Andrew Wiles (born 1953) is an English mathematician best known for proving Fermat's Last Theorem, a statement in number theory that had resisted proof for more than three centuries. [1] Completed in 1994, his work established the modularity of a broad class of elliptic curves and is regarded as a landmark in modern mathematics. [2] For this achievement he received numerous honours, including the 2016 Abel Prize. [3]
Early life and education
Andrew John Wiles was born on 11 April 1953 in Cambridge, England. [1] He attended The Leys School before reading mathematics at Merton College, Oxford, and then pursued doctoral research at Clare College, Cambridge, completing his PhD in 1980 under the number theorist John Coates. [1] His early work centred on the arithmetic of elliptic curves and Iwasawa theory, fields that would later prove central to his most famous result. [3]
Fermat's Last Theorem
Fermat's Last Theorem asserts that no three positive integers can satisfy the equation an + bn = cn for any integer exponent greater than two. First noted by Pierre de Fermat in the 1630s, the claim remained unproven for over 350 years despite the efforts of many mathematicians. [2] Working largely in private at Princeton University for roughly seven years, Wiles pursued the problem through the Taniyama-Shimura-Weil conjecture, which links elliptic curves to modular forms. [2]
Wiles first announced a proof in 1993, but reviewers identified a gap in the argument. With the help of his former student Richard Taylor, he repaired the flaw, and the completed proof appeared in the Annals of Mathematics in 1995. [1] By establishing the modularity of semistable elliptic curves, the proof yielded Fermat's Last Theorem as a consequence and united several strands of number theory. [2]
Recognition
Because Wiles was past the age of forty when the proof was confirmed, he was ineligible for the Fields Medal; in 1998 the International Mathematical Union presented him with a special silver plaque instead. [1] He was elected a Fellow of the Royal Society and, in 2000, appointed a Knight Commander of the Order of the British Empire. [1] Later honours included the Wolf Prize in Mathematics, the 2016 Abel Prize, and the Royal Society's Copley Medal in 2017. [3]
Later career and legacy
After many years as a professor at Princeton University, Wiles returned to the University of Oxford, where he was named Regius Professor of Mathematics. [1] His proof is widely viewed as one of the great achievements of twentieth-century mathematics, both for settling a celebrated open question and for demonstrating the depth of the connections between elliptic curves and modular forms. [3] The episode also brought unusual public attention to research in pure mathematics. [2]
