Perseverance led to proof of ancient theorem

The man who solved what seemed to be an insoluble problem is to address a Royal Irish Academy/'Irish Times' lecture

The man who solved what seemed to be an insoluble problem is to address a Royal Irish Academy/'Irish Times' lecture. Dick Ahlstrom reports

The mathematician who cracked Fermat's Last Theorem will deliver a free public lecture in Dublin later this month, describing how he overcame a supposedly insolvable mathematical problem. The work entailed a remarkable seven-year battle that has since sparked a popular book and garnered a collection of important awards.

Prof Andrew John Wiles was just 10 when he happened to pick up a book on mathematics at his local library that described Fermat's deceptively simple Theorem. It states that xn + yn = zn has no non-zero integer solutions for x, y or z when n is greater than two.

Wiles was captivated that he, a youngster, could understand the equation. But understanding it was one thing and providing a mathematical proof was another. It represented a challenge that he would need many years to overcome.

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Wiles comes to Dublin on Thursday, October 16th to deliver the annual Hamilton Lecture. Organised by the Royal Irish Academy and The Irish Times and sponsored by DEPFA Bank plc, the Hamilton Lecture commemorates Ireland's greatest mathematician, William Rowan Hamilton. October 16th is the anniversary of the day in 1843 on which Hamilton discovered quaternions, an advanced form of algebra that is used, amongst other things, to create the computer effects seen in the film, Matrix Reloaded.

Wiles' lecture, entitled "Solving Equations", takes place at 7 p.m.October 16th in the Burke lecture theatre in the Arts block, Trinity College, Dublin. He will also present the Hamilton Prize in Mathematics to nine students from each of Ireland's universities, north and south. The €1,000 prizes are given to the top students in the penultimate year of their mathematics studies at the universities.

The creator of the Theorem, Pierre de Fermat, who died in 1665, was a number theorist, but only in his spare time. In fact he was a lawyer and only an amateur mathematician. Even so, he was an accomplished one, and to avoid his work being lost forever, his son Samuel collected his correspondence and papers for publication. This brought the Last Theorem into the public domain and challenged generations of mathematicians who sought a proof for it.

The proof remained elusive until the 10-year-old Wiles encountered the Theorem in 1963. He studied at Cambridge, Harvard, and in Germany, but his PhD was not related to Fermat's Theorem. He took up a post in the early 1980s at the Institute for Advanced Studies in Princeton, and while there he encountered work done by others on a mathematical concept known as the "Shimura-Taniyama conjecture".

He immediately realised that if he could solve this conjecture then a proof of Fermat's Last Theorem would follow. Wiles abandoned all other research and spent the next seven years struggling with the conjecture and the Theorem. He got close to a proof in June 1993, but a subtle error prevented a claim being made that the Theorem had been proved. In late 1994 he decided to give it one more try.

"Suddenly, totally unexpectedly, I had this incredible revelation," he later wrote. "It was so indescribably beautiful, it was so simple and so elegant, and I just stared in disbelief for 20 minutes, then during the day I walked round the department. I'd keep coming back to my desk to see it was still there - it was still there."

He published the proof in 1995 and received a string of important awards for his work. "I had this very rare privilege of being able to pursue in my adult life what had been my childhood dream," Wiles wrote.

To obtain a free ticket for this event, tel: 1550 114709 or 0906 604 0249 (from Northern Ireland) and leave your name, address, telephone number and the number of tickets you require (maximum two tickets per person). The phone lines will remain open until the 400 placesare fully booked. Calls cost 74 cent per minute, but may be more expensive from mobile phones.

NUI Maynooth is organising its annual Hamilton Walk along the Royal Canal, which follows the route Hamilton took with his wife Helen on October 16th, 1843, from his residence at Dunsink Observatory to the Royal Irish Academy. He was inspired to create quaternion algebra as he reached Broombridge on the canal. Those wishing to join the walk should contact Dr Fiacre Ó Cairbre, tel: 01-7083763.