxygen engines have been suggested for early surface transportation use as both carbon monoxide and oxygen can be straightforwardly produced from the carbon dioxide atmosphere of Mars by zirconia electrolysis, without using any Martian water resources to obtain hydrogen, which would be needed to make methane or any hydrogen-based fuel.

Landis also proposed manufacturing the fuel from the similar carbon dioxide atmosphere of Venus for a sample return mission, in combination with solar-powered UAVs and rocket balloon ascent.

Physiology
Carbon monoxide is a bioactive molecule which acts as a gaseous signaling molecule. It is naturally produced by many enzymatic and non-enzymatic pathways, the best understood of which is the catabolic action of heme oxygenase on the heme derived from hemoproteins such as hemoglobin. Following the first report that carbon monoxide is a normal neurotransmitter in 1993, carbon monoxide has received significant clinical attention as a biological regulator.

Because of carbon monoxide's role in the body, abnormalities in its metabolism have been linked to a variety of diseases, including neurodegenerations, hypertension, heart failure, and pathological inflammation. In many tissues, carbon monoxide acts as anti-inflammatory, vasodilatory, and encouragers of neovascular growth. In animal model studies, carbon monoxide reduced the severity of experimentally induced bacterial sepsis, pancreatitis, hepatic ischemia/reperfusion injury, colitis, osteoarthritis, lung injury, lung transplantation rejection, and neuropathic pain while promoting skin wound healing. Therefore, there is significant interest in the therapeutic potential of carbon monoxide becoming pharmaceutical agent and clinical standard of care.

Medicine
Studies involving carbon monoxide have been conducted in many laboratories throughout the world for its anti-inflammatory and cytoprotective properties. These properties have the potential to be used to prevent the development of a series of pathological conditions including ischemia reperfusion injury, transplant rejection, atherosclerosis, severe sepsis, severe malaria, or autoimmunity. Many pharmaceutical drug delivery initiatives have developed methods to safely administer carbon monoxide, and subsequent controlled clinical trials have evaluated the therapeutic effect of carbon monoxide.

Microbiology
Microbiota may also utilize carbon monoxide as a gasotransmitter. Carbon monoxide sensing is a signaling pathway facilitated by proteins such as CooA. The scope of the biological roles for carbon monoxide sensing is still unknown.

The human microbiome produces, consumes, and responds to carbon monoxide. For example, in certain bacteria, carbon monoxide is produced via the reduction of carbon dioxide by the enzyme carbon monoxide dehydrogenase with favorable bioenergetics to power downstream cellular operations. In another example, carbon monoxide is a nutrient for methanogenic archaea which reduce it to methane using hydrogen.

Carbon monoxide has certain antimicrobial properties which have been studied to treat against infectious diseases.

Food science
Carbon monoxide is used in modified atmosphere packaging systems in the US, mainly with fresh meat products such as beef, pork, and fish to keep them looking fresh. The benefit is two-fold, carbon monoxide protects against microbial spoilage and it enhances the meat color for consumer appeal. The carbon monoxide combines with myoglobin to form carboxymyoglobin, a bright-cherry-red pigment. Carboxymyoglobin is more stable than the oxygenated form of myoglobin, oxymyoglobin, which can become oxidized to the brown pigment metmyoglobin. This stable red color can persist much longer than in normally packaged meat. Typical levels of carbon monoxide used in the facilities that use this process are between 0.4% and 0.5%.

The technology was first given "generally recognized as safe" (GRAS) status by the U.S. Food and Drug Administration (FDA) in 2002 for use as a secondary packaging system, and does not require labeling. In 2004, the FDA approved CO as primary packaging method, declaring that CO does not mask spoilage odor. The process is currently unauthorized in many other countries, including Japan, Singapore, and the European Union.

Weaponization
In ancient history, Hannibal executed Roman prisoners with coal fumes during the Second Punic War.

Carbon monoxide had been used for genocide during the Holocaust at some extermination camps, the most notable by gas vans in Chełmno, and in the Action T4 "euthanasia" program.

Prehistory
Humans have maintained a complex relationship with carbon monoxide since first learning to control fire circa 800,000 BC. Early humans probably discovered the toxicity of carbon monoxide poisoning upon introducing fire into their dwellings. The early development of metallurgy and smelting technologies emerging circa 6,000 BC through the Bronze Age likewise plagued humankind from carbon monoxide exposure. Apart from the toxicity of carbon monoxide, indigenous Native Americans may have experienced the neuroactive properties of carbon monoxide through shamanistic fireside rituals.

Ancient history
Early civilizations developed mythological tales to explain the origin of fire, such as Prometheus from Greek mythology who shared fire with humans. Aristotle (384–322 BC) first recorded that burning coals produced toxic fumes. Greek physician Galen (129–199 AD) speculated that there was a change in the composition of the air that caused harm when inhaled, and many others of the era developed a basis of knowledge about carbon monoxide in the context of coal fume toxicity. Cleopatra may have died from carbon monoxide poisoning.

Pre-industrial revolution
Georg Ernst Stahl mentioned carbonarii halitus in 1697 in reference to toxic vapors thought to be carbon monoxide. Friedrich Hoffmann conducted the first modern scientific investigation into carbon monoxide poisoning from coal in 1716. Herman Boerhaave conducted the first scientific experiments on the effect of carbon monoxide (coal fumes) on animals in the 1730s.

Joseph Priestley is considered to have first synthesized carbon monoxide in 1772. Carl Wilhelm Scheele similarly isolated carbon monoxide from charcoal in 1773 and thought it could be the carbonic entity making fumes toxic. Torbern Bergman isolated carbon monoxide from oxalic acid in 1775. Later in 1776, the French chemist de Lassone produced CO by heating zinc oxide with coke, but mistakenly concluded that the gaseous product was hydrogen, as it burned with a blue flame. In the presence of oxygen, including atmospheric concentrations, carbon monoxide burns with a blue flame, producing carbon dioxide. Antoine Lavoisier conducted similar inconclusive experiments to Lassone in 1777. The gas was identified as a compound containing carbon and oxygen by William Cruickshank in 1800.

Thomas Beddoes and James Watt recognized carbon monoxide (as hydrocarbonate) to brighten venous blood in 1793. Watt suggested coal fumes could act as an antidote to the oxygen in blood, and Beddoes and Watt likewise suggested hydrocarbonate has a greater affinity for animal fiber than oxygen in 1796. In 1854, Adrien Chenot similarly suggested carbon monoxide to remove the oxygen from blood and then be oxidized by the body to carbon dioxide. The mechanism for carbon monoxide poisoning is widely credited to Claude Bernard whose memoirs beginning in 1846 and published in 1857 phrased, "prevents arterials blood from becoming venous". Felix Hoppe-Seyler independently published similar conclusions in the following year.

Advent of industrial chemistry
Carbon monoxide gained recognition as an essential reagent in the 1900s. Three industrial processes illustrate its evolution in industry. In the Fischer–Tropsch process, coal and related carbon-rich feedstocks are converted into liquid fuels via the intermediacy of CO. Originally developed as part of the German war effort to compensate for their lack of domestic petroleum, this technology continues today. Also in Germany, a mixture of CO and hydrogen was found to combine with olefins to give aldehydes. This process, called hydroformylation, is used to produce many large scale chemicals such as surfactants as well as specialty compounds that are popular fragrances and drugs. For example, CO is used in the production of vitamin A. In a third major process, attributed to researchers at Monsanto, CO combines with methanol to give acetic acid. Most acetic acid is produced by the Cativa process. Hydroformylation and the acetic acid syntheses are two of myriad carbonylation processes.

title: Carbon monoxide


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Talk:Codex

Various, to 2005
Early Christian writers did not use page numbers. As anyone who has read the Bible knows they use references to chapter and verse. page numbers were unworkable in any case since there was no standardization of the page format and it would be most unlikely to have survived translation into Latin. The form used is Corinthians II Chapter 4 verse 12.

Page numbers were invented after the invention of the mechanical printing press, or at least that is what Alan Kay told me. I had come here to find out the full reference.

There seems to be a lot of other Christian propaganda here. References to 'pagan' religions should be 'non-Christian' to maintain the NPOV. Judaism is not a Pagan religion, nor is Zorastratharianism. The Torah is by tradition always a scroll. The Talmud and the glossaries are codex form.

 * There are a lot of misconceptions going on here, and in the edit you made.  Medieval book makers most certainly DID number the pages of their books.  Of course, as you note, there often was not a consistent division of the text into pages. (Although it happened more often than one might think, especially in the later Middle Ages when books were produced in an almost assembly-line fashion.)  The most common numbering method was not the modern pagination, but foliation, that is numbering each leaf, of the manuscript rather than each side of a leaf, however sometimes pagination was used.  Although the original text of the article was poorly worded, the codex form did allow for easier indexing than the scroll, and it was done. For the most famous example Eusebius of Caesarea made canon tables for the four Gospels that allowed readers to compare the accounts of various incidents in the life of Christ in the different Gospels.  This would not have been practical if the codex had not been invented. You are seriously mistaken about the form for citing biblical verses.  The most common form of citing the Bible was to just quote the bit you wanted and move on.  The division into chapters and verses took centuries to standardize. The division used today did not come about until the 16th century.

 * The use of the word "Pagan" is not quite as POV, or Christian propaganda, as you seem to think. Although it is possible that Christians embraced the  Codex for their scripture as a means of differentiating themselves from Jews, the relevent comparison is not between Judaism or Zorastratharianism, and Christianity, but between the wider Roman culture, which WAS predominatly Pagan, and Christianity.  The rise of the use of the codex and the rise of Christianity in the Roman Empire correspond closely.

 * Although Aldus Manutius was important in the history of the book, the very fact that we don't use italic script exclusively, as he did makes it difficult to credit him with invention of the modern codex form, especially if you are defining the modern codex form as small and compact. Small format books were made throughout the Middle ages, see Stonyhurst Gospel for an early example and Book of Hours (Milan, Biblioteca Trivulziana, Cod. 470) for a later example. Dsmdgold 21:12, July 19, 2005 (UTC)

I *think* that the word 'code' to refer to a law code indeed comes from the late antique and early Byzantine codifications of earlier legal works, culminating in the Justinianic Code in the 7th century. These were, in the fashion of the time, in codices rather than scrolls, and the nomenclature was transferred to the contents from the objects.

I think a codex is any book with pages, as opposed to a scroll, not necessarily hand-written. -- Marj Tiefert, Saturday, April 6, 2002

 * "the term is now used only for manuscript (hand-written) books, produced from Late Antiquity through the Middle Ages." this is incorrect, codex is also used to describe contemporary handmade books. ---199.79.170.211 (talk) 18:35, 9 December 2008 (UTC)

I agree with Marj, also , it would be good idea to check the ethyomology of 'codex' since 'liber' is the direct traduction of book in latin language. Library comes from this word, and in spanish libro (meaning book). --200.61.10.20 16:19, 15 Mar 2005 (UTC) Manuel

 * In Latin, codex originally meant the trunk of a tree, and from that, a wooden writing table -- as usual, etymology isn't particularly helpful for settling an issue of modern usage. In common academic use, codicology is the study of paginated manuscripts, while bibliography is the study of printed books. --Dpm64 12:36, 18 Mar 2005 (UTC)

 * My understanding of codicology is that it is the the study of the structure of a codex (i.e. how its sewn, how the covers are attached, etc.). This is done with manuscripts more than printed book because there is not a great deal of useful information to be gleaned from studying the structure of a mass produced item.  It is also my understanding that a codex is any book bound on one side with separate leaves, be it a manuscript or printed book. Dsmdgold 12:37, Apr 12, 2005 (UTC)

List of Codices with individual entries
Is the list, "some codices" really useful here? This list contain some of the codices that happen to have "Codex" in their name giving the false impression that other manuscripts like the Book of Kells are not codices. In reality almost every item catagorized on wikipedia as a "manuscript" or "illuminated manuscript" is a codex. Dsmdgold 12:42, Apr 12, 2005 (UTC)
 * Good point: I made some additions precisely that way, using the Index; the Book of Kells certainly belongs in the list: I'll add it now. But, among all the really trivial lists at Wikipedia, doesn't some version of this very selective list of Codices with individual entries belong somewhere, with redirects from here and from Manuscript etc? Perhaps New Testament codex is a better title? I'm scratching my head here... --Wetman 15:37, 12 Apr 2005 (UTC)

 * I propose removing the list of codices from here and creating a separate list for it. Personally I do not see the point of maintaining possibly endless list of books here, but if people think this would be useful... then I will create the article and remove the list from here in one week. If no one objects. → Aethralis 12:11, 2 December 2006 (UTC)

 * Yes, by all means please do this. I was just thinking that the list of codices needs to become, yes, a List of codices (or something similar).  Thanks for volunteering, Aethralis.   Madman 20:13, 4 December 2006 (UTC)

 * I worked on the first major expansion of List of books to include both published books and manuscripts -- anything that people would call "a book". It desn't make sense to have to update both the list of books and list of codices; someone might update one but not the other.  Many manuscripts have been published (in facsimile or retyped) with the same title, so they would be found in both lists.  Just have a selective list of examples in the article, and create a Category:Codices, as a subcategory of Category:Books. (Category:Illuminated manuscripts already exists, if that's close enough.) GUllman 21:08, 4 December 2006 (UTC)

 * I agree with the Category:Codices idea. → Aethralis 23:29, 4 December 2006 (UTC)

 * I disagree - Codex is an entirely arbitary title for certain manuscripts (often chosen because "gospels" etc has already been taken for that place); I know it will take longer but "Category: Illuminated manuscripts" should either:

 * a) be broadened (to include non-illuminated or not much illuminated ones),

Johnbod 02:52, 20 December 2006 (UTC)
 * b) or, better, made a sub-category of a new overall category for pre-printing Western manuscripts divided between those notably illuminated and those not.

 * In what way is codex arbitrary? In this sense the "illuminated manuscript" is far more arbitrary as it is not usually properly (what is decorated?) defined. I have a manuscript here what has some decorated initials, but it's not illuminated. But codex on the other hand has a very good definition. I consider scroll & codex to be the main types of manuscripts and all illuminated, minuscule, uncial, gothic, bastarda, anglicana etc are the subtypes, which are sometimes overlapping. But scroll and codex are _never_ overlapping. → Aethralis 08:47, 20 December 2006 (UTC)

 * You're misreading me. I said "entirely arbitary title for certain manuscripts " - ie as a Name. As a term it it is clear. But the list here mainly consist of books which happened to have "codex" in their usual name, or one of their names, which is arbitary. The various bits of the List of manuscripts are already much fuller, better described and organized. But they don't distinguish between those mainly notable for their decoration and those mainly notable for their content - which would be useful. Johnbod 15:29, 20 December 2006 (UTC)

 * Ok. I get your point. I agree that the can be no category of _notable_ codices (notable is not categorizeable) and maybe indeed the "list of notable codices" is more meaningful to have. → Aethralis 19:44, 20 December 2006 (UTC)

Hard to read in places
From the article:

 * The designation Codex is less used in conventional names given Medieval manuscripts, when the codex form is universal and understood.

It strikes me that this sentence is actually rather hard to parse. Perhaps someone who is certain of what it means could rephrase it in clearer language?

— Haeleth Talk 23:50, 6 April 2006 (UTC)

 * I spent some time today copyediting the article. It seemed that this is one of those Wikipedia articles that have just accumulated over time, bits and pieces from here and there.  So I tried to put it into some sort of structure.  Hopefully I didn't offend anyone by cutting their favorite piece of prose.

 * I tried to limit the article to handwritten codices. Nearly every document referred to as a Codex is handwritten, and info about printed books is contained in the printing and book articles.  Hope this helps, Madman 19:41, 29 April 2006 (UTC)

Mistaking Codex for Code
I moved this mis-stated misunderstanding here: "A legal text or code of conduct is sometimes called a codex (for example, the Justinian Codex), since laws were recorded in large codices." This is simply an error, one that doesn't come into educated or official discourse. --Wetman 20:14, 9 May 2006 (UTC)

Italicize named Codices??
Fellow editors: When typing the name of a Codex, e.g. Codex Rios, should I italicize it (e.g. Codex Rios)?? I see that the convention in the Codex article is "No", but I thought I'd ask as I've seen it italicized elsewhere in Wikipedia. Curiously yours, Madman 02:16, 29 July 2006 (UTC)

tv show
codex is allso a kind of tv show /halo

The origin of our books today
Don't we have with codices a similar case as with printing insofar as all books today derive from Western books (and therefore, ultimately, from the Roman codex)? Amerindian book tradition was destroyed by the Spanish, dunno about India, but Chinese books were only printed on every second page and the bookbinding remained different. Leaves Muslim and Christian which are derived from the Roman codex. Does the Roman codex rule globally now? Gun Powder Ma 01:29, 7 December 2006 (UTC)

some unknow to wikipedia books ?
Codex Neapoletanus

Sometime it art on it may be under other name. If you know contrubute. Nasz 01:53, 6 February 2007 (UTC)

Shelving of Books
According to Henry Petroski's "The Book on the Book Shelf", books did not get shelved spine out until the practice of chaining books ended. See chapter 5, the Press of Books. Chaining ended when printed books became commonplace (as opposed to manuscript books). The chains attached to the clasps on the manuscript books, and therefore to the non-spine side. On page 125 he has an illustration of books with authors and titles on their spines, and the caption reads "In the sixteenth century, books began to have authors and titles, and the date of the edition, imprinted on their spines." Remember that very early books often did not have titles, and the idea of authorship was a fairly recent invention (I don't have time to look it up right now.) LaMona 14:50, 18 March 2007 (UTC)

 * Some books in chained libraries were placed spine out, though they mostly lied on their backs or fronts (depending on the chained library type) or were shelved spine inwards. For different methods of shelving chained books see J. A. Szirmai, The Archaeology of Medieval Bookbinding (Scolar Pr, 1999), p. 269 . → Aethralis 19:29, 18 March 2007 (UTC)

Book vs. Codex
Although it's probably reflected in the fuzzy boundary in reality, the article is confusing as to what the practical distinction between a codex and a modern book is. "The codex in turn became the printed book, for which the term is not used." - So what was the turning point/main feature which caused the transition between 'codex' and 'book'? "Although technically any modern paperback is a codex ..." - So what about modern hard-covers? It would be nice to have a clarification/history lesson as to why there is a Book/Codex distinction. The history section peters out in the Middle Ages. -- 20:14, 15 January 2008 (UTC)
 * My guess is that modern books simply are intimately associated with the printing press as opposed to codices, but the evolution in bookbinding technique is probably a more relevant distinguishing factor. Abvgd (talk) 21:43, 26 February 2012 (UTC)

Definition wrong (29 May 2012)
The definition here as of today—a bound book with pages, including modern books—is plain wrong. The OED says a code of laws, a manuscript volume, or a collection of receipts for the preparation of drugs, and nothing more. According to the definition here, Maya codices such as the Dresden codex (not in book form) are not codices; a modern perfect-bound book is. Both untrue.

A stab at a definition following sources and including the Maya, Ethiopian, etc. codices would be something like: "a handwritten manuscript divided into pages, as distinct from a continuous scroll; the pages are usually bound into the form of a book, but may be folded in accordion folds as, for example, the Dresden Codex." I don't think that quires, stitching, or a cover are necessary for a volume to be a codex. Pol098 (talk) 15:56, 29 May 2012 (UTC)
 * First, "handwritten manuscript" is like saying "frozen ice". Second, pages are one side of a leaf; each leaf consists of two pages. The fundamental definition of codex is that there is folding, and often binding, as opposed to a scroll. I'm surprised by the OED's handling of the word; Wiktionary does a better job (http://en.wiktionary.org/wiki/codex). See also the Online Dictionary for Library and Information Science (http://www.abc-clio.com/ODLIS/odlis_C.aspx?#codex). —Diiscool (talk) 19:48, 29 May 2012 (UTC)
 * News to me—I thought authors prepared their manuscripts on computers nowadays, even typewriters being abandoned. Anyway, seriously, my alternative is no more than a starting suggestion. I'm not sure of the exact definition of a codex (is there an agreed one?); couldn't you make a codex of cut, but not folded sheets? Are there any books handwritten on single unfolded sheets of parchment sewn together? I have no idea. My point is that what passes for a definition in the article is nonsense (and unsourced); I won't make any claims for my proposal (which is why I didn't put it in the article). My "divided into" pages (or leaves or sheets) is pretty bad too. BTW, I agree that the OED is pretty bad—I had sent them an email to that effect before seeing above comments; their definition doesn't exclude a scroll (according to the OED a volume can be a scroll). Pol098 (talk) 20:29, 29 May 2012 (UTC)
 * I would call that a typescript but I know that people do refer to typescripts as manuscripts. You could certainly make a codex out of cut, not folded sheets. That's how most modern paperbacks—and even some hardbacks—are made unless they are very high quality in which case they might have sewn quires. I think we need to look at some more reliable sources in the field of book history. —Diiscool (talk) 21:28, 29 May 2012 (UTC)
 * Does a modern, printed book count as a codex? I don't know the answer; possibly authorities will disagree. I was relying on the OED which specified manuscript (which I interpret as being holograph, or at least not mass-printed). BTW, manuscript in the modern sense is not a synonym of typescript (nor is typescript a subset of manuscripts); it's the original version of a written work, which a typescript need not be. Getting this article right is a matter of finding sources. We might find several sources meeting the criteria for reliability with contradictory definitions. Pol098 (talk) 08:05, 30 May 2012 (UTC)

As there doesn't seem to be much interest in this, or intervention by an expert, I'll edit the article's introduction. Pol098 (talk) 17:29, 1 June 2012 (UTC)

 * Codex may be like some other technical words, which beside their narrow technical meaning also have acquired a wider popular meaning. Abvgd (talk) 17:19, 30 October 2012 (UTC)
 * The potential problem that I see with the above definition is that it might leave an important development in the history of writing without its own dedicated term by giving undue weight to the geometric shape over book-binding technique and reading style. The random-access format of the Roman codex was the most important characteristic, as this made possible pagination and with it tables of contents, chapters, etc. This all in turn changed the nature of reading itself. Are Maya codices random-access codices? It seems to me that they are sequential just as scrolls are? If so, that difference should be underlined in the introductory section. Maybe the best solution would be to keep the current use of 'codex' to denote handwritten historical manuscripts of a book-like format but to use a more detailed term like "codex format" or "codex book format" to specifically denote the random access book-binding format as developed by the Romans? Such a distinction would acknowledge the subsequent spread of the word 'codex' to include any handwritten rectangular-shape manuscripts, but it would also retain the original and technically more rigorous definition, which is of significant historical importance for the development of the modern book. Abvgd (talk) 19:25, 30 October 2012 (UTC)

Systemic bias
Should we point out somewhere that this article discusses codices in western civilization rather than, for instance, east Asia? Stating that the scroll was extinct by the sixth century is obviously wrong when discussing non-western culture. Hijiri 88 ( 聖やや ) 08:18, 9 December 2015 (UTC)

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Lead
I'm not happy with the sentence "The book is usually bound by stacking the pages and fixing one edge to a spine...". Until the invention of modern glues and perfect binding there was no way to hold the edges to the spine. All books, even early paperbacks, had their sheets assembled into quires or sections and sewn through the middle. Can someone who is knowledgeable about ancient books (and who, unlike me, has access to sources) please sort this out? Thanks. Martin of Sheffield (talk) 08:38, 18 July 2020 (UTC)
 * Indeed. Sorted - talk of spines is unhelpful & not needed here. Johnbod (talk) 14:08, 18 July 2020 (UTC)
 * Agreed that spines don't help, but it still talked about attaching the edges. I've changed it, but feel free to improve! Martin of Sheffield (talk) 17:36, 18 July 2020 (UTC)
 * Hi Johnbod. It's not "one set of edges", but the middle of the quire to form the signature.  Sort of <<<< rather than //// if that helps. Martin of Sheffield (talk) 17:57, 18 July 2020 (UTC)
 * Sometimes, but not always. Depends on the type of binding, which we don't need to go into here. Johnbod (talk) 20:15, 18 July 2020 (UTC)

IP Address
Their are those that are the beginning to the one that is going to the place. — Preceding unsigned comment added by 174.128.176.116 (talk) 00:14, 3 January 2021 (UTC)

Inconsistent definition of codex
In the lede: The codex (plural codices /ˈkoʊdɪsiːz/) was the historical ancestor of the modern book. Instead of being composed of sheets of paper, it used sheets of vellum, papyrus, or other materials.

In Etymology and origins: Technically, even modern paperbacks are codices, ...

Clearly, the use of the word "instead" in the lede is not consistent with the sentence in Etymology, since paperbacks are made of, well, paper.

This article seems to get hung up on Aristotelian concepts of substance and accidentals. All of the historical objects discussed have the substance of a book ... recording of information, etc. Some of the accidentals are different, which does not change their bookish nature. Which accidental distinguishes the codex from any other form of "book"? Is it the structure (sheets vs roll) or the material (paper vs animal skin vs papyrus). I believe from the references given that the main difference is in the format being sheets of writing material, not the material itself.

If this is correct, the sentence in the lede could be changed to:  The codex (plural codices /ˈkoʊdɪsiːz/) was the historical ancestor of the modern book. It commonly consisted of sheets of vellum, papyrus, or other materials. And if we don't know for sure, then we should remove the "Instead" anyway, since it's being presented as a fact. •Bobsd• (talk) 17:52, 15 October 2022 (UTC)

 * Clearly, I have to read the talk pages before adding a new section ... old news with no probable solution. •Bobsd•  (talk) 18:14, 15 October 2022 (UTC)

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

title: Talk:Codex


text:
Conjecture

In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis (still a conjecture) or Fermat's Last Theorem (a conjecture until proven in 1995 by Andrew Wiles), have shaped much of mathematical history as new areas of mathematics are developed in order to prove them.

Proof
Formal mathematics is based on provable truth. In mathematics, any number of cases supporting a universally quantified conjecture, no matter how large, is insufficient for establishing the conjecture's veracity, since a single counterexample could immediately bring down the conjecture. Mathematical journals sometimes publish the minor results of research teams having extended the search for a counterexample farther than previously done. For instance, the Collatz conjecture, which concerns whether or not certain sequences of integers terminate, has been tested for all integers up to 1.2 × 1012 (over a trillion). However, the failure to find a counterexample after extensive search does not constitute a proof that the conjecture is true—because the conjecture might be false but with a very large minimal counterexample.

Nevertheless, mathematicians often regard a conjecture as strongly supported by evidence even though not yet proved. That evidence may be of various kinds, such as verification of consequences of it or strong interconnections with known results.

A conjecture is considered proven only when it has been shown that it is logically impossible for it to be false. There are various methods of doing so; see methods of mathematical proof for more details.

One method of proof, applicable when there are only a finite number of cases that could lead to counterexamples, is known as "brute force": in this approach, all possible cases are considered and shown not to give counterexamples. In some occasions, the number of cases is quite large, in which case a brute-force proof may require as a practical matter the use of a computer algorithm to check all the cases. For example, the validity of the 1976 and 1997 brute-force proofs of the four color theorem by computer was initially doubted, but was eventually confirmed in 2005 by theorem-proving software.

When a conjecture has been proven, it is no longer a conjecture but a theorem. Many important theorems were once conjectures, such as the Geometrization theorem (which resolved the Poincaré conjecture), Fermat's Last Theorem, and others.

Disproof
Conjectures disproven through counterexample are sometimes referred to as false conjectures (cf. the Pólya conjecture and Euler's sum of powers conjecture). In the case of the latter, the first counterexample found for the n=4 case involved numbers in the millions, although it has been subsequently found that the minimal counterexample is actually smaller.

Independent conjectures
Not every conjecture ends up being proven true or false. The continuum hypothesis, which tries to ascertain the relative cardinality of certain infinite sets, was eventually shown to be independent from the generally accepted set of Zermelo–Fraenkel axioms of set theory. It is therefore possible to adopt this statement, or its negation, as a new axiom in a consistent manner (much as Euclid's parallel postulate can be taken either as true or false in an axiomatic system for geometry).

In this case, if a proof uses this statement, researchers will often look for a new proof that does not require the hypothesis (in the same way that it is desirable that statements in Euclidean geometry be proved using only the axioms of neutral geometry, i.e. without the parallel postulate). The one major exception to this in practice is the axiom of choice, as the majority of researchers usually do not worry whether a result requires it—unless they are studying this axiom in particular.

Conditional proofs
Sometimes, a conjecture is called a hypothesis when it is used frequently and repeatedly as an assumption in proofs of other results. For example, the Riemann hypothesis is a conjecture from number theory that — amongst other things — makes predictions about the distribution of prime numbers. Few number theorists doubt that the Riemann hypothesis is true. In fact, in anticipation of its eventual proof, some have even proceeded to develop further proofs which are contingent on the truth of this conjecture. These are called conditional proofs: the conjectures assumed appear in the hypotheses of the theorem, for the time being.

These "proofs", however, would fall apart if it turned out that the hypothesis was false, so there is considerable interest in verifying the truth or falsity of conjectures of this type.

Fermat's Last Theorem
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers $$a$$, $$b$$, and $$c$$ can satisfy the equation $$a^n + b^n = c^n$$ for any integer value of $$n$$ greater than two.

This theorem was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of Arithmetica, where he claimed that he had a proof that was too large to fit in the margin. The first successful proof was released in 1994 by Andrew Wiles, and formally published in 1995, after 358 years of effort by mathematicians. The unsolved problem stimulated the development of algebraic number theory in the 19th century, and the proof of the modularity theorem in the 20th century. It is among the most notable theorems in the history of mathematics, and prior to its proof it was in the Guinness Book of World Records for "most difficult mathematical problems".

Four color theorem

In mathematics, the four color theorem, or the four color map theorem, states that given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map—so that no two adjacent regions have the same color. Two regions are called adjacent if they share a common boundary that is not a corner, where corners are the points shared by three or more regions. For example, in the map of the United States of America, Utah and Arizona are adjacent, but Utah and New Mexico, which only share a point that also belongs to Arizona and Colorado, are not.

Möbius mentioned the problem in his lectures as early as 1840. The conjecture was first proposed on October 23, 1852 when Francis Guthrie, while trying to color the map of counties of England, noticed that only four different colors were needed. The five color theorem, which has a short elementary proof, states that five colors suffice to color a map and was proven in the late 19th century; however, proving that four colors suffice turned out to be significantly harder. A number of false proofs and false counterexamples have appeared since the first statement of the four color theorem in 1852.

The four color theorem was ultimately proven in 1976 by Kenneth Appel and Wolfgang Haken. It was the first major theorem to be proved using a computer. Appel and Haken's approach started by showing that there is a particular set of 1,936 maps, each of which cannot be part of a smallest-sized counterexample to the four color theorem (i.e., if they did appear, one could make a smaller counter-example). Appel and Haken used a special-purpose computer program to confirm that each of these maps had this property. Additionally, any map that could potentially be a counterexample must have a portion that looks like one of these 1,936 maps. Showing this with hundreds of pages of hand analysis, Appel and Haken concluded that no smallest counterexample exists because any must contain, yet do not contain, one of these 1,936 maps. This contradiction means there are no counterexamples at all and that the theorem is therefore true. Initially, their proof was not accepted by mathematicians at all because the computer-assisted proof was infeasible for a human to check by hand. However, the proof has since then gained wider acceptance, although doubts still remain.

Hauptvermutung
The Hauptvermutung (German for main conjecture) of geometric topology is the conjecture that any two triangulations of a triangulable space have a common refinement, a single triangulation that is a subdivision of both of them. It was originally formulated in 1908, by Steinitz and Tietze.

This conjecture is now known to be false. The non-manifold version was disproved by John Milnor in 1961 using Reidemeister torsion.

The manifold version is true in dimensions m ≤ 3. The cases m = 2 and 3 were proved by Tibor Radó and Edwin E. Moise in the 1920s and 1950s, respectively.

Weil conjectures
In mathematics, the Weil conjectures were some highly influential proposals by on the generating functions (known as local zeta-functions) derived from counting the number of points on algebraic varieties over finite fields.

A variety V over a finite field with q elements has a finite number of rational points, as well as points over every finite field with qk elements containing that field. The generating function has coefficients derived from the numbers Nk of points over the (essentially unique) field with qk elements.

Weil conjectured that such zeta-functions should be rational functions, should satisfy a form of functional equation, and should have their zeroes in restricted places. The last two parts were quite consciously modeled on the Riemann zeta function and Riemann hypothesis. The rationality was proved by, the functional equation by , and the analogue of the Riemann hypothesis was proved by.

Poincaré conjecture
In mathematics, the Poincaré conjecture is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space. The conjecture states that: "Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere." An equivalent form of the conjecture involves a coarser form of equivalence than homeomorphism called homotopy equivalence: if a 3-manifold is homotopy equivalent to the 3-sphere, then it is necessarily homeomorphic to it.

Originally conjectured by Henri Poincaré in 1904, the theorem concerns a space that locally looks like ordinary three-dimensional space but is connected, finite in size, and lacks any boundary (a closed 3-manifold). The Poincaré conjecture claims that if such a space has the additional property that each loop in the space can be continuously tightened to a point, then it is necessarily a three-dimensional sphere. An analogous result has been known in higher dimensions for some time.

After nearly a century of effort by mathematicians, Grigori Perelman presented a proof of the conjecture in three papers made available in 2002 and 2003 on arXiv. The proof followed on from the program of Richard S. Hamilton to use the Ricci flow to attempt to solve the problem. Hamilton later introduced a modification of the standard Ricci flow, called Ricci flow with surgery to systematically excise singular regions as they develop, in a controlled way, but was unable to prove this method "converged" in three dimensions. Perelman completed this portion of the proof. Several teams of mathematicians have verified that Perelman's proof is correct.

The Poincaré conjecture, before being proven, was one of the most important open questions in topology.

Riemann hypothesis
In mathematics, the Riemann hypothesis, proposed by, is a conjecture that the non-trivial zeros of the Riemann zeta function all have real part 1/2. The name is also used for some closely related analogues, such as the Riemann hypothesis for curves over finite fields.

The Riemann hypothesis implies results about the distribution of prime numbers. Along with suitable generalizations, some mathematicians consider it the most important unresolved problem in pure mathematics. The Riemann hypothesis, along with the Goldbach conjecture, is part of Hilbert's eighth problem in David Hilbert's list of 23 unsolved problems; it is also one of the Clay Mathematics Institute Millennium Prize Problems.

P versus NP problem
The P versus NP problem is a major unsolved problem in computer science. Informally, it asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer; it is widely conjectured that the answer is no. It was essentially first mentioned in a 1956 letter written by Kurt Gödel to John von Neumann. Gödel asked whether a certain NP-complete problem could be solved in quadratic or linear time. The precise statement of the P=NP problem was introduced in 1971 by Stephen Cook in his seminal paper "The complexity of theorem proving procedures" and is considered by many to be the most important open problem in the field. It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute to carry a US$1,000,000 prize for the first correct solution.

Other conjectures

 * Goldbach's conjecture
 * The twin prime conjecture
 * The Collatz conjecture
 * The Manin conjecture
 * The Maldacena conjecture
 * The Euler conjecture, proposed by Euler in the 18th century but for which counterexamples for a number of exponents (starting with n=4) were found beginning in the mid 20th century
 * The Hardy-Littlewood conjectures are a pair of conjectures concerning the distribution of prime numbers, the first of which expands upon the aforementioned twin prime conjecture. Neither one has either been proven or disproven, but it has been proven that both cannot simultaneously be true (i.e., at least one must be false). It has not been proven which one is false, but it is widely believed that the first conjecture is true and the second one is false.
 * The Langlands program is a far-reaching web of these ideas of 'unifying conjectures' that link different subfields of mathematics (e.g. between number theory and representation theory of Lie groups). Some of these conjectures have since been proved.

In other sciences
Karl Popper pioneered the use of the term "conjecture" in scientific philosophy. Conjecture is related to hypothesis, which in science refers to a testable conjecture.

title: Conjecture


text:
Christoph Ludwig Agricola

Christoph Ludwig Agricola (5 November 1665 – 8 August 1724) was a German landscape painter and etcher. He was born and died at Regensburg (Ratisbon).

Life and career
Christoph Ludwig Agricola was born on 5 November 1665 at Regensburg in Germany. He trained, as many painters of the period did, by studying nature.

He spent a great part of his life in travel, visiting England, the Netherlands and France, and residing for a considerable period at Naples, where he may have been influenced by Nicolas Poussin. He also stayed for some years circa 1712 in Venice, where he painted many works for the patron Zaccaria Sagredo.

He died in Regensburg in 1724.

Work
Although he primarily worked in gouache and oils, documentary sources reveal that he also produced a small number of etchings. He was a good draughtsman, used warm lighting and exhibited a warm, masterly brushstroke.

His numerous landscapes, chiefly cabinet pictures, are remarkable for fidelity to nature, and especially for their skilful representation of varied phases of climate, especially nocturnal scenes and weather anomalies such as thunderstorms. In composition his style shows the influence of Nicolas Poussin and his work often displays the idealistic scenes associated with Poussin. In light and colour he imitates Claude Lorrain. His compositions include ruins of ancient buildings in the foreground, but his favourite figure for the foreground was men dressed in Oriental attire. He also produced a series of etchings of birds.

His pictures can be found in Dresden, Braunschweig, Vienna, Florence, Naples and many other towns of both Germany and Italy.

Legacy
He probably tutored the artist, Johann Theile, and had an enormous influence on him. Art historians have also noted that the work of the landscape painter, Christian Johann Bendeler (1699–1728), was also influenced by Agricola.

title: Christoph Ludwig Agricola