{"id":8162,"date":"2016-03-17T17:13:20","date_gmt":"2016-03-18T01:13:20","guid":{"rendered":"http:\/\/experimentalmath.info\/blog\/?p=8162"},"modified":"2016-03-17T17:13:20","modified_gmt":"2016-03-18T01:13:20","slug":"andrew-wiles-wins-the-abel-prize","status":"publish","type":"post","link":"https:\/\/experimentalmath.info\/blog\/2016\/03\/andrew-wiles-wins-the-abel-prize\/","title":{"rendered":"Andrew Wiles wins the Abel Prize"},"content":{"rendered":"

In a certainly well-deserved recognition, the Norwegian Academy of Science and Letters has awarded the 2016\u00a0Abel Prize<\/a> to Andrew Wiles<\/a> of the University of Oxford, who in 1995 published a proof of Fermat’s Last Theorem, that centuries-old, maddening conjecture that an<\/sup> + bn<\/sup> = cn<\/sup> has no nontrivial integer solutions except for n = 2.<\/p>\n

Fermat’s Last Theorem<\/a> was first conjectured in 1637 by Pierre de Fermat in 1637, in a cryptic annotated marginal note that Fermat wrote in his copy of Diophantus’ Arithmetica. For 358 years, the problem tantalized generations of mathematicians, who sought in vain for a valid proof. In the 1995 edition of the Guiness Book of World Records, it was cited as the world’s most difficult mathematical problem<\/a>, in part because of the large number of unsuccessful proofs through the ages. Some of these proofs were foolish, but others helped build modern number theory.<\/p>\n

In the mid-1970s, Wiles had trained under Cambridge University based Australian mathematician John Coates<\/a>, who had recently returned to England from teaching at Stanford University. They studied the arithmetic of elliptic curves<\/a>, using the various methods, including Iwasawa theory<\/a>. (A personal note: Prior to working with Wiles, in 1972 John Coates taught one of the present authors (Bailey) a course in Algebra at Stanford.)<\/p>\n

The proof of Fermat’s Last Theorem had its origin in a series of results in the 1980s by Gerhard Frey<\/a> of the University of Duisburg-Essen, Jean-Pierre Serre<\/a> of the Centre National de la Recherch\u00e9 Scientifique College de France, and Ken Ribet<\/a> of the University of California, Berkeley. From their work, it became clear that Fermat’s Last Theorem might be proven as a consequence of a limited form of the Taniyama-Shimura-Weil conjecture, which is now known as the modularity theorem<\/a>.<\/p>\n

Wiles, who had been fascinated by Fermat’s Last Theorem since childhood, decided to pursue a proof. After\u00a0working in secret for several years on the project, on 24 June 1993, he announced<\/a> his result in a lecture at Cambridge University.<\/p>\n

Alas, a few months later a flaw was uncovered in his proof. Finally, in 1995, a full corrected proof was published in Annals of Mathematics<\/a>, with one of the two final papers co-authored with Richard Taylor<\/a>. The proof has stood the test of time — 20 years later no flaw has been uncovered.<\/p>\n

We add our congratulations to Wiles for his landmark achievement, and hope that his example will inspire many other mathematicians to pursue lines of research traditionally thought to be “too difficult.” A brief outline of Andrew Wiles’ proof is presented in the Wikipedia article<\/a> on the topic. Additional information on both\u00a0Wiles and the Abel Prize, modeled on\u00a0the Nobel prize, is available at the Norwegian Academy’s website<\/a>, and in well-written articles in New Scientist<\/a> and Nature<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

In a certainly well-deserved recognition, the Norwegian Academy of Science and Letters has awarded the 2016 Abel Prize to Andrew Wiles of the University of Oxford, who in 1995 published a proof of Fermat’s Last Theorem, that centuries-old, maddening conjecture that an + bn = cn has no nontrivial integer solutions except for n = 2.<\/p>\n

Fermat’s Last Theorem was first conjectured in 1637 by Pierre de Fermat in 1637, in a cryptic annotated marginal note that Fermat wrote in his copy of Diophantus’ Arithmetica. For 358 years, the problem tantalized generations of mathematicians, who sought in vain for a <\/p>\n

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