OpenLLM-France/wikimedia huggingface dataset:
# Proofs from THE BOOK

Proofs from THE BOOK is a book of mathematical proofs by Martin Aigner and Günter M. Ziegler. The book is dedicated to the mathematician Paul Erdős, who often referred to "The Book" in which God keeps the most elegant proof of each mathematical theorem. During a lecture in 1985, Erdős said, "You don't have to believe in God, but you should believe in The Book."

## Content

Proofs from THE BOOK contains 32 sections (45 in the sixth edition), each devoted to one theorem but often containing multiple proofs and related results. It spans a broad range of mathematical fields: number theory, geometry, analysis, combinatorics and graph theory. Erdős himself made many suggestions for the book, but died before its publication. The book is illustrated by Karl Heinrich Hofmann [de]. It has gone through six editions in English, and has been translated into Persian, French, German, Hungarian, Italian, Japanese, Chinese, Polish, Portuguese, Korean, Turkish, Russian, Spanish and Greek.
The American Mathematical Society awarded the 2018 Leroy P. Steele Prize for Mathematical Exposition to Aigner and Ziegler for this book.
The proofs include:
* Six proofs of the infinitude of the primes, including Euclid's and Furstenberg's
* Proof of Bertrand's postulate
* Fermat's theorem on sums of two squares
* Two proofs of the Law of quadratic reciprocity
* Proof of Wedderburn's little theorem asserting that every finite division ring is a field
* Four proofs of the Basel problem
* Proof that e is irrational (also showing the irrationality of certain related numbers)
* Hilbert's third problem
* Sylvester–Gallai theorem and De Bruijn–Erdős theorem
* Cauchy's theorem
* Borsuk's conjecture
* Schröder–Bernstein theorem
* Wetzel's problem on families of analytic functions with few distinct values
* The fundamental theorem of algebra
* Monsky's theorem (4th edition)
* Van der Waerden's conjecture
* Littlewood–Offord lemma
* Buffon's needle problem
* Sperner's theorem, Erdős–Ko–Rado theorem and Hall's theorem
* Lindström–Gessel–Viennot lemma and the Cauchy–Binet formula
* Four proofs of Cayley's formula
* Kakeya sets in vector spaces over finite fields
* Bregman–Minc inequality
* Dinitz problem
* Steve Fisk's proof of the art gallery theorem
* Five proofs of Turán's theorem
* Shannon capacity and Lovász number
* Chromatic number of Kneser graphs
* Friendship theorem
* Some proofs using the probabilistic method
# Sarah Hubbard

Sarah Hubbard is a member of the Regents of the University of Michigan first elected in 2020. She is a Republican.

## Education

She attended the University of Michigan for her B.A. and M.B.A. and Western Michigan University for her M.P.A.

## Career

Hubbard was first elected statewide in 2020 for a term ending in 2029 defeating the Democratic incumbent. She served as chair of the board for the 2023–2024 academic year.
# Wall Street Mill

The Wall Street Mill in Joshua Tree National Park was a complete and operable gold ore crushing mill featuring late-19th century two-stamp mill machinery. Consequently, the significance encompasses the mill machinery, the building which houses it, the well which supplied water for the mill's operation, and the well pump. It is the only gold ore crushing mill in the region that retains integrity.
The stamp mill building is framed with heavy timber and built on a downward sloping hillside to take advantage of gravity in the milling process. The roof and some of the exterior walls are covered with corrugated sheet metal, while some of the exterior walls have either vertical or horizontal wooden siding. At the top of the building a long wooden ramp supports the track of an ore tramway which carried ore from where it was unloaded from trucks to the top of the mill above the two-stamp Baker Iron Works crusher. A gasoline engine powered the mill; it was built by the Western Gas Engine Company of Los Angeles. A Myer concentrating table was used in separating the gold from the ore.
The complex included the mill, a well, a bunkhouse and an outhouse. The supporting buildings are largely ruinous.
The mill was built by Bill Keys, a local rancher and miner, using equipment moved from Pinon Wells. In the 1940s, Keys was involved in a dispute with Worth Bagley over access to the Wall Street Mill. Keys shot and killed Bagley in 1943. Keys then turned himself and was convicted of manslaughter. He was sent to San Quentin State Penitentiary for 10 years. His wife Frances wrote to lawyer Earle Stanley Gardner for help and, with the lawyers aide, had the case reopened. They found many facts that were not brought out during the trial, leading to Keys's release. He served five years of a ten-year sentence and ultimately received a full pardon. Upon arriving back home from prison, Keys erected a stone commemorating the event with the inscription "Here is where Worth Bagley bit the dust at the hand of W. F. Keys, May 11, 1943." The marker is not a part of the Wall Street Mill historic district.
# U Know It Ain't Love

"U Know It Ain't Love" is the debut single by R.J., featuring vocals from American rapper Pitbull. The song was written by Giovanbattista Giorgilli, Armando Christian Perez, Stephen Singer, Steve Obas, Shauna Gaye, Melissa McKenzie and produced by David May, Michel Schuhmacher, Marc "Marquito" Zibung. It was released in Belgium and Kontor, Ultra Records, JVC Japan, as a digital download on 28 November 2011.

## Music video

A music video to accompany the release of "U Know It Ain't Love" was first released onto YouTube on 25 November 2011 at a total length of three minutes and twenty-nine seconds.

## Track listing

* Digital download
* "U Know It Ain't Love" (David May Radio Edit) – 3:23
* "U Know It Ain't Love" (David May Extended Mix) – 4:19

## Credits and personnel

* Lead vocals – R.J. and Pitbull
* Producers Stephen Singer, Vanni Giorgilli, David May, Michel Schuhmacher, Marc "Marquito" Zibung, Sebastian Knaak
* Lyrics – Giovanbattista Giorgilli, Armando Christian Perez, Stephen Singer, Steve Obas, Shauna Gaye, Melissa McKenzie
* Label: BIP Records

## Charts

| Chart (2011–2012) | Peak position |
| Austria (Ö3 Austria Top 40) | 52 |
| Belgium (Ultratop 50 Flanders) | 50 |
| Belgium (Ultratip Bubbling Under Wallonia) | 34 |
| France (SNEP) | 185 |
| Germany (GfK) | 49 |
| Netherlands (Single Top 100) | 18 |
| Romania (Romanian Top 100) | 29 |
| Switzerland (Schweizer Hitparade) | 43 |

## Release history

| Region | Date | Format | Label |
| Belgium | 28 November 2011 | Digital Download | BIP Records |
# Freddy Oncoy

Freddy Alejandro Oncoy Huarote (born 29 September 2000) is a Peruvian footballer who plays as a midfielder for Peruvian Primera División side UTC.

## Ccareer
### Club career

Oncoy was promoted to the first team squad in the summer 2018 at the age of 17. He got his official debut for Sport Boys on 28 October 2018 against Carlos A. Mannucci. Oncoy started on the bench, before replacing Luis Magallanes in the 58th minute. Oncoy made a total of 4 appearances for Sport Boys in the 2019 Torneo Descentralizado season.
In December 2024, ahead of the 2025 season, Oncoy signed with Peruvian Primera División side UTC Cajamarca.

## International career

Oncoy made two appearances for Peru U17 in the 2017 South American U-17 Championship against Brazil U17 and Argentina U17. He also played in a friendly game against Bolivia U17.
# Lamson

Lamson may refer to:

## Surname

* Chuck Lamson (1939–2015), American football player
* Father Lamson, 19th-century American eccentric, attended abolitionist meetings in a long white beard and white robe, and carrying a large scythe
* Fred I. Lamson (1910–1981), American politician, Mayor of Malden, Massachusetts, and member of the Massachusetts Senate
* George Henry Lamson (1852–1882), American doctor and murderer
* Gertrude Lamson, or Nance O'Neil (1874–1965), American actress of stage and silent cinema of the early 20th century
* Justin Lamson (born 2002), American football player
* Laura Lamson (1948–2008), American screenwriter and university lecturer, based in England throughout her career
* Lucy Stedman Lamson (1857–1926), American business woman, educator
* Otis Lamson (1876–1956), American football player and coach
* Roswell Lamson (1838–1903), officer in the United States Navy during the American Civil War
* William Lamson (born 1977), American installation, performance and generative artist

## Middle name

* Carl Lamson Carmer (1893–1976), American author of nonfiction, memoirs and novels
* Mortimer Lamson Earle (1864–1905), American classical scholar
* Edward Lamson Henry (1841–1919), American genre painter
* Flora Lamson Hewlett (1914–1977), American philanthropist
* Nathaniel Lamson Howard (1884–1949), American railroad executive
* Thomas Lamson Ludington (born 1953), United States federal judge
* Edwin Lamson Stanton (1814–1869), Secretary of War under the Lincoln Administration during most of the American Civil War

## Buildings

* Lamson Farm, a working 18th century farm and town-owned conservation land in Mont Vernon, New Hampshire
* Newton Lamson House, historic house at 33 Chestnut Street in Stoneham, Massachusetts
* Rufus Lamson House, historic house at 72-74 Hampshire Street in Cambridge, Massachusetts

## Ships

* USS Lamson (DD-18), Smith class destroyer in the United States Navy during World War I
* USS Lamson (DD-328), Clemson-class destroyer in the United States Navy following World War I
* USS Lamson (DD-367), Mahan-class destroyer of the United States Navy named for Roswell Hawkes Lamson

## Engineering

* Lamson L-106 Alcor, American, high-wing, experimental, pressurized research glider
* Lamson tube, systems in which cylindrical containers are propelled through a network of tubes by compressed air or by partial vacuum
* Lamson Engineering Company Ltd, the best known British manufacturer of Cash Ball, Rapid Wire and Pneumatic tube delivery systems from 1937 to 1976
* Lamson PL-1 Quark, American high-wing, single-seat, glider that was designed and constructed by Philip Lamson, first flying in early 1965

## Other

* Battle of Lamson or Operation Lam Son 719, offensive campaign conducted in Laos by the armed forces of the Republic of Vietnam in 1971
* Flora Lamson Hewlett Library, houses one of the largest collections of theological books in the United States
# Islara Rodríguez

Islara U. Rodríguez Vega (born 24 April 1988) is an American-born Puerto Rican lawyer and a retired footballer who has played as a forward. She has been a member of the Puerto Rico women's national team.

## Early and personal life

Rodríguez was born and raised in Houston, Texas to José Rodríguez and Amarilis Vega. She has married a Turk named Volkan Irgit.

## International goals

Scores and results list Puerto Rico's goal tally first.
| No. | Date | Venue | Opponent | Score | Result | Competition |
| 1 | 19 March 2010 | Juan Ramón Loubriel Stadium, Bayamón, Puerto Rico | Saint Kitts and Nevis | 3–0 | 7–0 | 2010 CONCACAF Women's World Cup Qualifying qualification |
| 2 | 28 July 2010 | Estadio Metropolitano, Mérida, Venezuela | Trinidad and Tobago | 1–2 | 2–3 | 2010 Central American and Caribbean Games |
# 15–16th & Locust station

15–16th & Locust station is the western terminus of the PATCO Speedline rapid transit route at 15th and Locust Streets in the Rittenhouse Square neighborhood of Center City Philadelphia. The station has a single island platform with a fare mezzanine above. The mezzanine level connects to the Downtown Link concourse, which connects to Walnut–Locust stations in the Center City area.

## Notable places nearby

The station is within walking distance of the following notable places:
* Academy of Music
* Avenue of the Arts
* Kimmel Center for the Performing Arts
* Miller Theatre
* Rittenhouse Square
* University of the Arts
* Wilma Theater
# Le Vésinet–Le Pecq station

Le Vésinet–Le Pecq is a railway station in Le Vésinet, France, built in 1972, on the A1 branch of the Paris Region RER commuter rail line A. It primarily serves the communities of Le Vésinet, Le Pecq, and southern Montesson in the western suburbs of Paris.

## History

The station was first established as the western terminus of the Paris–Saint-Germain-en-Laye railway in 1937. The desired terminus at Saint-Germain-en-Laye was on a bluff at the far side of the Seine, at the end of a gradient that the steam locomotives of the time could not climb. Instead, an atmospheric railway was built across the Seine to Saint-Germain, which could accommodate the grade. The atmospheric railway operated beginning in 1847. In 1860, when more powerful steam locomotives were introduced that could reach Saint-Germain, the atmospheric line was removed. A new station was built in 1861, and the old station was abandoned. The buried site was exhumed during archaeological excavations in 2017. The time from Le Pecq to Paris dropped from a four-hour boat trip to 25-30 minutes by train. An 1858 accident attributed to faulty brakes on the atmospheric line killed three people, hastening the conversion to steam power.
The second station was built farther back from the river in Le Vésinet rather than Le Pecq in 1861, but retained its name. This was replaced in 1955 with a much more utilitarian structure on Rue Watteau. The old station was retained as a baggage facility by the SNCF and RATP. When the line came under the control of the RATP in 1972, the present station was constructed for RER Line A, somewhat to the south of the 1955 station, which remains as a community center. The new station adopted the name Le Vésinet–Le Pecq. The second station survived until 2019, when structural failure led the town to demolish it.

## Services and Station

The frequency of services is a train every 10 minutes during peak hours, 12 trains per hour at peak times, and a train every 15 minutes in the evenings. It also acts as a terminus for some trains at peak hours.
This station contains 2 platforms with 3 tracks, for which the third (center track) is used solely for westbound trains making their terminus here instead of Saint-Germain-en-Laye. The two outer tracks are used for standard routing trains.
Trains departing eastward from this station take about 25 minutes (with stops) to reach the central Châtelet – Les Halles station in Paris. Westbound trains take about 6 minutes to reach the terminus station St. Germain-en-Laye.

## Connections
### Bus

The station is served by lines 3A, 3AC, 3C, 7, 7SC, 7SG, 19, 20, 21, 21M, and 22 of the RATP/SNCF bus network, and afterhours via line N153 of the Noctilien (night-time) bus network.
48°53′53″N 2°07′19″E﻿ / ﻿48.898°N 2.122°E﻿ / 48.898; 2.122
# Podzamcze, Lubusz Voivodeship

Podzamcze is a village in the administrative district of Gmina Babimost, within Zielona Góra County, Lubusz Voivodeship, in western Poland.
# Department of Huancavelica

Huancavelica (Spanish pronunciation: ) is a department and region in Peru with an area of 22,131.47 km$^2$ (8,545.01 sq mi) and a population of 347,639 (2017 census). The capital is the city Huancavelica. The region is bordered by the departments of Lima and Ica in the west, Junín in the north, and Ayacucho in the east.

## Political division

The department is divided into seven provinces.
Province (Capital)
* Acobamba Province (Acobamba)
* Angaraes Province (Lircay)
* Castrovirreyna Province (Castrovirreyna)
* Churcampa Province (Churcampa)
* Huancavelica Province (Huancavelica)
* Huaytará Province (Huaytará)
* Tayacaja Province (Pampas)
The main cities are Huancavelica, Pampas and Lircay. There are many little districts like Querco in Huancavelica. Querco is a nice little town. Most of the residents are agricultors. They own cattle, sheep, pigs, horses, mules, llamas, goats, chickens, and donkeys.

## Demographics

The region is mostly inhabited by indigenous people of Quechua descent.

### Languages

According to the 2007 Peru Census, the language learnt first by most of the residents was Quechua (64.03%) followed by Spanish (35.67%). The Quechua variety spoken in Huancavelica is Chanka Quechua. The following table shows the results concerning the language learnt first in the department of Huancavelica by province:
| Province | Quechua | Aymara | Asháninka | Another native language | Spanish | Foreign language | Deaf or mute | Total |
| Acobamba | 51,338 | 49 | 11 | 10 | 8,261 | - | 78 | 59,747 |
| Angaraes | 40,669 | 62 | 7 | 7 | 10,922 | - | 56 | 51,723 |
| Castrovirreyna | 4,093 | 14 | 1 | 3 | 14,168 | - | 73 | 18,352 |
| Churcampa | 33,025 | 27 | 4 | 19 | 8,542 | 3 | 127 | 41,747 |
| Huancavelica | 73,340 | 117 | 28 | 13 | 59,544 | 4 | 157 | 133,203 |
| Huaytara | 5,670 | 13 | 4 | 3 | 16,218 | 2 | 28 | 21,938 |
| Tayacaja | 63,950 | 91 | 23 | 15 | 33,900 | 1 | 242 | 98,222 |
| Total | 272,085 | 373 | 78 | 70 | 151,555 | 10 | 761 | 424,932 |
| % | 64.03 | 0.09 | 0.02 | 0.02 | 35.67 | 0.00 | 0.18 | 100.00 |

## Education

The National University of Huancavelica is the only university in the region and it has branches in Pampas, Lircay, Acobamba and Castrovirreyna.

## Health

The region has two hospitals located in Huancavelica and Pampas. There are clinics and medical post in most of the towns.

## Transportation

The region is connected with the neighboring regions by national roads, which are paved in most cases. There are regional and local roads that are serving the towns of the regions. Huancavelica has a train service with the city of Huancayo.

## Notable natives

* Lina Medina, world's youngest mother

## Authorities

* Governor: Rubén Alva Ochoa (2015–2018)
# Połupin

Połupin is a village in the administrative district of Gmina Dąbie, within Krosno Odrzańskie County, Lubusz Voivodeship, in western Poland. It lies approximately 3 km (2 mi) north-west of Dąbie, 3 km (2 mi) east of Krosno Odrzańskie, and 28 km (17 mi) west of Zielona Góra.
# Parmjit Singh Gill

Parmjit Singh Gill (born 20 December 1966) is a British Liberal Democrat politician. As Member of Parliament for Leicester South from July 2004 to May 2005, he was the first ethnic-minority Liberal Democrat MP.
He was first elected as Liberal Democrat councillor for Leicester City Council's Stoneygate Ward, before being elected to the House of Commons at the Leicester South by-election on 15 July 2004. He contested the seat again at the 2005 general election, but this time came second to the Labour Party candidate, Sir Peter Soulsby. He continued to serve as councillor for Stoneygate Ward until he was defeated in May 2011.
He was initially selected to run as the Liberal Democrat candidate for the 2011 Leicester South by-election after Soulsby stood down to run for mayor for Leicester. However, he stood down after a short time, citing family pressures and was replaced by Zuffar Haq.
He works as a local authority information management and security consultant for Charnwood Borough Council. Prior to that he worked as a data protection administrator for Leicester City Council.
Gill was the Liberal Democrat candidate in the 2023 Leicester mayoral election. He came in third place. Gill was the Liberal Democrat candidate in West Bromwich at the 2024 general election and came in sixth place out of seven candidates.

## Personal life

He is married to Juliet Gill, and the couple have a son and daughter.
# Pożarów, Lubusz Voivodeship

Pożarów is a village in the administrative district of Gmina Żagań, within Żagań County, Lubusz Voivodeship, in western Poland. It lies approximately 4 km (2 mi) north of Żagań and 35 km (22 mi) south of Zielona Góra.
# Xavier Chen

Xavier Chen (Chinese: 陳昌源/夏維耶; born 5 October 1983) is a former professional footballer who played as a right-back. He began his youth career with Anderlecht before moving to KV Kortrijk where he first played at senior level (2003–2007). After Kortrijk, he spent six years at KV Mechelen (2007–2013) and two at Guizhou Renhe (2013–2015) before returning to KV Mechelen. Born in Belgium, he represented Chinese Taipei at international level.

## Personal life

Chen was born to a French mother and a Taiwanese father. His paternal grandfather is a former diplomat who still lives in Taiwan.

## Club career

Chen started his senior career in KV Kortrijk, but gained recognition in his first stint with KV Mechelen, where he became captain. Due to the inconvenience of traveling back and forth between Belgium and Taiwan, Chen decided to move to Chinese side Guizhou Renhe when he accepted CTFA's invitation to play for the national team. In January 2016, Chen returned to KV Mechelen, stating that he only wanted to play for a maximum of three years in China. A few Chinese teams showed interest to sign him, but he ultimately decided to return to his country of birth. Altogether, Chen spent seven seasons with KV Mechelen.

## International career

Chen's eligibility to play for Chinese Taipei was discovered by the CTFA public relations director Chen Chia-Ming in 2009 and Chen was invited to play for the national team. The Chinese Football Association of the mainland had also made an attempt to recruit Chen three months after the CTFA did. On 24 May 2011, encouraged by his relatives, Chen elected to play for Chinese Taipei.
Chen made his international debut against Malaysia on 3 July 2011 and scored the winning goal. This marked the first time in 10 years that Chinese Taipei beat an opponent that was ranked in the FIFA top 150. The attendance of the game was a record breaking at 15,335, which was 10,000 higher than average. On 9 October 2015, Chen scored the third goal in a 5–1 victory over Macau.

### International goals

    Scores and results list Taiwan's goal tally first, score column indicates score after each Chen goal.
List of international goals scored by Xavier Chen :
| No. | Date | Venue | Opponent | Score | Result | Competition |
| 1 | 3 July 2011 | Taipei Municipal Stadium, Taipei, Taiwan | Malaysia | 3–2 | 3–2 | 2014 FIFA World Cup qualification |
| 2 | 9 October 2015 | Taipei Municipal Stadium, Taipei, Taiwan | Macau | 3–1 | 5–1 | Friendly |
| 3 | 10 June 2017 | Jalan Besar Stadium, Kallang, Singapore | Singapore | 1–1 | 2–1 | 2019 AFC Asian Cup qualification |

## Honours

Guizhou Renhe
* Chinese FA Cup: 2013
* Chinese FA Super Cup: 2014
# Jiří Brdečka

Jiří Brdečka (24 December 1917 – 2 June 1982) was a Czech writer, artist, and film director.

## Life

Brdečka was born in Hranice (then in Austria-Hungary) to a literary family, as his father, Otakar Brdečka (1881 – 1930), was a writer under the pseudonym Alfa. Brdečka studied philosophy and aesthetics at Charles University in Prague until the German occupation of Czechoslovakia forced the closing of the school in 1939. He then became an administrative clerk at the Prague Municipal Museum and found occasional work as a newspaper journalist and cartoonist.
He worked as a press agent for the studio Lucernafilm [cs] from summer 1941 to the end of 1942. In 1943 Brdečka took a job as an animator, and by 1949 he was working as a film director and screenwriter at Barrandov Studios. He began directing animated films on his own in 1958. In addition to his film work he also worked as a journalist, a film critic and a novelist. Brdečka's work is marked by its droll intellectual humor, often featuring an extensive use of hyperbole, satire, and literary illusions.
He had one daughter, the writer and film critic Tereza Brdečková [cs] (born 1952).
Brdečka died in 1982 in Prague.

## Selected filmography
### Director

* Wedding in the Coral Sea (1944)
* Springman and the SS (1946)

### Screenwriter

* Springman and the SS (1946)
* The Emperor's Nightingale (1948)
* The Emperor and the Golem (1951)
* Old Czech Legends (1951)
* Lost Children (1956)
* The Fabulous World of Jules Verne (1958)
* A Midsummer Night's Dream (1959)
* The Fabulous Baron Munchausen (1961)
* The Cassandra Cat (1963)
* Lemonade Joe (1964)
* Dinner for Adele (1977)
* The Prince and the Evening Star (1979)
* The Mysterious Castle in the Carpathians (1981)