Essay on Andrew Wiles and His Contributions to Modern Math

In the current paper I will write about Andrew Wiles and share some brief facts about his life and the contributions he has made to science of math.

Sir Andrew John Wiles (was born April 11, 1953, Cambridge, UK, Knight-Commander of the Order of the British Empire in 2000) – is English and American mathematician and professor of mathematics at Princeton University and head of its Department of Mathematics, member of the Scientific Council of the Institute Clay Mathematics. He received his bachelor’s degree in 1974 at Merton College, Oxford. Academic career began in the summer of 1975 under the guidance of Professor John Coates Claire College at Cambridge University, where he received his doctorate. In the period from 1977 to 1980, Wiles served as a research assistant at the college and associate professor Clare at Harvard University. Together with John Coates, he worked on the arithmetic of elliptic curves with complex multiplication methods Iwasawa theory. In 1982, Wiles moved from Britain to the United States, according to Who is Andrew Wiles? (2010).

One of the highlights of his career was proof of Fermat’s Last Theorem in 1993 and the detection technique, which made it possible to complete the proof by his former graduate student, Robert Taylor, in 1994. Work on Fermat’s theorem, he began in the summer of 1986 after Ken Ribet proved the connection of semistable elliptic curves (a special case of Theorem Taniyama – Shimura) and Fermat’s theorem. The basic idea of such a connection belongs to Gerhard Fry, German mathematician, according to Andrew Wiles on solving Fermat (2000).

The work of Wiles Fermat’s Last Theorem has been reflected in the musical “Grand Tango Farm” Lessner and Rosenblum. Wiles and his work are mentioned in the episode “Facets” series “Star Trek: Deep Space Nine”.

Sir Andrew John Wiles is a British mathematician, who gained fame in 1993 by the demonstration of Fermat’s last theorem. Wiles was able to prove Fermat’s Last Theorem from the connection, outlined by Frey, and demonstrated by Ken Ribet in 1985, that a demonstration of the so-called Taniyama-Shimura conjecture would lead directly to a proof of Fermat’s last theorem. In summary, the Taniyama-Shimura conjecture states that every elliptic curve can be associated unambiguously with a mathematical object called a modular fashion. If Fermat’s last theorem were false, then there would be an elliptic curve such that it can not associate with any modular form, and therefore the Taniyama-Shimura conjecture would be false. Therefore, the Taniyama-Shimura proves Fermat’s last theorem.

The proof of the Taniyama-Shimura already assumed an important challenge as it was one of the so-called Langlands program, which aims to unify areas of mathematics apparently unrelated to each other. Wiles spent 8 years following the demonstration of Ribet in isolation working on the problem, which is an unusual way of working in mathematics, where it is common for mathematicians from around the world share their thoughts often. To avoid suspicion, Wiles was publishing articles regularly, as any mathematician of any university in the world.

Wiles’s odyssey began in 1986 when Ken Ribet, an idea inspired by Gerhard Frey showed that UTF result as a consequence of the Taniyama-Shimura conjecture, because each one could be of elliptic curves parametrized by modular forms. Being less singular UTF, the Taniyama-Shimura conjecture is broader because it involves very fundamental ideas of number theory. Nobody had any idea how to prove it.

Working in secrecy and sharing your progress only with Nicholas Katz, a professor of mathematics at Princeton, has developed Wiles proof of the Taniyama-Shimura, and from it the UTF. The proof is difficult and introduces many new ideas.

Wiles was quite dramatic in the presentation of evidence. In June 1993, not advertising the topics in advance, he has scheduled three lectures at the Newton Institute. The audience and the world were eager to know its contents.

In the following months, the manuscript of the statement was circulated only among a small number of mathematicians. The first version of the proof depended on building a system of Euler and this aspect proved difficult, resulting in a final version of the statement than the original. This difficulty was overcome with the help of Richard Lawrence Taylor.

The fictionalized story of the statement of UTF is presented in detail in the book by Simon Singh: “Fermat’s Last Theorem”, Editora Record (BR), 1998. The book version was the television documentary series on the science of the BBC “Horizon”.

Fermat’s Last Theorem (or Fermat’s last theorem) – is one of the most popular theory of mathematics, and its condition is formulated on the conceptual level of secondary education, and proof of many mathematicians have searched for more than three hundred years. It was finally proved in 1995 by Andrew Wiles, according to Andrew Wiles- Mathematics (2011).

Wiles has been awarded several major prizes in mathematics and science: Junior Whitehead Prize of the LMS (1988); Fellow of the Royal Society (1989); Schock Prize (1995); Fermat Prize (1995); Wolf Prize (1995/6); NAS Award in Mathematics from the National Academy of Sciences (1996); Royal Medal (1996); Ostrowski Prize (1996); Cole Prize (1997); Wolfskehl Prize (1997) – A silver plaque from the International Mathematical Union (1998) recognizing his achievements, in place of the Fields Medal, which is restricted to those under 40 (Wiles was born in 1953 and proved the theorem in 1994); King Faisal Prize (1998); Clay Research Award (1999); Shaw Prize (2005); Pythagoras Award (Croton, 2004), according to Andrew John Wiles (2009).

Public honors are: The asteroid 9999 Wiles was named for Wiles in 1999; Wiles was appointed to the rank of Knight Commander of the Order of the British Empire in the United Kingdom in 2000.

All in all, it should be noted that Sir Andrew John Wiles, who is an English and American mathematician, professor of mathematics at Princeton University, head of its Department of Mathematics, member of the Scientific Council Clay Mathematics Institute, received bachelor degree in 1974 at Merton College of Oxford University. His career began in the summer of 1975 under the leadership of Professor John Coates of Clare College in Cambridge University where he received the degree and PhD. In the period from the year 1977 – 1980 Wiles hold office junior fellow at Clare College and professor at Harvard University. In 1982 he moved to the United States.

One of the most important events in his career was his application, he has shown great theorem Fermat in 1993 and the publication of elegant method that allows proof to be completed in 1994, professional work of the Great Fermat theorem by early summer of 1986. It can be said that the contribution of Andrew Wiles was considerable and very important for the society.