### Sir Andrew John Wiles

Born 11 April 1953, Cambridge, UK

Silver Plaque of the IMU (1998) “for the proof of Fermat’s Last Theorem.”

Abel Prize (2016) “for his stunning proof of Fermat’s Last Theorem by way of the modularity conjecture for semi-stable elliptic curves, opening a new era in number theory.”

Wiles was fascinated by Fermat’s Last Theorem already as a teenager. His father was a theologian and later became Regius Professor of Divinity at the University of Oxford. Wiles studied mathematics at Oxford. In 1974 he got the Bachelor’s degree at Merton College there. The following year he went to Clare College, Cambridge to begin his doctorate, advised by John Coates. In this work, Wiles collaborated with Coates on the Iwasawa theory of elliptic curves. Although elliptic curves played a role in Wiles’ later solution of Fermat’s theorem, his doctoral thesis dealt with another famous problem in mathematics, the conjecture of Birch and Swinnerton-Dyer. Between 1977 and 1980 he worked as a Benjamin Peirce Assistant Professor at Harvard University and was at the same time a Junior Research Fellow at Clare College, Cambridge. After brief visits to Bonn and Paris, in 1982 he became a professor at Princeton University, where he stayed for nearly 30 years. In later years he divided his time with the Institute for Advanced Study. In 2011 he moved to Oxford as a Royal Society Research Professor.

Sir Andrew Wiles received besides the silver plaque of the IMU numerous other awards, including the Fermat Prize (1995), the Ostrowski Prize (1995), the Cole Prize (1996), the Wolf Prize (1995/96), the Royal Medal of the Royal Society (1996), the Wolfskehl Prize (1997), the Shaw Prize (2005) and the Abel Prize (2016). In 1989 he became a Fellow of the Royal Society and in 1996 he became a foreign member of the National Academy of Sciences of the United States. In 2000 he received a knighthood from the Queen of England. Sir Wiles also received the Copley Medal 2017 of the Royal Society.

Andrew Wiles has been a celebrity since he completed the proof of Fermat’s theorem in the 1990s – a project to which he had devoted himself with immense stamina and strategic planning over a decade. He occasionally published work on other themes he had previously written and saved up, to not raise any discussion on what he was actually working on.

Fermat’s conjecture dates from about 1637. At that time the judge and mathematician Pierre de Fermat (1601-1665) was studying Diophantine equations, that is polynomial equations in more than one variable, and devising methods for finding solutions in integers or rationals, or proving that none exist. Fermat had suspected that the equation x^n + y^n = z^n cannot be satisfied with integers x, y and z when n is greater than or equal to 3 – and he claimed to have a proof for it (which he never published).

It took around 340 years until Gerhard Frey and Ken Ribet found a relationship between Fermat’s conjecture and a contemporary mathematical conjecture, called the Shimura-Taniyama conjecture. This conjecture said that every rational elliptic curve is associated to a so-called modular form. Frey and Ribet showed that one can construct an elliptic curve by the means of a fictitious solution of Fermat and that this elliptic curve could not then be associated to a modular form. If the Shimura-Taniyama conjecture was true, then such a solution could not be constructed and so Fermat’s conjecture should be correct.

After many years of hard work, Sir Andrew Wiles proved enough of the Shimura-Taniyama conjecture to finally settle ‘Fermat’s Last Theorem’.