Andrew Wiles

Sir Andrew John Wiles is a highly distinguished English mathematician. He specializes in number theory, which is the study of numbers and their patterns. Currently, he is a Royal Society Research Professor at the University of Oxford. Wiles is most famous for proving Fermat's Last Theorem. This achievement earned him many prestigious honors. He received the 2016 Abel Prize and the 2017 Copley Medal. In 2000, he was also appointed a Knight Commander of the Order of the British Empire.

Wiles was born on 11 April 1953, in Cambridge, England. His parents were Maurice Frank Wiles and Patricia Wiles. Much of his childhood was spent in Nigeria. While he was not always enthusiastic about formal schooling, he always loved solving mathematical problems. At age ten, he discovered Fermat's Last Theorem in a library book. The theorem was easy to state, but no one could prove it. This fascinated him deeply. He decided he would be the person to solve it. However, he realized his knowledge was too limited at that age. He set the dream aside for many years.

His mathematical career began in earnest after he graduated from Oxford in 1974. He earned his PhD at Clare College, Cambridge, in 1980. Wiles worked on complex topics like elliptic curves and modular forms. He also studied Iwasawa theory and Galois representations. During his career, he held positions at the University of Cambridge and Princeton University. He also worked at the Institute for Advanced Study in Princeton. In 1989, he was elected a Fellow of the Royal Society. These academic roles allowed him to build the deep expertise needed for his greatest challenge.

In 1986, Wiles's focus returned to Fermat's Last Theorem. He read the work of Ken Ribet regarding the epsilon conjecture. This work showed that Fermat's Last Theorem was linked to the modularity theorem. The modularity theorem involves elliptic curves, which are mathematical objects resembling the surface of a torus. It states that these curves are associated with modular forms. Wiles realized that if he could prove a specific part of the modularity theorem, Fermat's Last Theorem would be proven too. This part concerned semistable elliptic curves. He began working on this problem in near-total secrecy for over six years.

Wiles presented his proof to the public in June 1993. However, a major problem arose shortly after. In August 1993, mathematicians discovered a flaw in his proof. The error involved the Selmer group and a tool called an Euler system. Wiles spent more than a year trying to fix this mistake. He was very close to giving up on the project. Then, on 19 September 1994, he had a sudden insight. He worked with his student, Richard Taylor, to find a way around the flaw. They used Galois representations to replace the problematic elliptic curves. They published their successful, completed results in May 1995.

The impact of Wiles's work was massive for the mathematical community. He did not just solve one old puzzle. He created new tools that allowed mathematicians to unify different ideas. For example, in 1999, Richard Taylor and others used his work to prove the full modularity theorem. Wiles's legacy also lives on through his students. Many of them, such as Manjul Bhargava, have won major awards like the Fields Medal. His work helped push mathematics toward the Langlands program. This is a grand vision that tries to unify many different branches of mathematics.

Today, Wiles remains a central figure in the world of mathematics. In 2018, he became the first Regius Professor of Mathematics at Oxford. His life's work is celebrated globally. The Czech Republic even honored his achievement on a postage stamp in 2000.

From a ten-year-old boy in a library to a knighted professor, his journey shows the power of persistence. He turned a childhood fascination into a discovery that changed how we see numbers forever.