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Smothered mate

In chess, a smothered mate is a checkmate delivered by a knight in which the mated king is unable to move because it is completely surrounded (or smothered) by its own pieces, which a knight can jump over.

The mate is usually seen in a corner of the board, since only three pieces are needed to surround the king there, less than anywhere else. The most common form of smothered mate is seen in the adjacent diagram. The knight on f7 delivers mate to the king on h8, which is prevented from escaping the check by the rook on g8 and the pawns on g7 and h7. Similarly, White can be mated with the white king on h1 and the knight on f2. Analogous mates on a1 and a8 are rarer because castling is more common than  castling and brings the king closer to the corner.

Methods
For a smothered mate to occur in a game, it is usually necessary to sacrifice to compel pieces to smother the king – a player is unlikely to voluntarily surround their king with pieces in a way that makes a smothered mate possible.

Philidor's mate
Philidor's mate, also known as Philidor's legacy, is a checkmating pattern that ends in smothered mate. This method involves checking with the knight forcing the king out of the corner of the board, moving the knight away to deliver a double check from the queen and knight, sacrificing the queen to force the rook next to the king, and mating with the knight.

The technique is named after François-André Danican Philidor; this is something of a misnomer, however, as it is earlier described in Luis Ramirez Lucena's 1497 text on chess, Repetición de Amores e Arte de Axedrez, which predates Philidor by several hundred years.

An example is to be found in the game Jan Timman–Nigel Short at the 1990 Tilburg tournament. From the diagrammed position, play continued '''27. Nf7+ Kg8 28. Nh6+ Kh8 29. Qg8+ Rxg8 30. Nf7#'''. (Note that White would force mate even if his rook, and pawn on e7, were removed from the board, and Black had a knight on f6. In that case, 27.Nf7+ Kg8 28.Nh6+ Kh8 [28...Kf8 29.Qf7#] 29.Qg8+ Nxg8 [or 29...Rxg8] 30.Nf7 still mates.)

Opening traps
Occasionally, a smothered mate may be possible in the opening of a game. One of the most famous, and most frequently occurring, is in the Budapest Gambit. It arises after '''1. d4 Nf6 2. c4 e5 3. dxe5 Ng4 4. Bf4 Nc6 5. Nf3 Bb4+ 6. Nbd2 Qe7 7. a3 Ngxe5 8. axb4?? Nd3#''' (see diagram). Note that the knight cannot be taken because the pawn on e2 is pinned to the white king by the black queen on e7.

Another notorious example is the so-called "Blackburne Shilling Gambit" (named after the 19th-century English player Joseph Henry Blackburne, supposedly because he used it to win shillings from amateurs). It goes: '''1. e4 e5 2. Nf3 Nc6 3. Bc4 Nd4?! 4. Nxe5!? Qg5! 5. Nxf7?? Qxg2 6. Rf1 Qxe4+ 7. Be2 Nf3#''' (see diagram). There is also a well-known trap in the Caro–Kann Defence: '''1. e4 c6 2. d4 d5 3. Nc3 dxe4 4. Nxe4 Nd7 5. Qe2!? Ngf6?? 6. Nd6#'''. This trap has occurred in many games, perhaps the earliest recorded example being Alekhine–Four Amateurs, simultaneous exhibition, Palma de Mallorca 1935.

Examples from games
An example of a similar smothered mate in master-level play is the game Edward Lasker–Israel Horowitz, New York City 1946, which went: '''1. d4 Nf6 2. Nf3 d5 3. e3 c5 4. c4 cxd4 5. Nxd4 e5 6. Nf3 Nc6 7. Nc3 d4 8. exd4 exd4 9. Nb5 Bb4+ 10. Bd2 0-0 11. Bxb4 Nxb4 12. Nbxd4 Qa5 13. Nd2 Qe5+ 14. Ne2 Nd3#'''.

Another example is the game Unzicker–Sarapu, Siegen Olympiad 1970: '''1. e4 c5 2. Nf3 Nf6 3. e5 Nd5 4. Nc3 e6 5. Nxd5 exd5 6. d4 Nc6 7. dxc5 Bxc5 8. Qxd5 Qb6 9. Bc4 Bxf2+ 10. Ke2 0-0 11. Rf1 Bc5 12. Ng5 Nd4+ 13. Kd1 Ne6 14. Ne4 d6 15. exd6 Bxd6?? 16. Nxd6 Rd8 17. Bf4! Nxf4? 18. Qxf7+ Kh8 19. Qg8+!''' Sarapu now resigned in light of 19...Rxg8 20.Nf7#.

title: Smothered mate


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Cristino García

Cristino García Granda (3 June 1913 – 21 February 1946) was a fighter with the French Resistance in France during World War II. He was born in Gozón, Asturias, Spain and was executed by the Francoist regime.

He took part in the Spanish Civil War as a member of the, a special unit of the Spanish Republican Army which performed attacks behind the Nationalist lines.

After the war, he escaped to France where he was part of the French Resistance as a member of the Agrupación de Guerrilleros Españoles (AGE, Spanish Guerilla Group). Highly successful in fighting the German occupiers (he took part in the Battle of Madeleine and in the attack of the prison in Nîmes), at the end of the war, he returned to Spain to work with Resistance groups (Spanish Maquis) to oust caudillo Francisco Franco. Captured on 15 October 1945, he was tortured and was executed by firing squad on 21 February 1946.

In Paris, the rue Cristino Garcia in Saint-Denis, next to the street of Émile Zola and the Joffre avenue in the 20th arrondissement, was named for him. The Quartier Cristino Garcia in Aubervilliers, Île-de-France, was also named after him.

He is buried in the Cementerio de Carabanchel, southwest of Madrid.

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

title: Cristino García


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Joan Sebastian

José Manuel Figueroa Sr. (April 8, 1951 – July 13, 2015), known professionally as Joan Sebastian, was a Mexican singer and songwriter. Born in Juliantla, Guerrero, he composed more than 1,000 songs, including compositions for artists such as Bronco, Vicente Fernández, Lucero, Pepe Aguilar, and Rocío Dúrcal. The first several years of his career were primarily focused on Soft rock and Latin pop songs, but later focused primarily on regional Mexican music, specifically banda, mariachi, and norteño. Throughout his career, he also recorded various country songs in Spanish. Sebastian was awarded seven Latin Grammy Awards and five Grammy Awards, making him the most awarded Mexican performer in Grammy history.

Known for composing "Así es la Vida", Sebastian also worked sporadically as an actor. In 1996, he made his acting debut in the Mexican soap opera Tú y Yo (You and I), sharing credits with Maribel Guardia, his former wife and mother to his son, Julian. In 2015, Sebastian died at the age of 64 of bone cancer. At the time of his death, Sebastian had two number-one albums on the Billboard Top Latin Albums chart and seven top ten songs on the Hot Latin Songs chart in the United States, including "Eso Y Más", "Me Gustas", "Secreto de Amor", and "Más Allá del Sol".

Early life
Joan Sebastian was born in the rural town of Juliantla in Guerrero. He began composing at the age of seven. His mother enrolled him in a school near Guanajuato when he was eight years old, and returned to his hometown three years later.

At age fourteen, his father sent him away to a monastery in Morelos where he was under the care of Father David Salgado. Due to the clergyman's influence on Sebastian, he considered becoming a priest. He enrolled in the Seminario Conciliar de San José in Cuernavaca, Morelos, but realized that he wanted to pursue a music career, and decided to leave the seminary to dedicate himself to music.

Career
Before embarking on a singing career, Sebastian was an administrative assistant at a vacation resort in Oaxtepec, Morelos, where he would sing through the intercom. In 1968, Sebastian met Mexican actress Angelica Maria. They stayed together and she asked him to sing some songs for her. She suggested to Sebastian that he record the songs and give them to music producer Eduardo Magallanes, though Sebastian never managed to contact him. He later moved to Mexico City and began asking Discos Capitals Records to listen to his music and produce it. In 1974, he recorded his first album, Pedro Parrandas, and received positive feedback from the public.

In 1977, Sebastian decided to stop using his legal name, Jose Manuel Figueroa and took on his artistic name, Joan Sebastian, partly in tribute to San Sebastian, where he previously worked. That same year, he signed a record deal with the label Musart. Later on he would make his known hit "Juliantla" and the famous duet "Maracas" with Alberto Vazquéz. In 2000, he released Secreto de Amor which was certified 4× platinum in the Latin field in the United States by the Recording Industry Association of America (RIAA). The album and title track won the Lo Nuestro Awards for Regional Mexican Album of the Year and Regional Mexican Song of the Year; he also received the Excellence Award for his musical contributions.

In 2006, Sebastian was inducted into the Billboard Latin Music Hall of Fame for his prolific songwriting and musical arrangements. Sebastian was awarded Songwriter of the Year three times by ASCAP and received the Golden Note Award in 2007 in recognition of his songwriting career.

In 2012, Joan Sebastian teamed up with American songwriter and producer Will.i.am for the song and video "Hey You."

Personal life
Sebastian had eight children from five different women. Their names are José Manuel Figueroa González (who is also a singer and composer), Juan Sebastián Figueroa González, Trigo de Jesús Figueroa González (first three children with Teresa González, his first wife), Zarelea Figueroa Ocampo (who is also a singer and composer), Julián Figueroa Fernández (son of Maribel Guardia, who was a singer and left behind a son with Imelda Tuñon), Joana Marcelia Figueroa Espín, Juliana Joeri Figueroa Alonso and D'Yavé Figueroa Espín. His third oldest son, Trigo, was shot in the back of the head after one of Joan Sebastian's concerts in Mission, Texas on August 27, 2006. Trigo had been trying to control the crowd after the show. He was transported to McAllen Medical Center where he was pronounced dead.

On June 12, 2010, his second oldest son, Juan Sebastián was shot dead in Cuernavaca, Morelos, after arriving at a night club with some friends and being refused entrance. Joan Sebastian said his son's death had nothing to do with the Mexican drug cartels.

A few months after his death Televisa announced that a series about his life would begin filming. His youngest son, Julian Figueroa, portrayed his father in his younger days while his older son, José Manuel Figueroa, portrayed his father in his later days. Livia Brito was also confirmed to portray Maribel Guardia. The series Por Siempre Joan Sebastian premiered on June 27, 2016 on Univision and concluded on July 25, 2016.

Illness and death
Sebastian was first diagnosed with bone cancer in 1999. He underwent cancer treatment and survived; however, he announced that the cancer had returned in 2007. Undergoing cancer treatment once again, he later announced he was in remission. On July 26, 2012, during one of his concerts, he announced that the cancer had returned for the third time. In 2014, he revealed that he was battling cancer for the fourth time during his performances in Zacatecas.

Weeks prior to his death, he confirmed to the media that he had been hospitalized and undergoing cancer treatment under medical supervision. On July 13, 2015, Joan Sebastian died at 7:15pm (UTC-06:00) at his ranch Cruz de la Sierra, Teacalco Guerrero, Mexico, due to bone cancer. He was 64 years old. His body was buried in a cemetery in Juliantla near his son Trigo.

Relatives of the late singer complained in July 2020 that Sebastian's mausoleum had been broken into and the family feared that his remains might be stolen. Security measures were increased.

Discography
Sebastian recorded the following studio albums during his music career:

Studio albums
• Mi Mujer (1975) (first album on Musart)

• Y Las Mariposas (1977)

• Con Mariachi Vargas de Tecalitlan (1984)

• Rumores (1985)

• Oiga (1986)

• Mascarada (1987)

• Norteño (1988)

• Cariño Como Tú (1990)

• Norteño Vol. 2 (1990)

• Bandido de Amores (1992)

• El Peor de Tus Antojos (1993)

• En Vivo En La Mexico (1995)

• Con Mariachi (1996)

• Tu y Yo (1996)

• Gracias Por Tanto Amor (1998)

• Rey del Jaripeo (1999)

• Nostalgia y Recuerdos (2000)

• Secreto de Amor (2000)

• En Vivo: Desde la Plaza El Progreso en Guadalajara (2001)

• Afortunado (2002)

• Lo Dijo el Corazón (2003)

• Mujeres Bonitas (2003)

• Que Amarren a Cupido (2004)

• Inventario (2005)

• Canta Para Ti (2006)

• De Relajo y Pa' Bailar (2006)

• Más Allá del Sol (2006)

• No Es de Madera (2007)

• Pegadito al Corazón (2009) (last album on Musart & first album on Fonovisa)

• Joan Sebastian En Vivo (2009)

• Huevos Rancheros (2011)

• Un Lujo (2012)

• 13 Celebrando el 13 (2013)

•  Corridos con Banda (2013)

• Celedon Sin Fronteras 2 (2014)

• El Ultimo Jaripeo (2017)

• Atemporal (2020)

title: Joan Sebastian


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Metrophanes of Byzantium

Saint Metrophanes (Greek: Μητροφάνης; died 326) was the bishop of Byzantium from 306 to 314. He may have retired from his episcopacy and died as late as 326.

There is a tradition that, before his death, the Emperor Constantine I bestowed upon him the honorary title of Patriarch; however, Byzantium did not become the capital of the Empire until 330 (when it was renamed New Rome or Constantinople), and the see was not elevated to a patriarchate until 451. Metrophanes I could not partake in the first Ecumenical Council, which was held at Nicaea, due to age and ill health (he was already bedridden). He sent instead Alexander, the first among his presbyters, an honest man, whom he destined as his successor. For it is said that, when the Council had ended and the king with the god-bearing fathers returned, he was told by God that Alexander, and after him Paul, pleased God, and are good for this position.

Metrophanes has been canonized a saint, and is revered in both the Eastern Orthodox Church and the Roman Catholic Church. His feast day is June 4.

His predecessor as Bishop of Byzantium was Probus, son of Dometius, and Metrophanes may have been the son of Probus.

title: Metrophanes of Byzantium


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Sak Kʼukʼ

Sak Kʼukʼ also known as Muwaan Mat, Lady Sak Kʼukʼ and Lady Beastie (died 640), was queen of the Maya city-state of Palenque. She acceded to the throne in October, 612 and ruled until 615.

Biography
Her father was Janahb Pakal and her mother was Yohl Ikʼnal or unknown. As Janaab Pakal seems to have had no male heirs, she ascended to the throne on 19 October 612, a few months after her father's death. After his maturity, her son Kʼinich Janaab Pakal I succeeded her as ruler on 9.9.2.4.8 5 Lamat 1 Mol. She seems to have continued to wield considerable influence over Palenque in the early decades of her son's reign. For example, Sak Kʼukʼ is recorded on Pakal's sarcophagus lid as the ruler who celebrated the sealing of the Kʼatun on 9.10.0.0.0 (25 January 633 AD). She was probably mother of Ajen Yohl Mat.

title: Sak Kʼukʼ


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Talk:Gröbner basis

Untitled
If I'm not mistaken, this algorithm generalizes not only Euclid's algorithm but also Gaussian elimination and the simplex algorithm. I don't know enough about it to incorporate those topics into the article. Can someone do that? 128.101.13.104 02:15, 6 Nov 2003 (UTC)

I think you're mistaken about the simplex algorithm. I'm pretty sure that it is wasteful to do Gauss-Jordan elimination this way. In fact it seems to be like doing numerous eliminations in parallel.

Charles Matthews 09:26, 6 Nov 2003 (UTC)

I think the rewrite of the article has made it less accessible. For example, trying to give an exact characterisation of a GB in the opening sentence means that the technical density is immediately at a maximum.

Charles Matthews 11:13, 9 Jun 2004 (UTC)

About polynomial systems
The text implies that a polynomial system with finitely many solutions can be "solved" using the Gröbner basis. But if the system has zero solutions, then this technique won't always demonstrate that fact, right? Perhaps the article should say "If the system has a finite nonzero number of solutions..." or some such. I'd change it myself, but I'm a bit new to Gröbner bases, and would like some assurance that I'm right. Staecker 17:46, 25 Jun 2005 (UTC)
 * In fact, if there is no solution, then by the Nullstellensatz the polynomial 1 belongs to the ideal, and since its leading monomial is 1 and is the smallest element in every term order, the reduced minimal GB will be exactly {1}, so You would know. For the other thing, look up lexikographic order, FGLM (Jean C. Faugere is the F), RUR by Fabrice Rouillier, also called "geometric solution" in other contexts. A first result on finite numbers of solutions is that for each variable there has to be a polynomial in the GB with a pure power of said variable as leading monomial.--LutzL 14:28, 29 August 2005 (UTC)

Gröbner basis and Hironaka
''Copied from User talk:LutzL for possible use by others. --Lambiam Talk 14:49, 5 May 2006 (UTC) (Lambiam adressing LutzL:) Hi. Concerning your recent edit of Gröbner basis, I am not sure that Hironaka's theory of "standard bases" is exactly the same. See for example [http://lips.informatik.uni-leipzig.de/pub/showDoc.Fulltext/dokument.pdf?lang=de&doc=1995-18&format=pdf&compression=&rank=0 Joachim Apel, Division of entire functions by polynomial ideals, in ''Proc. AAECC 11,'' LNCS 948 (1995), pp. 82-95]. So if you agree but think the addition is nevertheless important, I propose that you change the text into something like: "In 1964, at almost the same time and independently, Heisuke Hironaka had developed a closely related theory, which he called standard bases." I'm not sure how close this is to your areas of expertise, but I you have interest, time and patience, perhaps you could also add some of this to the Hironaka article, putting it in context, and if possible cite the references as provided by Apel's paper. Cheerio. Lambiam Talk 13:46, 3 May 2006 (UTC)

 * As I understand it now, the standard bases are defined for ideals in the ring of Puisseux series. Thus they contain Gröbner bases as a special case. The real contribution of Buchberger to the fundamentals is the proof that his algorithm stops in finite time. Perhaps it should be mentioned somewhere that the idea comes from the non-constructive proof by Hilbert of the Basissatz (Kronecker had a constructive proof, but only formulated for bivariate polynomials) -- No, I'm not an expert in the whole of the topic of Gröbner bases. They are interesting to me in the aspect of their inefficiency. I got most of my knowledge from Gethgen/vonzur Gathen: Modern Algebra, where they mention H. Hironaka  in the second sentence of the introduction. And from M. Guisty: Bases standard, élimination et complexité, notes of a lecture given at X, where some propositions are attributed to Hironaka.--LutzL 07:29, 5 May 2006 (UTC)

I'm not an expert either and I don't have access to a library, so I wouldn't be comfortable making any changes of substance. I'll copy this exchange to the talk page of the article in the hope that a next reader can do something with it. --Lambiam Talk 14:43, 5 May 2006 (UTC)

Definition of Reduced Gröbner Bases
The definition of reduced bases didn't make sense. As it was written, it referred to the "ideal generated by the leading coefficient", which is always all of R. Therefore, the condition for a reduced basis could never be satisfied.

I changed "coefficient" to "term". Now at least it at least makes sense, although I don't have a reference to be sure whether it is correct. If anyone would care to look it up and check it that would be good. When I find a reference I will do so. Heatkernel 10:58, 8 May 2006 (UTC)

Example of Groebner basis
Hello. I am aware that a Groebner basis, in general, may be tremendously verbose. Even so I wonder if we can give some kind of example. A set of examples which shows the increasingly verbose Groebner bases for a progression of simple problems would be terrific. 207.174.201.18 21:15, 23 June 2006 (UTC)

 * I have just produced what I think is a relatively simple example and counterexample for the Dutch Wikipedia. Feel free to verify and copy that.--Lieven Smits (talk) 09:21, 9 April 2014 (UTC)

 * Update: I have tried a quick translation of my own Dutch text but I would appreciate it if someone could check its content and style.--Lieven Smits (talk) 21:08, 9 April 2014 (UTC)
 * Thanks for adding this example. Its formatting deserves some improvement; I'll do this later, if it will not be done before by another editor (just now I have not too much time for WP). Some hints for further improvements:
 * It could be useful to show the difference if lexicographical ordering is replaced by a degree ordering.
 * Gaussian elimination and Euclid's algorithm for polynomials are special instances of Gröbner basis computation, which deserve to appear in the example section.
 * D.Lazard (talk) 09:00, 10 April 2014 (UTC)

Solving equations
Solving equations is the elementary application which, from my point of view, motivates the theory. The formulas, { f1[x1, ..., xn] = a1, ..., fm[x1, ..., xn] = am} and g(xn) = b, can be simplified into {f1[x1, ..., xn] = 0, ..., fm[x1, ..., xn] = 0} and g(xn) = 0. For example a circle cutting a straight line: x2+y2−4 = y−1 = 0. You do not need to understand ideals in order to understand the problem of solving systems of equations with several unknowns. Bo Jacoby 08:17, 8 August 2007 (UTC).
 * Hi Bo, nice to see You again. And now, what was the point? The main application of GB, as it is my experience, is to prove structural theorems in algebraic geometry. Such as estimates on the Hilbert polynomial, number of rational points etc. Your point is valid, but the number of solvable systems is rather small.--LutzL 06:45, 9 August 2007 (UTC)

Thanks LutzL! Regarding Gröbner bases I am a pupil and not a teacher. I may have got it wrong. I was looking for methods for solving algebraic equations in several unknowns. It is a practical and elementary problem. If the system of equations is fm[xn] = 0, where each fm is a polynomial in the variables xn, then any polynomial, p, in the ideal spanned by the fm makes an equation p[xn] = 0. Elimination of variables is construction of a system of algebraic equations, pn[xn] = 0, each in one unknown. Algebraic equations in one unknown can be solved numerically by the Durand-Kerner method, and so we are done. Am I on the track? Bo Jacoby 14:51, 9 August 2007 (UTC).

Earliest examples
An IP hinted at a paper "Les Invariants des formes binaires" in Jour. Des Mathematiques Pure and Applique'es, (1900), se'rie 5/ T 6, pp 141-156.", which is available from a digitisation project site (PDF). There exists an english translation at a Gröbner bibliography project (PDF) which claims it as an early example of a computed Gröbner basis. Perhaps someone might include in in the article.--LutzL (talk) 09:37, 6 December 2007 (UTC)

Examples please
I wish this article had some examples. I was not able to get a clue about what was going on even though I know what a polynomial ring is and I know what an ideal is. —Mark Dominus (talk) 14:58, 12 October 2011 (UTC)

 * Rather than add an example, I added an intuitive description. If you still think that is insufficient, please say so. Simplex (talk) 15:02, 21 March 2013 (UTC)

 * See above under "Example of Groebner basis"--Lieven Smits (talk) 21:09, 9 April 2014 (UTC)

Info from the Russian Wikipedia
Their article differs substantially from ours. We could improve ours by using information from theirs. Here is the Google Translation of http://ru.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B5_%D0%BC%D0%BD%D0%BE%D0%B3%D0%BE%D0%BE%D0%B1%D1%80%D0%B0%D0%B7%D0%B8%D0%B5:

röbner basis of some ideal I of the algebra of polynomials K [x_1, \ ldots, x_n] concerning the order of " \ Prec "On monomials - is a finite set of polynomials G K [x_1, \ ldots, x_n] such that the highest (relative \ Prec ) Member of each polynomial of I divided by a senior member of at least one polynomial of G. The order \ Prec must be complete and in addition to the following two conditions:

Multiplicativity: x ^ a \ prec x ^ b entails x ^ {a + c} \ prec x ^ {b + c}. Minimum unit: 1 \ prec x ^ a For a> 0.

Content

1 Types of Gröbner 1.1 Minimum Gröbner 1.2 The reduced Gröbner 2 Algorithms for constructing 3 Applications 4 History 5 Notes 6 Links

Types of Gröbner Minimum Gröbner

Minimal Gröbner basis of a polynomial ideal I is called its Gröbner G, such that:

Coefficient of the leading monomial of each p \ in G equal to one. Each leading monomial p \ in G is the leading monomial of any other q \ in \ {G \ setminus {p} \}

The reduced Gröbner

Reduced Gröbner basis of a polynomial ideal I is called its Gröbner G, such that:

Coefficient of the leading monomial of each p \ in G equal to one. Each leading monomial p \ in G not divisible by the leading monomial one other elements of the basis.

For the reduced Gröbner basis of the ideal we have the following statement:

Let I - polynomial ideal, and given a monomial ordering. Then there is a unique reduced Gröbner basis of the ideal I. Algorithms for constructing

The earliest construction algorithm reduced Gröbner basis of the ideal is Buchberger algorithm. Interestingly, the well-known Gaussian elimination for solving systems of linear equations is a special case of the Buchberger algorithm.

In addition, the French mathematician Jean-Charles Fougeres proposed algorithms F4 and F5 finding Gröbner basis. Applications

Gröbner basis is the most important concept of computer algebra, algebraic geometry and computational commutative algebra. History

Austrian mathematician Wolfgang Graebner developed the theory of standard bases for the free commutative case in the early 30's, and published it in 1950, [1] where he wrote: '

I started using this method 17 years ago for a variety of examples, including the very complex. The original text (in German) [показать] '

In 1964 a similar concept for the local rings was developed Heysuki Hironaka, received Fildovskuyu Prize in 1970. He introduced a system of polynomials called the standard basis.

The concept of Gröbner basis was introduced in 1965 an Austrian mathematician Bruno Buchberger, a former student of Graebner. Buchberger proposed a constructive procedure for constructing Gröbner basis in the form of efficient computer algorithm, which was later called Buchberger algorithm.

The existence of a standard basis of the ideal is based on the "lemma of composition", which was first proved for the most complex of the known cases (free Lie ) A. Shirshov. [2] The correct similar result for the free associative and commutative case was considered obvious and did not attract much attention until later works LI bokuto on the theory of attachment in the body of associative rings and rings with specified properties. In 1972 L. I. Bokut published "lemma Shirshov's Song" for the free associative case the notes of a course on associative algebras Novosibirsk University. From this and oral communication, it became known to American algebraist J. Bergman, who published it in 1979 under the name of «Diamond Lemma» (Diamond Lemma), however, strong evidence in missing and was identified only mimic diagram of "fusion" needed to understand the idea of the Shirshov composition. After the publication of Bergman "Diamond Lemma" became popular among algebraists and geometers, it also drew attention to the "Gröbner basis" Buchberger. In the mid 80's the standard basis for superalgebras and color Lie was built Moscow algebraists AA Mikhalev. Notes

↑ W. Gröbner (1950). " Über Die Eliminationstheorie ". Monatshefte für Mathematik 54: 71-78. ↑ CSF, 1962, Volume 3, № 2, p. 292-296.

References

Pankratiev EV Introduction to computer algebra. Arzhantsev IV Gröbner bases and algebraic equations. - M.: MCCME, 2003. - 68. - ISBN 5-94057-095-X Churkin VA Systems of polynomial equations, ideals and their bases, dividers. D. Cox, J. Little, D. O'Shea, Ideals, varieties and algorithms. Introduction to computational aspects of algebraic geometry and commutative algebra. Bernd Sturmfels. What is a Gröbner Basis?

Crasshopper (talk) 16:23, 19 February 2013 (UTC)

Intuitive explanation
I removed the following from the article. I cannot see how it contributes anything of value. --345Kai (talk) 23:37, 18 April 2013 (UTC)

Intuitive notion

 * The study of ideals is fundamental to commutative algebra and algebraic geometry. Ideals contain infinitely many elements, so, as in linear algebra, it is preferable to obtain a finite generating set with certain desirable qualities.

 * It is no surprise that not all generating sets possess these qualities; after all, in linear algebra one typically desires a basis of the vector space, which, in addition to generating the space, can contain only elements that are linearly independent. This property allows us to compute easily properties of the space, such as its dimension.

 * In this vein, a Gröbner basis is a generating set of an ideal, with certain desirable qualities that allow one to answer important questions about the ideal or an object it describes. The similarities do not end there; as noted already, the computation of a Gröbner basis generalizes Gaussian elimination of a system of linear polynomials to non-linear polynomials.

 * As explained above, I had added it in lieu of an example. I wish you had taken the time to look through the discussion first, but if you find it unhelpful for the task, I shan't bother putting it back. Simplex (talk) 17:56, 18 March 2014 (UTC)

Gjunter's work
Thanks to for adding to this article the reference to Gjunters work to this article. Since I have modified Spidsen's edit to follow the guidelines of the Manual of style, this user has introduced several modifications, that I will revert for the following reasons: For these reasons, I will revert all the last Spidsen's edits. D.Lazard (talk) 18:58, 18 August 2014 (UTC)
 * He has changed "doctoral advisor" into "doctoral supervisor", although the correct word is "advisor".
 * "was the first to introduce": This is an editorial comment (see WP:PEACOCK), not supported by the source and controversial (Janet and Riquier bases, in differential algebra, have been introduced earlier, and some people consider them as precursors of Gröbner bases)
 * "these polynomial ideals, commonly know as Gröbner bases": A Gröbner basis is not an ideal. Thus this sentence is a mathematical nonsense.
 * asserts implicitly that Gjunter's bases are exactly the same as Gröbner bases. This is not supported by the source. On the contrary, as far I understand, the source asserts that Spidsen considers only homogeneous polynomials, while, at least at the beginning, Buchberger did consider only the non-homogeneous case. This the reason for talking of the similarity than of the identity of the theories.

 * (1) The mathematical community http://www.ams.org/notices/201103/rtx110300365p.pdf https://cms.math.ca/Community/intl will decide on the fate of this article.

 * (2) Gjunter was definitely the first who developed the concept of monomial and polynomial ideals, long before Buchberger did. It was only that during the First Word war and the ensuing Russian revolution his publications did not get any attention until the Forties. His publications were rediscovered by some East German mathematicians, who had access to the Leningrad mathematical archives in the late Eighties.

 * (3) Ph.D. or doctoral ""supervisor"" would be the correct term. I have had one at the University of Glasgow, where I did my research. http://www.timeshighereducation.co.uk/features/10-truths-a-phd-supervisor-will-never-tell-you/2005513.article

 * — Preceding unsigned comment added by Spidsen (talk • contribs) 10:07, 21 August 2014 (UTC)

 * Please, sign your post with four tildes (< ~ ). Also, follow the guidelines of WP:TALK for placing and formatting them correctly. Its is boring to do that in your place.

 * Your point (1): the fate of a Wikipedia article depends only on Wikipedia community. See WP:CONSENSUS for understanding how decisions are taken in case of conflict.

 * Your point (2): "Gjunter was definitely the first who developed the concept of monomial and polynomial ideals". This is definitely wrong, as David Hilbert and Francis Sowerby Macaulay have developed the theory of polynomial ideals before him. It is true that it seems to be the first to have developed a theory which seems equivalent to that of Gröbner bases. However, the rules of Wikipedia requires that every fact of this kind must be supported by a reliable source (see WP: No original research). In your formulation, "the first" is not supported by any reliable source, and the equivalence between Gröbner bases and Gjunter theory in not clearly supported by Renschuch et al. article, which is the only paper that I know of, which cite Gjunter work. It follows that "the Georgian mathematician N.M. Gjunter introduced in 1913 a notion which is similar to Gröbner bases" is the only one which can be sourced and therefore the only one that is compatible with Wikipedia policies. Moreover, in view of the low impact of Gjunter work there is no reason to emphasize too much on it (see WP:DUE).

 * Your point (3): The choice of the terms doctoral advisor or doctoral supervisor depends on the countries, and probably, sometimes, of the universities. However, doctoral advisor seems the most widely used. In any case, the Wikipedia article is Doctoral advisor, while is only a redirect to the preceding. It follows that changing "advisor" to "supervisor" must not been done without specific good reasons.
 * It follows that your last edits break Wikipedia guidelines and policies. I'll revert them. Please, do not insert them unless if some other editors support them in this talk page, for reaching a consensus. D.Lazard (talk) 13:38, 21 August 2014 (UTC)

Performance of Implementations
Is this still up to date? The anwsers to this question on Computational Science Stack Exchange and this benchmark seem to suggest that the fastest implmentation is now mgb, the Gröbner basis library shipped with Maple. 212.201.44.244 (talk) 18:36, 24 January 2018 (UTC)

April 2021
I would like to add a detailed explanation of the full reduction of f by a set of polynomials G which is implemented by the Buchberger algorithm used to compute the Groebner basis. I would like to add this right after the paragraph "Given a finite set of polynomials" in the reduction section. This would include at least one long-division example to compute this. Shall I first post this explination here for everyone's review?Youriens (talk) 22:18, 8 April 2021 (UTC)
 * Be bold and proceed. It is easier to discuss your project if it is in the article. However, if you are reverted, do not take it personally: this could mean that a discussion is needed to reach a consensus, per the process WP:BRD. D.Lazard (talk) 09:16, 9 April 2021 (UTC)

Ok I added a sub-section "Example reductions with Lexicographic ordering" under "Reduction" section however, my long-division is somewhat poorly formatted as I was unable to use the latex \hspace command to align the rows. If the members here approve of this addition, could someone help me better format the long-division rows?Youriens (talk) 19:46, 9 April 2021 (UTC)
 * For horizontal alignment, the standard way is using `\begin{align}...\end{align} environment (see Help:math). However you have this problem because your use of long division notation. IMO, this is not a good idea, for several reasons: this is a notation that is specific to some countries and may be confusing for readers from other countries; this is a notation that is generally not used by reliable sources on this subject; this suggests wrongly that one must finish the division by a polynomial before starting the division by another polynomial. By the way, your examples are not well chosen, as they do not show two fundamental facts; firstly one may have to divide, say, by $$f_1,$$ then by $$f_2,$$ and again by $$f_1;$$ secondly, the result of the division may depend on order in which the divisors are chosen, and Buchberger's algorithm is specifically designed for making unique the result of the division process.
 * Instead of long division notation, is is commonly clearer to use a notation similar to that of rewriting theory, such as $$f_1\;\overset {-mg}\longrightarrow \;f_2$$ for expressing the division step consisting to substract $$mg$$ from $$f_1.$$
 * There are various other issues in your edit, some are minor, such as the excess of capitalization (see MOS:COMMONNAMECAPS). Some are more fundamental. For example, you give too much details for things that are well described in other articles (such as Monomial ordering), and this hides the main points that must be illustrated, such as the above mentioned ones. D.Lazard (talk) 09:13, 10 April 2021 (UTC)

Thanks for that critique above. I see someone has already improved the section nicely and I am grateful. So as not to change too much, I made only a minor correction describing how f needs to be "continuously" reduced by the elements in G until the remainder is no longer reducible. I personally would like to keep the long-division and I realize I could use \! and \; to manually adjust the indentations so will try to improve the formatting today; however I am only a novice in the matter and wished to add this section because I could not find a clearly-written and complete description elsewhere on the web; however, I realize I'm a novice with the subject so if others more knowledgeable wish to replace them with the suggestion above or something else, I won't add them back. Also, I was not aware Buchberger's algorithm required any specific ordering of the divisors. This is important to me because I was planning to request likewise, adding a full example of computing a reduced basis in the Buchberger's article. I could also come up with an example which includes dividing by $$f_1,f_2,f_1$$. — Preceding unsigned comment added by Youriens (talk • contribs) 12:29, 10 April 2021 (UTC)
 * Please, don't forget to sign your posts in talk pages with four tildes ( ~ )
 * I have completely rewritten your example for focusing on facts that are fundamental for Gröbner bases, and removing computational details that tend to hide these important properties. For this, I have changed the polynomial $f$ for having an example of two different complete reductions. D.Lazard (talk) 13:22, 11 April 2021 (UTC)

Complexity references
The section title Complexity contains the following sentence:

On the other hand, if all polynomials in the reduced Gröbner basis a homogeneous ideal have a degree of at most D, the Gröbner basis can be computed by linear algebra on the vector space of polynomials of degree less than 2D, which has a dimension $$O(D^n)$$.

I'm struggling to find the reference that contains this result. Could someone please cite the correct source. Anon65536 (talk) 16:07, 13 May 2024 (UTC)

 * The original result is mine, modulo the standard formula for the dimension of the homogeneous polynomials of a given degree. It because of this result and the results in Giusti's paper in the same proceeeings that most texts about the complexity of computation with multivariate polynomials focus on the degrees of involved polynomials rather than on the arithmetic or bit complexity.
 * D.Lazard (talk) 16:51, 13 May 2024 (UTC)

 * Thank you very much. It’s a nice result. Maybe you should cite it the corresponding paragraph. Anon65536 (talk) 07:17, 14 May 2024 (UTC)
 * Because of the WP:COI, it is difficult to add it myself. D.Lazard (talk) 08:49, 14 May 2024 (UTC)

title: Talk:Gröbner basis


text:
Hokkaido University

Hokkaido University (北海道大学), or Hokudai (北大), is a public research university in Sapporo, Hokkaido, Japan. Founded in 1918, it is the fifth-oldest government-authorised university in Japan and one of the former Imperial Universities.

The university finds its roots in Sapporo Agricultural College, which was a pioneer in the country's modern agricultural education and research, founded in 1876. The university's motto is 'Boys, Be Ambitious', which is said to be the parting words of the American dean of the Agricultural College, William S. Clark.

The university has 12 undergraduate faculties and 21 postgraduate schools. The university mainly operates on two campuses: the main campus is located in downtown Sapporo, just north of Sapporo Station, and the other campus is located in Hakodate, primarily used by the Faculty of Fishery Sciences.

History
The history of the university dates to the formal incorporation of Yezo as Hokkaido into the Japanese realm. Director of the Hokkaidō Development Commission Kuroda Kiyotaka, having traveled to America in 1870, looked to the American model of settling the new lands. Upon return he brought General Horace Capron, a commissioner of agriculture who pushed for the adoption of new agricultural practices and crops in Hokkaido's colder clime. To achieve this an agriculture college was proposed, leading to the founding of Sapporo Agricultural College (札幌農學校) in 1876 by William S. Clark with the help of five faculty members and a first class size of 24 students. In September 1907, Tohoku Imperial University (東北帝國大學) set up the faculty of Agriculture in Sapporo. Tohoku Imperial University ceded the Faculty of Agriculture to Hokkaido Imperial University (北海道帝國大學) on April 1, 1918. It was one of nine Imperial Universities. The School of Medicine was established in 1919, at which time the Agricultural College became the Faculty of Agriculture. This was followed by the Faculty of Engineering, the Faculty of Science, and finally in 1947, the Faculty of Law and Literature. The current name of Hokkaido University also came into use in 1947. In 1953, the Graduate School was established.

Since 2004 the university has been incorporated as a National University Corporation under a new law which applies to all national universities. Although the incorporation has led to increased financial independence and autonomy, Hokkaido University is still partially controlled by the Japanese Ministry of Education.

In 2014 the university was selected under the Super Global Universities program that began as an initiative of Prime Minister Shinzō Abe who stated its aim was to help more of Japan's universities rank in the top 100 worldwide. Under the program, it is listed in the top university category or Type A—(Top Type) The Top Type is for world-class universities that have the potential to be ranked in the top 100 in world university rankings. Each Type A university will receive ¥420 million ($US 4.2 million) annually until 2023.

In June 2020, Hokkaido University president Toyoharu Nawa was dismissed by Japanese education minister Koichi Hagiuda for abuse of power at the workplace, becoming the first national university president to be dismissed since national universities became independent in 2004. He was succeeded by former neurosurgeon and director of Hokkaido University Hospital Kiyohiro Houkin.

Faculties
• Letters

• Education

• Law

• Economics

• Medicine

• Health Sciences (radiation technology, laboratory technology, physical therapy, occupational therapy)

• Nursing

• Dental medicine

• Engineering

• Veterinary medicine

• Fisheries sciences

• Agriculture

• Pharmaceutical sciences

• Science (mathematics, physics, chemistry, biology, biological chemistry, earth and planetary sciences)

Graduate schools
• Agriculture

• Biomedical Science and Engineering

• Chemical Sciences and Engineering

• Dental Medicine

• Economics and Business

• Education

• Engineering

• Environmental Science

• Fisheries Sciences

• Global Food Resources

• Health Sciences

• Information Science and Technology

• Infectious Diseases

• International Media, Communication, and Tourism Studies

• Law

• Letters

• Life Science

• Medicine

• Pharmaceutical Sciences

• Public Policy

• Science

• Veterinary Medicine

Postgraduate degree programs in English
The following departments offer postgraduate degrees taught entirely in English

 * Agriculture
 * Chemical Sciences and Engineering
 * Engineering
 * Environmental Science
 * Life Sciences
 * Science
 * Veterinary Medicine

Both international and domestic students may apply for graduate programs taught in English. Competitive scholarships are available for all graduate and undergraduate students enrolled in English degree programs, which range in amount from tuition discounts to full funding.

Special degree programs for international students
The university offers two programs aimed exclusively at international students: One, four-year undergraduate degree program, the Modern Japanese Studies Program (MJSP), and one, five-year degree program comprising both undergraduate- and graduate-level study, the Integrated Science Program (ISP). As with other English-based degree programs at the university, competitive scholarships are available for all graduate and undergraduate students, which range in amount from tuition discounts to full funding.

Modern Japanese Studies Program (MJSP)
The Modern Japanese Studies Program is a bilingual, bachelor's degree program that aims to educate students about the history, culture, society, and political economy of modern Japan while raising them to fluency in the Japanese language. The program offers two majors, one in History and Culture and one in Society and Political Economy. The majors share coursework, so whichever of the previous specializations a student does not choose as their major becomes their minor.

Integrated Science Program (ISP)
The Integrated Science Program is a multifaceted degree program that aims to provide students with a bachelor's degree in either physics, chemistry, or biology. Upon enrolling, students will spend the first semester attaining an all-round education in the three sciences along with mathematics and Japanese language. After this intensive first semester, students will join the department of Physics, chemistry or biology within the school of science. The final allocation is decided by a combination of student preference, availability and GPA. Japanese language education continues until the first semester of the second year. After graduation, students have the choice of enrolling in one of Hokkaido University's graduate schools. Through the unique, accelerated methodology of the program, students are able to graduate with a master's degree in five years (made up of three-and-a-half years of undergraduate study and one-and-a-half years of graduate study and research). All classes, besides Japanese language, are carried out in English by professors with native or fully professional proficiency.

Institutes
The university's Institute of Seismology and Volcanology was founded in 1998 in collaboration with several seismological observatories around Hokkaido. The institute is represented on the national Coordinating Committee for Earthquake Prediction.

In 2016, the university launched the Hokkaido Summer Institute, a three-month-long program from June to August which offers a variety of classes for both undergraduate and graduate students. Guest lecturers are invited from all over the world to share their expertise for the courses, which usually run for 1–2 weeks and grant students a small amount of academic credit. Both Japanese and foreign students participate in this unique program, which is conducted entirely in English.

Sapporo campus

The main Sapporo campus is located just north of Sapporo Station, in the heart of Sapporo City. The entirety of the campus measures approximately 180 hectares and houses academic and administrative buildings, research laboratories, student dormitories, and farmland. The main academic buildings are found along a 1.5 kilometer stretch of road that runs from the Main Gate to the Kita 18 Gate, roughly encompassing the distance between Kita-Juni-Jo and Kita 18-jo subway stations on the Namboku Subway Line. A campus-wide bus service runs regular routes between the southern and northern end of the university, although access is restricted to university staff only.

The abundance of accessible green space has continued to be popular not only among students, but also the general public, who can often be seen using the campus area in a similar way to a public park. Walking tours of the campus for interested foreign and domestic tourists are provided by several businesses in Sapporo, although no tour is needed to visit the campus. Fall is an especially popular time for campus visits, with tourists and Sapporo residents flocking to get a view of the golden ginkgo trees that line Ginkgo Avenue.

Hakodate campus
The campus is located in Hakodate, a city located in the southern part of Hokkaidō. The Faculty and Graduate School of Fisheries Science are located there. However, students of Fisheries Science start their education at the Sapporo campus in order to complete three semesters of compulsory liberal arts education courses and move to the Hakodate campus from the second semester of their sophomore year. As the minimum requirement to study at the Hakodate campus is only one year of a four-year bachelor's program, the turn-over rate of students entering and leaving the Hakodate campus is fairly high. To provide students in the Faculty and Graduate School of Fisheries Science with practical hands-on experience, the university has two fully operational research vessels, the Oshoru Maru and the Ushio Maru, based in nearby Hakodate harbor. Graduate students and professors also use these vessels to carry out their research.

Overseas satellite offices
In order to raise awareness of the university internationally, as of June 2018 Hokkaido University was operating eight satellite offices worldwide. After opening its first overseas satellite office in Seoul, South Korea, Hokkaido University has also established satellite offices in Helsinki (Finland), Beijing (China), Lusaka (Zambia), Bandung (Indonesia), Quezon City (Philippines), Kamphaeng Saen (Thailand), and a special China Office in Beijing. Interested parties can not only obtain information regarding the university at these offices, but prospective students can also take university entrance exams there, a procedure which previously was only offered in Japan.

Educational philosophy

 * Frontier Spirit (フロンティア精神)
 * Global Perspectives (国際性の涵養)
 * All-round Education (全人教育)
 * Practical Learning (実学の重視)

General rankings
In 2017, the CWTS Leiden Ranking ranked them at 120th in the world and 6th in Japan. In 2018, QS World University Rankings ranked Hokkaido University at 122nd in the world (7th in Japan).

In 2019, the Times Higher Education(THE) Japan ranked them 5th in Japan. Also in that year, they ranked as 6th or 7th in Japan according to the Academic Ranking of World Universities (ARWU), and between 151st and 200th in the world.

In 2013, their highest score in QS Ranking was for Faculty Student Score (88 out of 100). Their lowest was for International Faculty Score (13.5 out of 100). In an effort to boost their International Faculty Score, Hokkaido has recently been selected to be part of Japan's Super Global Universities Program. This program provides special funding to hire international faculty.

Research performance
In the Nature index 2023 annual table, Hokkaido University was ranked 142nd for its output in selected journals in the fields of natural sciences and Health Sciences research, among all leading research institutions in the world (5th in Japan).

Popularity and selectivity
Hokkaido University's selectivity for undergraduate degrees is usually regarded as amongst the top 15 in the country.

Notable people

 * Uchimura Kanzō, Christian evangelist, founder of Non-church Christianity Movement
 * Akira Ifukube, composer
 * Nitobe Inazō, the author of Bushido: the Soul of Japan, a Quaker
 * Ryuzo Yanagimachi, assisted fertilization and cloning pioneer
 * Mamoru Mohri, astronaut
 * Takeo Arishima, novelist
 * Riko Muranaka, medical doctor and journalist
 * Hiroshi Ishii, computer scientist
 * Junko Ohashi, pop singer
 * Akira Suzuki, Nobel Prize in Chemistry (2010)
 * Yuichiro Miura, alpinist, the oldest person to reach the summit of Mount Everest
 * Juhn Atsushi Wada, neurologist, described the Wada test
 * Ken-Ichi Honma, chronobiologist, awarded the SRBR award.

The Nobel Prize
As of 2021, two alumni and faculty members have won the Nobel Prize in Chemistry. The university received attention in 2010 when Professor Akira Suzuki won the Nobel Prize for Chemistry jointly with Richard F. Heck and Ei-ichi Negishi. Benjamin List, winner of the 2021 Nobel Prize in Chemistry, is the principal investigator at the Institute for Chemical Reaction Design and Discovery of the Hokkaido University. Also, Ei-ichi Negishi, special invited professor at the Institute for Catalysis (ICAT) of the Hokkaido University, was awarded the Nobel Prize in Chemistry as well.

Points of interest

 * Hokkaido University Botanical Gardens

title: Hokkaido University


text:
Evangelical Baptist Mission of South Haiti

The Evangelical Baptist Mission of South Haiti (Mission Evangélique Baptiste du Sud d'Haïti) is a Baptist Christian association of churches in Haiti, headquartered in Les Cayes. MEBSH is a member of the Protestant Federation of Haiti, the Evangelical Council of Haitian Churches and the Baptist World Alliance.

History
Evangelical Baptist Mission of South Haiti (MEBSH) began with the evangelistic efforts of repatriated Haitians from Cuba in the 1920s. The organization was officially formed in 1936 in Les Cayes when the movement's leaders invited the non-denominational agency World Team (then West Indies Mission) to open a Bible school.

In 1958, the Mission founded Radio Lumière in Les Cayes.

In 1993, the Light University was founded by the Mission.

Since 2012 the president of the Evangelical Baptist Mission of South Haiti is Rev. Alnève Emile, who succeeded Rev. Luders Erase for a five-year term. He was re-elected in 2017.

According to a census published by the association in 2023, it claimed 488 churches and 60,000 members.

Social work
The MEBSH operates numerous educational, health and development institutions in Haiti.

Schools
It has 413 primary schools and secondary schools.

It also has 1 professional training institute.

It has 3 affiliated theological institutes.

Health Services
It manages the Lumière Hospital in Bonne Fin and the Lumière Health Center in Les Cayes.

Development

 * Women's domestic training center: Centre Lumière aux Cayes
 * Integrated Rural Development
 * Well drilling
 * Orphanages
 * Youth Camp Mahanaim


text:
Saint Thomas Church (Manhattan)

Saint Thomas Church is an Episcopal parish church of the Episcopal Diocese of New York at 53rd Street and Fifth Avenue in Midtown Manhattan, New York City. Also known as Saint Thomas Church Fifth Avenue or Saint Thomas Church in the City of New York, the parish was incorporated on January 9, 1824. The current structure, the congregation's fourth church, was designed by the architects Ralph Adams Cram and Bertram Grosvenor Goodhue in the French High Gothic Revival style and completed in 1914. In 2021, it reported 2,852 members, average in-person attendance of 224 (due to pandemic restrictions) and $1,152,588 in plate and pledge income.

In 2020, following a gift from the family trust of the late John and Mary Alyce Merrow, a camera system with a dozen 360-degree-rotating cameras was installed. Online attendance has remained significant; during Advent and Christmas, 2022, on-line participation was 38,000 with an average attendance of 25 minutes.

The church is home to the Saint Thomas Choir of Men and Boys, a choral ensemble comprising men and boys which performs music of the Anglican tradition at worship services and offers a full concert series during the course of the year. The men of the Saint Thomas Choir are professional singers and the boys are students enrolled at the Saint Thomas Choir School, the only church-affiliated residential choir school in the United States where the choristers make up the whole student body. Only three such schools remain in the world currently; the two Anglican Choir Schools are Saint Thomas Choir School and Westminster Abbey Choir School in the United Kingdom.

Broadway and Houston Street
On October 12, 1823, members of three Episcopal parishes in Lower Manhattan collaborated to organize a new episcopal church in New York. These included William Backhouse Astor, a wealthy Manhattan landowner; Charles King, later president of Columbia University; and jurist William Beach Lawrence. The congregation came from Grace Church, Trinity Church, and St. George's Church.

Saint Thomas Church was incorporated on January 9, 1824, and the cornerstone of the new church building laid in July 1824 at the northwest corner of Broadway and Houston Street. The first church edifice opened in 1826 and was described as "the best specimen of Gothic in the city." The location was the northern extent of developed settlement in Manhattan during the early 19th century. It was designed in a Gothic Revival style by architect Joseph R. Brady and John McVickar, professor of moral philosophy at Columbia College (now Columbia University). The church was enlarged and remodeled in 1844 to accommodate a growing congregation.

The first Saint Thomas's Church was destroyed by fire on March 2, 1851. The congregation built a new church at the same location, completed in 1852. The character of the neighborhood at the corner of Broadway and Houston, the southeastern corner of Greenwich Village, broadly speaking, had "degenerated into anchorage for cheap dance halls and 'concert salloons'" by the 1860s. This led to the congregation seeking to relocate.

Move to midtown
A third church was built from 1865 to 1870 at the corner of 53rd Street and Fifth Avenue based upon a design by Richard Upjohn and his son Richard Michell Upjohn. The cornerstone for the new church was laid on October 14, 1868. Two years later, on October 6, 1870, the congregation moved into its new home. This structure, in a neighborhood at the time dominated by the mansions of Manhattan's upper class, featured a prominent 260 ft high tower and a bas-relief reredos by Augustus Saint-Gaudens and murals by John LaFarge. Though the new Saint Thomas's was a parish church, its location and design evoked that of a cathedral.

The third building was also the site of many high society weddings and funerals, including that of Consuelo Vanderbilt to Charles Spencer-Churchill, 9th Duke of Marlborough, the first cousin of Winston Churchill. This structure was destroyed by fire on August 8, 1905. Only the tower remained from the third church. The congregation built a 1,200-seat chapel on the rest of the site.

Current church
The fourth and current church, designed in 1906, was built from 1911 to 1913 to a design by Ralph Adams Cram and Bertram Grosvenor Goodhue of the architectural firm of Cram, Goodhue and Ferguson. The cornerstone was laid on November 21, 1911, and the new building opened to congregants on October 4, 1913. It was consecrated on April 25, 1916. The design by Cram and Goodhue won an architectural competition to build the new Saint Thomas Church, winning over entries by George Browne Post and Robert W. Gibson.

The 1906 San Francisco earthquake had so shocked the church's rector, Rev. Ernest M. Stires, that he rushed the accumulated balance in his parish's building fund to aid the stricken city. The public responded in kind to his generosity with unsolicited gifts that more than replenished the fund.

Cram and Goodhue are also noted for having designed Saint Bartholomew's Church on Park Avenue and East 50th Street, the Cathedral of St. John the Divine on Amsterdam Avenue and West 110th Street, the chapel and a large portion of the campus at the United States Military Academy in West Point, New York, the Princeton University Chapel at Princeton University and the Rockefeller Chapel at the University of Chicago.

September 11 ministry
In the wake of the September 11 attacks in 2001, Saint Thomas Church reached out to the British expatriate community in recognition of its Anglican heritage. This culminated in an interfaith service held at the church on September 20, 2001. The service was addressed by Prime Minister Tony Blair and broadcast live in its entirety throughout the United Kingdom. On October 28, 2002, the rector of Saint Thomas Church, Andrew C. Mead, was made an honorary Officer of the Order of the British Empire (OBE) by Queen Elizabeth II. The honor was conferred at a ceremony at the British Embassy in Washington, D.C.

Bicentennial and twinning anniversaries
In October 2023 Saint Thomas Church commemorated the bicentennial of its founding in 1823, with an exhibition, lectures and special services. The Assistant Bishop of New York, the Rt. Rev. Mary Glasspool, and the Sub-Dean of the Chapel Royal, Paul Wright, preached in celebration of the anniversary.

The following year, in May 2024, the 100th anniversary of the twinning of the cities of New York City and York in England was marked with special services attended by the Presiding Bishop of the Episcopal Church, the Most Rev. Michael Curry, the Archbishop of York, Stephen Cottrell, the Mayor of New York City, Eric Adams, the Lord Mayor of York, Chris Cullwick, the Dean of York, the Very Rev. Dominic Barrington, and the British Consul General in New York, Hannah Young.

Architecture

The present church, a New York City designated landmark, was designed by a partnership of Ralph Adams Cram and Bertram Grosvenor Goodhue. Lee Lawrie designed the sculptures and decorations. It measures 214 ft long and 100 ft wide. The church building rises 95 ft.

Facade
Saint Thomas Church has plain ashlar limestone exterior surfaces in the French High Gothic style. The church's asymmetrical main elevation on Fifth Avenue is divided into three sections, reflecting the interior divisions. The nave is slightly off-center, with a wide chantry to the south and a narrow aisle to the north.

Main entrance
The main entrance, which leads to the nave, is flanked by large buttresses. The entrance portal contains niches with sculptures. The center of the portal is divided vertically by a trumeau with a sculpture depicting Thomas the Apostle. There are three sculptures on each side, depicting six of the apostles. These sculptures, part of the original plan, were not installed until 1963. There are gilded low relief panels above the main doors, which depict the congregation's four buildings.

Above the portal are more sculptures, interspersed with small windows. These depict the six remaining apostles as well as Mary Magdalene and Martha. Decorative archivolts above these niches and windows contain depictions of Thomas the Apostle's life, the sacraments, and the gifts of the holy spirit. These in turn are topped by more figures of saints. The entrance is topped by a large rose window with a tetramorph in low relief.

Other sections
To the left (south) of the main entrance, there is a square tower at the southeast corner of the church, facing Fifth Avenue and 53rd Street. The tower has a simpler design than the main entrance, with band courses and other horizontal design features that relate to the main entrance's design. At the top is a bell tower, which was cited in 1940 as having 25 chimes.

To the right (north) of the main entrance is a narrow section of wall, leading to the north aisle. The northern entrance contains a depiction of Ernest M. Stires holding a model of the current church. Stires was the rector when the church was completed.

The southern elevation contains five bays, which are separated by buttresses. Next to the square tower, in the easternmost bay, is an entrance to the chantry. Above the entrance there are motifs relating to the sanctity of marriage. The other bays contain stained glass windows in the chantry. To the west is the gallery, which contains five bays of tripartite windows made of stained glass. The three center bays of the gallery contain an arcade of three arched doorways. The buttresses contain sculptures of ancient leaders and philosophers. Above the four windows in the chantry and the five windows in the south gallery are nine recessed clerestory windows, illuminating the top of the nave.

To the west of the main church is the parish house, which is a separate structure. The parish house is five stories tall and contains an oriel window in its eastern bay, separating it from the rest of the church. The entrance to the parish house is on 53rd Street; it was originally at the rear of the gallery arcade. The roof of the parish house is covered in lead.

Stained glass

The first stained glass window placed in the fourth Saint Thomas Church structure was designed by Nicola D'Ascenzo, an Italian-born American stained glass artist. The window was designed in 1926 and completed and installed in 1927. The last window, designed and installed in 1974, came from the Willet Stained Glass Studios, headed by E. Crosby Willet and founded by William Willet. Both those studios were located in Philadelphia, Pennsylvania, at the time of the fabrication of their windows for Saint Thomas Church.

James Powell & Sons (Whitefriars), Ltd, of London, secured a contract for the remaining windows in the present church structure, including all except one of the clerestory windows. Each window measures 32 ft tall and 18 ft wide and depict biblical figures interacting with notable American bishops. The windows for the present structure were designed beginning in 1929 by English stained glass artist James Humphries Hogan, who also the main American sales agent for the firm. He labored from 1926 to 1928 to acquire the commission for the Saint Thomas Church windows. Hogan's son, Edmond Humphries Hogan, designed some of the windows, including those in the Rector's office. The actual fabrication and installation of the Powell & Sons windows was not completed until 1970, but most of the windows were designed by Hogan before his death in 1948. Five windows were designed and completed after his death: one in 1950, one in 1954, two in 1959, and one in 1970. Those windows were the work of another Powell & Sons artist, Edward Liddall Armitage.

In 2007, conservation began in earnest on all the stained glass windows in the present structure. It took ten years and $20 million to renew the splendor of 33 windows, with their 9 million pieces of glass. The restoration was completed in February 2017.

Interior
The interior surfaces are made of sandstone. Saint Thomas Church is characterized by a high main arcade, an open triforium, and a clerestory. The narthex, just inside the main portal, was originally decorated with symbols of four classical elements, four seasons of the year, and four angels. After World War II, these were replaced with motifs that represented peace and honored those who were killed in the war. These motifs include mosaics on the floors as well as an altar at the north end. The narthex and nave were initially separated by an oak screen, which was replaced in 1961 by glass.

At the front of the nave is a parapet with eight mosaics. The four mosaics on the left depict symbols of the church, while those on the right depict major events in the history of the United States. There is also an octagonal pulpit made of oak. The pulpit is surrounded by statues of preachers. Above it is a sounding board depicting prophecies of the Old Testament. The lectern of the pulpit is also inlaid in wood. Ornate wooden carving is placed around the rest of the chancel, including on the choir stalls, altar rail, and kneeling rail. The altar rail also has a bronze grill flanked by oak carvings of angels. There is an organ screen that depicts notable organists.

The elaborate reredos, gifted by the family of Harris C. Fahnestock, was designed by Goodhue and Lawrie and executed by the Ardolino Brothers. The reredos contains niches with depictions of saints, prophets, reformers, and Christian dignitaries. It is 80 ft high, covering the west wall of the chancel, and consists of more than 60 stone figures relating to the discovery of Thomas the Apostle.

The church's superstructure is built of stone and originally did not contain any steel reinforcement. This contrasted with many other buildings from the early 20th century, which tended to be steel-framed. The architects believed that, if the church was designed in the Gothic style, then its superstructure had to be built the same way. In 1925, eleven years after completion, the north wall of the church was found to be bulging dangerously and hidden steelwork added. The construction of the New York City Subway's 53rd Street Line in the 1930s prompted additional steel under the altar and massive reredos as a precaution.

Acoustics
The architects realized that the sound associated with a Gothic look would not work for a more sermon-focused Protestant service. Wallace Sabine, founder of the field of architectural acoustics, was hired to reduce reverberation in order to make the sermon more intelligible. Sabine avoided changing the church's aesthetic by hanging panels and drapes to absorb sound. Instead he worked with Rafael Guastavino Jr. to create Rumford tile, a ceramic tile with porous surfaces that absorb sound. The church was among the first to be acoustically engineered for environmental control.

Worship
The style of worship at Saint Thomas Church has varied greatly over the history of the parish. Beginning with the rectorship of John Andrew in 1972, however, it has informally followed the Anglo-Catholic or high-church tradition within the Episcopal Church that developed out of the Oxford Movement. This was further developed under the rectorship of Andrew Mead. Sunday services include Low Mass, High Mass, and Evensong, and Solemn Mass on Christmas, Easter and major feast days. Special liturgies and processions are held for Advent, Epiphany, Candlemas and Holy Week. The Litany is sung in procession in Advent and Lent. For masses at the High Altar, the Church uses a variation on the three traditional sacred ministers ad orientem, however as with many other Anglo-Catholic parishes that do not look to Tridentine Rome for liturgical cues, many of the unique traditional roles of sacred ministers are currently in use--the Deacon reads the Gospel and the Subdeacon reads the Epistle. The two sacred ministers who are not celebrating the mass essentially vest and act as priests in tunicles. The readings are not chanted. The choir of men and boys sing most Sundays in term time and, if there are no visiting choirs during the school vacation, the gentlemen of the choir sing the services. The church uses traditional language for many of its services on Sundays and weekdays and the King James Version of the Bible is used at Sunday choral services and at Choral Evensong and Solemn Mass on feast days during the week. Rite II of the BCP 1979 is used for the 12:10 pm mass Mondays to Fridays. In Lent 2015 Shrine Prayers were started at the image of Our Lady of Fifth Avenue and intercessions are offered at noon after the Angelus Mondays to Saturdays; these intercessions may be left in the church or submitted online via the church website, and many prayer requests come from around the world every week. Confessions are heard each Saturday from 11:00–11:45 am. Since 2021, the 9 am Sunday mass has become a Low-Church Novus Ordo-type children and family focused service, using Rite II and ad populum altar placed in the Chancel. A robed children's outreach choir called the Noble Singers and composed of local girls and boys sings at the 9 am service. On the second Sunday of each month, a Sunday mass is offered in Korean Language. The church is open every day of the year.

Choir of Men and Boys

Music is an important component of worship and liturgy at Saint Thomas Church. It follows in the Anglican tradition of the all-male choral ensemble. The choir's primary function is to provide music for five services each week, as well as an annual concert series sponsored by the church. In addition, the choir has toured throughout the United States and Europe, with performances at Westminster Abbey, St. Paul's Cathedral, London, King's College, Cambridge, and the Aldeburgh Festival. In 2004, the choir toured Italy and received a papal audience at the Vatican.

In 2005, the choir toured in the southern United States, with a benefit concert in New Orleans. Upon returning to New York, they performed in Saint Matthew Passion at Carnegie Hall. Other appearances have included performances at Lincoln Center with the New York Philharmonic, the Cleveland Orchestra, and alongside artists such as Jessye Norman and Plácido Domingo. In addition, the choir gave the world-premiere performance of Andrew Lloyd Webber's Requiem, which was subsequently televised internationally by the BBC. The choir was also featured in a recording of Carly Simon's "Let the River Run".

The boy choristers reside at Saint Thomas Choir School, founded in 1919 and the only church-affiliated boarding choir school in the United States. In 2007, there were three tours to Mexico City, Baton Rouge along with other domestic cities, and a tour to the United Kingdom in the early summer.

The choir typically records and releases one CD a year.

Organs
Musical offerings at Saint Thomas Church are enhanced through three organs. The Arents Memorial Chancel Organ, which has been replaced with the Irene D. and William R. Miller Chancel Organ in Memory of John Scott, was initially built as the "Opus 205" of the Ernest M. Skinner Company of Boston, Massachusetts, in 1913. This organ, which was revised in 1945, boasted 4 manuals and 77 ranks. In 1956, the organ was rebuilt, as "Opus 205-A", by the Aeolian-Skinner Company by G. Donald Harrison (died 1956), who died before the work was completed. This rebuilding expanded the organ to comprise 172 ranks. With damage to the reredos and the organ due to construction of the Museum of Modern Art, the church's immediate neighbor on West 53rd Street, Gilbert F. Adams of Brooklyn was contracted in 1969 to repair and rebuilt the organ. This revision decreased the number of ranks to 156. Further revisions were completed in the early 1980s by Mann & Trupiano. With the exception of the Trompette-en-Chamade, located under the Rose Window above the narthex, the entire instrument of the Great Organ was located in the church's chancel. The now-dismantled Great Organ featured an Electro-pneumatic and electric-slider stop and chest action, a Solid-State combination action, 4 manuals, 158 ranks and 9,050 pipes.

The Loening-Hancock Gallery Organ was built as "Opus 27" of Taylor & Boody Organbuilders of Staunton, Virginia, in 1996 to honor Gerre Hancock for 25 years of service to Saint Thomas Church. Located in the gallery beneath the church's Rose Window, this organ features a mechanical key and stop action, originally possessing 2 manuals, 25 stops, and 32 ranks. In 2015 it was slightly enlarged, according to original preparations, to its current 3 manuals, 31 stops and 44 ranks. Its case sports fumed white oak with pipe shades gilded in 23 carat gold. Its predecessor, the Loening Memorial Organ, dedicated in memory of Hermine Rubino Leoning, was built by Gilbert F. Adams in 1969 and featured 4 manuals, 59 stops, and 90 ranks.

The Martha J. Dodge Positiv Organ was built and installed in December 2001 by Taylor & Boody Organbuilders. This organ consists of 5 ranks, and is used as a continuo organ.

Miller-Scott Organ
On October 3, 2008, Saint Thomas Church announced its Vestry's decision to replace the aging Arents Memorial Chancel Organ with a new instrument. The announcement noted that as part of a substantial renovation effort to the church, a new instrument from Dobson Pipe Organ Builders of Lake City, Iowa, would be installed to replace the current instrument. Plans called for the retention of the especially ornate 1913 organ case-front and console cabinetry and, to better respect the church's well-developed neo-Gothic design aesthetic, the elimination of visible organ pipes added above the choir stall canopies in the 1956 rebuild.

The Irene D. and William R. Miller Chancel Organ in Memory of John Scott, dedicated on October 5 and 7, 2018, is one of North America's most significant new pipe organs. In addition to supporting the parish's internationally renowned liturgical and musical life, the Miller-Scott Organ serves as a showcase for recitalists from all over the world and helps Saint Thomas train the next generation of organists.

The new organ contains 7,069 pipes, a number of which are from the former instrument. Fifteen sets of pipes, including some of the largest existing wooden ones, have been rebuilt and reinstated; these include the very softest sounds, several flutes and strings, and some specialty trumpet stops. Much of the design and decoration form for the new organ case are derived from precedents throughout the rest of the building, and Gothic revival style in general. In the 1913 north organ case, imagery is taken from Psalm 150: trumpet and lyre, string and cymbal. The new organ case takes as its decorative program the themes of music, ministry and praise. Carved texts include "Soli Deo Gloria" and quotations from the Psalms. Major carvings depict symbols of the Four Evangelists, and there are portraits of persons important in the recent life of Saint Thomas Church, including former directors of music Gerre Hancock and John Scott, Rector Emeritus Fr. Andrew Mead, and Irene and William Miller, whose benefaction was central to the creation of the Miller-Scott Organ.

Organists

 * George William Warren, 1870–1900
 * William C. Macfarlane, 1900–1912
 * T. Tertius Noble, 1913–1943
 * T. Frederick Candlyn, 1943–1953
 * William Self, 1954–1971
 * Gerre Hancock, 1971–2004
 * John Scott, 2004–2015
 * Daniel Hyde, 2016–2019
 * Jeremy Filsell, 2019–present

title: Saint Thomas Church (Manhattan)


text:
Aloha Stadium

Aloha Stadium is a closed multi-purpose stadium located in Halawa, Hawaii, a census-designated place that is a western suburb of Honolulu. It is the largest stadium in the state of Hawaii. , the stadium ceased fan-attended operations indefinitely, and placed a moratorium on the scheduling of new events. It is located next to the Hālawa station of the Skyline rail system.

Aloha Stadium served as home to the University of Hawaii Rainbow Warriors football team (Mountain West Conference, NCAA Division I FBS) for the 1975 through 2020 seasons. It also hosted college football's Hawaii Bowl (2002–2019) and Hula Bowl (1976–1997, 2006–2008, 2020–2021), and formerly was home to the National Football League's Pro Bowl from 1980 through 2016 (except in 2010 and 2015). It also hosted numerous high school football games, and served as a venue for large concerts and events, including high school graduation ceremonies. The stadium was home field for the AAA Hawaii Islanders of the Pacific Coast League (PCL) from 1975 to 1987, before the team moved to Colorado Springs. Frequent swap meets in the stadium's parking lot often draw large crowds.

History

Before 1975, Honolulu's main outdoor stadium had been Honolulu Stadium, a wooden stadium on King Street. However, it had reached the end of its useful life by the 1960s, and was well below the standards for Triple-A baseball. The need for a new stadium was hastened by the move of the Hawaii Rainbows football program to NCAA Division I. Located west of downtown Honolulu and 2 mi north of Honolulu International Airport, Aloha Stadium was constructed in 1975 at a cost of $37 million. Constructed of steel, the stadium was nicknamed the "Metal Mecca". The baseball field was aligned north-northwest (home plate to centerfield), as was the football field.

The first sporting event at Aloha Stadium was a college football game between Hawaii and Texas A&I (now Texas A&M-Kingsville) on September 13, 1975. Played on Saturday night, the crowd was 32,247, and the visitors prevailed,43–9.

The final sporting event held in Aloha Stadium was the 2021 Hula Bowl. The last points scored at Aloha Stadium were a “pick 6” touchdown scored by Carlo Kemp of the University of Michigan.

The stadium was somewhat problematic for its initial primary tenant, the minor league baseball Hawaii Islanders. Located in south-central Oahu, it was far from the team's fan base in Mōʻiliʻili, and many were unwilling to make the drive. Additionally, while local public transportation (TheBus) stopped at the main gate of Honolulu Stadium, the stop for Aloha Stadium was located some distance from the gate. As a result, attendance plummeted and never really recovered—a major factor in the franchise's ultimate move to the mainland.

Additionally, stadium management initially refused to allow the use of metal spikes on the AstroTurf. During a game in early May 1976, the starting pitcher for the Tacoma Twins, Bill Butler, wore metal spikes to comply with a directive from Tacoma's parent club. In response, stadium management turned off the center field lights, and after 35 minutes, umpires forfeited the game to the Twins. The Islanders protested, claiming they had no control over the lights. However, the Pacific Coast League (PCL) sided with the Twins, citing a league rule that the home team is responsible for providing acceptable playing facilities. After the teams ended the season in a tie for first in the PCL's Western Division, Hawaii won a one-game playoff in Tacoma. As originally built, Aloha Stadium had various configurations for different sport venues and other purposes. Four movable 7,000-seat sections, each 3.5 e6lbs could move using air casters into a diamond configuration for baseball (also used for soccer), an oval for football, or a triangle for concerts. In January 2007, the stadium was permanently locked into its football configuration due to cost and maintenance issues. An engineer from Rolair Systems, the NASA spin-off company that engineered the system, claims that the problem was caused by a concrete contractor that ignored specifications for the concrete pads under the stadium.

Concerns
There were numerous discussions with Hawaii lawmakers who were concerned with the physical condition of the stadium. There were also several issues regarding rusting of the facility, several hundred seats that need to be replaced, and restroom facilities that need to be expanded to accommodate more patrons. Much of the rust was due to building the stadium with weathering steel. U.S. Steel Corporation suggested the steel would develop a protective patina that would eliminate the need for painting. However, given Honolulu's ocean-salt laden climate, the steel never stopped rusting.

A 2005 study by Honolulu engineering firm Wiss, Janney, Elstner Associates, Inc. determined that the stadium required $99 million to be completely restored and an additional $115 million for ongoing maintenance and refurbishment over the next 20 years to extend its useful life. In early 2007, the state legislature proposed to spend $300 million to build a new facility as opposed to spending approximately $216 million to extend the life of Aloha Stadium for another 20–30 years.

One council member said that if immediate repairs were not made within the next seven years, then the stadium would probably have to be demolished due to safety concerns. In May 2007, the state allotted $12.4 million to be used towards removing corrosion and rust from the structure.

Expansion and improvements
In 2003, the stadium surface was changed from AstroTurf (which had been in place since the stadium opened) to FieldTurf. In July 2011, the field was replaced with an Act Global UBU Sports Speed S5-M synthetic turf system.

In 2008, the state of Hawaii approved the bill of $185 million to refurbish the aging Aloha Stadium. In 2010, Aloha Stadium completely retrofitted its scoreboard and video screen to be more up to date with its high definition capability. The Aloha Stadium Authority planned to add more luxury suites, replacing all seats, rusting treatments, parking lots, more restrooms, pedestrian bridge supports, an enclosed lounge, and more. There was also a proposal that would have enclosed the four openings in the corners of the stadium to add more seats.

In 2011, the playing field was refurbished in part due to a naming rights sponsorship from Hawaiian Airlines. As a result of the sponsorship deal, the field was referred to as Hawaiian Airlines Field at Aloha Stadium. The airline did not renew sponsorship after the deal expired in 2016. As a result, the field went unnamed until late August, when Hawaiian Tel Federal Credit Union signed a three-year $275,000 agreement. As of 2016, the field was known as Hawaiian Tel Federal Credit Union Field at Aloha Stadium.

In early 2017, there was a study in the Honolulu Star-Advertiser about replacing Aloha Stadium due to safety concerns and a liability risk. The plan was then to build a smaller 30,000 seat stadium on the existing property and also build commercial development around the stadium. In theory, this would save the state millions of dollars instead of renovating and keep the existing stadium as it was.

In July 2019, Governor of Hawaii David Ige signed Act 268 into law, appropriating $350 million for an Aloha Stadium redevelopment project. The funds were to go toward the construction of a new stadium and land development, including a mixed-use sports and entertainment complex.

Closure to new events
A December 17, 2020, announcement by the Aloha Stadium Authority stated that the stadium would be ceasing fan-attended operations indefinitely. The closure was related to financial issues caused by the COVID-19 pandemic. The stadium, built in 1975, was also plagued by maintenance issues in recent years. A 2019 story from the Honolulu Star-Advertiser noted that the stadium needed $30 million in repairs. KHON-TV reported that the stadium would be condemned and was deemed unsafe to hold any crowds at all. The scheduling of new events was also halted. In January 2021, the University of Hawaii announced that the Rainbow Warriors football team would play their home games on campus "for at least the next three years".

New stadium
The New Aloha Stadium is a proposed 35,000-seat multi-purpose stadium to be built in Halawa, Hawaii, for the Hawaii Rainbow Warriors football program, with demolition of the old stadium to begin in 2025. The area around the stadium will also include entertainment venues, retail stores, restaurants, housing, hotels, recreational sites, cultural amenities, and green space. It will replace, and be constructed on the site of, the current Aloha Stadium.

College football
Aloha Stadium served as the home field of the Hawaii Rainbow Warriors college football program, representing the University of Hawaiʻi at Mānoa, from 1975 through 2020.

The Hula Bowl, a college football all-star game, was first played at the stadium in January 1976 and returned to the stadium annually through 1997. It was again held at Aloha Stadium in 2006–2008 and 2020–2021. The 2021 Hula Bowl was the last football game held at the facility before the halting of new events.

Three team-competitive college football bowl games were held annually at the stadium: the Aloha Bowl (1982–2000), Oahu Bowl (1998–2000), and Hawaii Bowl (2002–2019). The Hawaii Rainbow Warriors appeared in the Hawaii Bowl nine times and the other two bowl games once each.

Professional football
Starting in September 1975, the stadium was home to the World Football League's Hawaiians who played their last four home games there. The San Francisco 49ers and the San Diego Chargers played an NFL preseason game at Aloha Stadium on August 21, 1976. In August 2019, the NFL returned to the stadium with a preseason game between the Los Angeles Rams and Dallas Cowboys.

The National Football League's all-star game, the Pro Bowl, was held annually at the stadium from 1980 through 2016, except in 2010 and 2015.

Baseball
The stadium served as the home field for the Hawaii Islanders, a Triple-A team competing in the Pacific Coast League, from 1976 to 1987.

In, a three-game regular season series between St. Louis Cardinals and San Diego Padres of Major League Baseball (MLB) was held at the stadium. Called the Padres Paradise Series, the series was played as a doubleheader on April 19 and a nationally broadcast (ESPN) game on April 20. In 1979, the Padres had played a three-game preseason series against the Seibu Lions of Japan's Pacific League at the stadium.

Soccer
On April 7, 1976, the Aloha Soccer Festival triple-header was held at the stadium. In the feature match, Pelé scored four goals as his New York Cosmos defeated Japan, 5-0, in front of a crowd of 21,705. (In the other matches, the NASL's San Diego Jaws routed the Hawaii All-Stars, 6-0, while the Philippines edged Taiwan, 1-0.)

Encouraged by the tournament's success, the San Antonio Thunder became Team Hawaii in 1977, bringing the NASL to the Aloha State. Pelé and the Cosmos returned on April 13, 1977, as 12,877 watched New York defeat Hawaii, 2-1. (None of Team Hawaii's other twelve home games drew even half of that; they managed only 4,543 per game for the season, and moved to Tulsa in 1978.)

Aloha Stadium hosted the inaugural Pan-Pacific Championship (February 20–23, 2008), a knockout soccer tournament, involving four teams from Japan's J-League, North America's Major League Soccer (MLS) and Australia/New Zealand's A-League. The 2012 Hawaiian Islands Invitational was also held at the venue.

The United States women's national soccer team was scheduled to play a game against Trinidad and Tobago as part of their World Cup Winning Victory Tour at the stadium on December 6, 2015; however, the game was canceled the day before gameday due to concerns over the turf being unsafe to play on.

Rugby
On June 2, 2013, the stadium played host to a rugby league test match where Samoa defeated the USA 34–10.

In June, the Brisbane Broncos from the Australasian-based National Rugby League (NRL) competition organized for a rugby league match to be played at Aloha Stadium against NRL rivals Penrith Panthers later in 2015. However, in September the NRL blocked the idea and the game didn't go ahead.

Aloha Stadium also hosted the Aloha World Sevens.

In 2020 it was proposed that Kanaloa Hawai’i, a proposed Major League Rugby (MLR) team, be based at Aloha Stadium after "a few years" in a smaller venue; however, MLR and Kanaloa Hawai’i did not reach an agreement for the team to join the league.

Graduation ceremonies
Aloha Stadium is also the venue for five public high school graduation ceremonies: Radford High School, Mililani High School, Aiea High School, James Campbell High School, and Pearl City High School.

In popular culture
Aloha Stadium appeared in the climax of the 2006 animated television film Leroy & Stitch, the finale film to Lilo & Stitch: The Series and the main continuity of the Lilo & Stitch franchise. In the film's final act, Dr. Hämsterviel and his Leroy army dump Jumba Jookiba's first 624 genetic experiments into the stadium to be destroyed, only for Lilo, Stitch, Jumba, Pleakley, Gantu, and Reuben to arrive and stop Hämsterviel. After a fight between the experiments and the Leroys, the main heroes throw an impromptu concert (initially set up for a fictional event called "Alohapalooza"), performing "Aloha ʻOe" to trigger a failsafe to shut down the Leroys. Although the stadium is not identified by name, it is confirmed to be Aloha Stadium through a special thanks credit in the film's closing credits.

In season three, episode three of the CBS television series NCIS: Hawai'i (first aired February 26, 2024), titled "License to Thrill", Aloha Stadium was the setting for a fictional extreme motorsports exhibition, World of Hyperdrome.

title: Aloha Stadium


text:
Talk:º

Could someone upload an image of this character? I don't know what the characters should be rendered. -- Taku 02:41, Nov 6, 2003 (UTC)

title: Talk:º


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Talk:Moses Blah

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