Andrew Wiles
Andrew Wiles is a prominent British mathematician renowned for his proof of Fermat's Last Theorem, a mathematical challenge that remained unsolved for over 350 years. Born on April 11, 1953, in Cambridge, England, Wiles developed a passion for mathematics at a young age, influenced by the history surrounding Fermat's Last Theorem. He pursued his studies at Oxford and Cambridge, ultimately becoming a professor at Princeton University. After years of secretive work, Wiles announced his proof in 1993, which combined advanced concepts from number theory and modern mathematics. Despite an initial error in his proof, he successfully corrected it with assistance from a former student, securing his place in mathematical history. Wiles has received numerous prestigious awards throughout his career, including the Abel Prize and the Copley Medal. He continues to be active in mathematics, holding a position as a professor emeritus at Princeton and having the Mathematical Institute at Oxford named in his honor.
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Andrew Wiles
SUMMARY: British mathematician Andrew Wiles is known for his proof of Fermat's Last Theorem, which came over 350 years after the theorem's conjecture in a marginal comment. A renowned specialist in number theory, Wiles served as a professor at the University of Oxford and Princeton University and won many mathematics awards during his career.
Andrew Wiles is most well-known for solving Fermat’s Last Theorem, for which he received the Abel Prize and the Royal Society's Copley Medal. He also won many other awards across his illustrious career, including the prestigious MacArthur Fellowship. For seven years, Wiles worked in unprecedented secrecy, struggling to solve Fermat’s Last Theorem, a problem that had perplexed and motivated mathematicians for three centuries. Wiles’s eventual solution brought him both fame and personal satisfaction. He said of his accomplishment, "I had this very rare privilege of being able to pursue in my adult life what had been my childhood dream." This work also brought him pain when a subtle but fundamental error was discovered in his proof. Wiles eventually fixed the mistake, solidifying his magnificent achievement and permanent place in history.
Fermat’s Last Theorem
Fermat’s Last Theorem states that the equation xn+yn=zn has no positive whole number solutions for n>2. In other words, while the Pythagorean Theoremx2+y2=z2 has whole number solutions (such as x=3, y=4, and z=5), similar equations with larger exponents, like x3+y3=z3 and x4+y4=z4, have no positive whole number solutions. French mathematician Pierre Fermat (1601–1665) wrote in the margin of a book that he had discovered a remarkable proof for this theorem, but that the margin was too small to contain it. For the next three centuries, the best mathematicians in the world sought a solution to this problem, and these attempts inspired many new mathematical ideas and theories.
Wiles’s Proof
Andrew John Wiles was born in Cambridge, England, on April 11, 1953. As a ten-year-old, he already loved solving mathematical problems. He read about the history of Fermat’s Last Theorem in a library book about mathematics. Despite its long history, this problem was simple enough for him to understand, and it fascinated and motivated him. He went on to earn a BA from Merton College, Oxford, in 1974 and a PhD from Clare College, Cambridge, in 1980. He worked as a junior research fellow at Cambridge before taking an appointment at Harvard University, and then joined the faculty at Princeton University in 1982.
As Wiles's mathematical knowledge became more advanced, he realized that there were no new techniques available to solve Fermat’s Last Theorem. When the theorem became linked to modern mathematical methods in algebraic geometry, he resumed his work. The quest to find a proof of Fermat’s Last Theorem finally came to an end when Wiles announced his results in 1993. He had worked in isolation on the problem for many years while on the faculty at Princeton, and his announcement came as a surprise to the mathematics community. Wiles's work combined two fields of mathematics, elliptical functions and modular forms, to solve the elusive problem.
Wiles directly proved what is known as the Taniyama–Shimura Conjecture. Goro Shimura and Yutaka Taniyama were two Japanese mathematicians who, in the 1950s, conjectured that there was a relationship between elliptical equations and modular forms. Later, thanks to the earlier work of mathematicians Gerhard Frey, Ken Ribet, and Barry Mazur, it was shown that if the Taniyama–Shimura Conjecture were true, then so was Fermat’s Last Theorem. His results were presented in a dramatic series of lectures at a conference in Cambridge, England.
However, not long after Wiles announced his discovery, an error was found in one section of the long and difficult proof. With the help of one of his former students, Richard Taylor, Wiles was able to make the necessary changes. However, these corrections took over a year to complete, illustrating the complexity of the proof that Wiles had constructed.
Methods
Many people wondered how Andrew Wiles was able to solve a problem that had eluded so many others skilled mathematicians. Wiles himself said that he did not always know exactly where his new techniques came from, but he defined a good mathematical problem by the mathematics it generates, not by the problem itself. He was known for avoiding computers in his work, preferring to doodle, scribble, or find patterns via calculations. As do most scholars, he also read previous research for methods that he could adapt to his work. When he would get stuck working on a problem, he reportedly tried to change it into a new version that he could solve or stepped away from it entirely to relax and allow his subconscious to work. He described his personal process by the following analogy:
Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. One goes into the first room, and it’s dark, completely dark. One stumbles around bumping into the furniture, and gradually, you learn where each piece of furniture is, and finally, after six months or so, you find the light switch. You turn it on, and suddenly, it’s all illuminated. You can see exactly where you were. Then you move into the next room and spend another six months in the dark. So each of these breakthroughs, while sometimes they’re momentary, sometimes over a period of a day or two, they are the culmination of—and couldn’t exist without—the many months of stumbling around in the dark that proceed them.
Awards and Later Career
Wiles was awarded the Wolf Prize in Mathematics for 1995–96. Although he was one year beyond the age limit to receive the Fields Medal when he delivered his famous proof, in 1998 the International Mathematics Union presented him with a special silver plaque in honor of his achievement. In recognition of his great contributions to mathematics, he was appointed a Knight Commander of the Order of the British Empire in 2000.
In 2012, Princeton University named Wiles professor emeritus, and he returned to Oxford to continue his work. In 2013, Oxford named the Mathematical Institute at Oxford University for Wiles. He continued to earn many accolades, including the 2016 Abel Prize, the Copley Medal in 2017, and the De Morgan Medal in 2019. In 2018, Oxford University announced that Wiles had been appointed the first Regius Professor of Mathematics.
Bibliography
Aczel, Amir D. Fermat’s Last Theorem: Unlocking the Secret of an Ancient Mathematical Problem. New York: Basic Books, 2007.
“Andrew John Wiles - Office of the Dean of the Faculty.” Office of the Dean of the Faculty, dof.princeton.edu/people/andrew-john-wiles. Accessed 5 Oct. 2024.
“Autobiography of Andrew John Wiles.” The Shaw Prize, 2005, www.shawprize.org/autobiography/andrew-john-wiles/. Accessed 5 October 2024.
Hardy, G. H., Edward M. Wright, Andrew Wiles, and Roger Heath-Brown. An Introduction to the Theory of Numbers. New York: Oxford University Press, 2008.
Singh, Simon. Fermat’s Enigma. New York: Doubleday Press, 1997.
"Sir Andrew Wiles Appointed First Regius Professor of Mathematics at Oxford." Oxford University, 31 May 2018, www.ox.ac.uk/news/2018-05-31-sir-andrew-wiles-appointed-first-regius-professor-mathematics-oxford. Accessed 5 Oct. 2024.
WGBH Science Unit. "NOVA: Transcripts: The Proof." www.pbs.org/wgbh/nova/transcripts/2414proof.html. Accessed 4 Oct. 2024.