Question: What prize did Andrew Wiles win when he proved Fermat's Last Theorem in 1995?

Documents:
source: Andrew Wiles
text: Andrew Wiles Sir Andrew John Wiles (born 11 April 1953) is a British mathematician and a Royal Society Research Professor at the University of Oxford, specialising in number theory. He is best known for proving Fermat's Last Theorem, for which he received the 2016 Abel Prize. Wiles has received numerous other honours, including the Copley Medal, the Royal Society's highest honour, in 2017.

source: Fermat's Last Theorem (book)
text: Fermat's Last Theorem (book) Fermat's Last Theorem is a popular science book (1997) by Simon Singh. It tells the story of the search for a proof of Fermat's last theorem, first conjectured by Pierre de Fermat in 1637, and explores how many mathematicians such as Évariste Galois had tried and failed to provide a proof for the theorem. Despite the efforts of many mathematicians, the proof would remain incomplete until as late as 1995, with the publication of Andrew Wiles' proof of the Theorem. The book is the first mathematics book to become a Number One seller in the United Kingdom, whilst Singh's documentary "The Proof", on which the book was based, won a BAFTA in 1997.

source: P-adic number
text: P-adic number In mathematics, the p -adic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems. The extension is achieved by an alternative interpretation of the concept of "closeness" or absolute value. In particular, p -adic numbers have the interesting property that they are said to be close when their difference is divisible by a high power of p : the higher the power, the closer they are. This property enables p -adic numbers to encode congruence information in a way that turns out to have powerful applications in number theory—including, for example, in the famous proof of Fermat's Last Theorem by Andrew Wiles.

source: Victor Kolyvagin
text: Victor Kolyvagin Victor Alexandrovich Kolyvagin (Russian: Ви́ктор Алекса́ндрович Колыва́гин ) is a Russian mathematician who wrote a series of papers on Euler systems, leading to breakthroughs on the Birch and Swinnerton-Dyer conjecture, and Iwasawa's conjecture for cyclotomic fields. His work also influenced Andrew Wiles's work on Fermat's Last Theorem.

source: Modularity theorem
text: Modularity theorem In mathematics, the modularity theorem (formerly called the Taniyama–Shimura–Weil conjecture and several related names) states that elliptic curves over the field of rational numbers are related to modular forms. Andrew Wiles proved the modularity theorem for semistable elliptic curves, which was enough to imply Fermat's last theorem. Later, Christophe Breuil, Brian Conrad, Fred Diamond and Richard Taylor extended Wiles' techniques to prove the full modularity theorem in 2001. The modularity theorem is a special case of more general conjectures due to Robert Langlands. The Langlands program seeks to attach an automorphic form or automorphic representation (a suitable generalization of a modular form) to more general objects of arithmetic algebraic geometry, such as to every elliptic curve over a number field. Most cases of these extended conjectures have not yet been proved. However, proved that elliptic curves defined over real quadratic fields are modular.

source: Ribet's theorem
text: Ribet's theorem In mathematics, Ribet's theorem (earlier called the epsilon conjecture or ε-conjecture) is a statement in number theory concerning properties of Galois representations associated with modular forms. It was proposed by Jean-Pierre Serre and proven by Ken Ribet. The proof of the epsilon conjecture was a significant step towards the proof of Fermat's Last Theorem. As shown by Serre and Ribet, the Taniyama–Shimura conjecture (whose status was unresolved at the time) and the epsilon conjecture together imply that Fermat's Last Theorem is true.

source: Gerhard Frey
text: Gerhard Frey Gerhard Frey (] ; born 1944) is a German mathematician, known for his work in number theory. His Frey curve, a construction of an elliptic curve from a purported solution to the Fermat equation, was central to Wiles' proof of Fermat's Last Theorem.

source: Math Girls
text: Math Girls Math Girls (数学ガール , Sūgaku gāru ) is the first in a series of math-themed young adult novels of the same name by Japanese author Hiroshi Yuki. It was published by SoftBank Creative in 2007, followed by "Math Girls: Fermat's Last Theorem" in 2008, "Math Girls: Gödel's Incompleteness Theorems" in 2009, and "Math Girls: Random Selection Algorithms" in 2011. As of December 2010, the series had sold over 100,000 books in Japan. On November 23, 2011, an English translation of the book was released by Bento Books, who subsequently released translations of "Fermat's Last Theorem" () and "Gödel's Incompleteness Theorems" () on December 5, 2012 and April 25, 2016, respectively.

source: Wieferich prime
text: Wieferich prime In number theory, a Wieferich prime is a prime number "p" such that "p" divides 2 − 1 , therefore connecting these primes with Fermat's little theorem, which states that every odd prime "p" divides 2 − 1 . Wieferich primes were first described by Arthur Wieferich in 1909 in works pertaining to Fermat's last theorem, at which time both of Fermat's theorems were already well known to mathematicians.

source: Wiles's proof of Fermat's Last Theorem
text: Wiles's proof of Fermat's Last Theorem Wiles's proof of Fermat's Last Theorem is a proof, by British mathematician Andrew Wiles, of a special case of the modularity theorem for elliptic curves. Together with Ribet's theorem, it provides a proof for Fermat's Last Theorem. Both Fermat's Last Theorem and the modularity theorem were almost universally considered inaccessible to proof by contemporaneous mathematicians, seen as virtually impossible to prove using current knowledge.

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Answer: 2016 Abel Prize