Mathematicians Encyclopedia Entry 1781002807
Summary: This encyclopedia entry is about the life and work of Andrew Wiles, a renowned British mathematician who solved Fermat's Last Theorem, a problem that had gone unsolved for over 350 years.
CONTENT
Overview
Andrew Wiles is a British mathematician born on April 11, 1953, in Cambridge, England. He is best known for solving Fermat's Last Theorem, a problem that had gone unsolved for over 350 years. Wiles' work on this theorem has been hailed as one of the most significant achievements in mathematics in the 20th century. He is currently a professor of mathematics at the University of Oxford.
Wiles' interest in mathematics began at a young age, and he was particularly drawn to number theory. He studied mathematics at Clare College, Cambridge, and later earned his Ph.D. from the University of Cambridge. After completing his Ph.D., Wiles worked at several institutions, including Princeton University and Harvard University, before joining the University of Oxford.
Wiles' work on Fermat's Last Theorem was a culmination of over 7 years of intense research. He developed a new proof of the theorem, which was based on his work on modular forms and elliptic curves. The proof was a major breakthrough in number theory and had significant implications for many areas of mathematics.
History/Background
Fermat's Last Theorem was first proposed by Pierre de Fermat in 1637. Fermat claimed to have a proof of the theorem, but unfortunately, he did not leave behind any notes or explanations. The theorem states that there are no integer solutions to the equation a^n + b^n = c^n for n>2. Despite the efforts of many mathematicians over the centuries, the theorem remained unsolved until Wiles' proof in 1994.
Wiles' work on Fermat's Last Theorem was influenced by the work of several mathematicians, including Ernst Kummer and David Hilbert. He also drew on the work of other mathematicians, such as Gerd Faltings and Andrew Ogg. Wiles' proof of the theorem was a major achievement, and it has had significant implications for many areas of mathematics.
Key Information
- Fermat's Last Theorem: Wiles' proof of Fermat's Last Theorem was a major breakthrough in number theory. The theorem states that there are no integer solutions to the equation a^n + b^n = c^n for n>2.
- Modular Forms: Wiles' work on modular forms was a key component of his proof of Fermat's Last Theorem. Modular forms are a type of mathematical object that is used to study the properties of elliptic curves.
- Elliptic Curves: Wiles' work on elliptic curves was also a key component of his proof of Fermat's Last Theorem. Elliptic curves are a type of mathematical object that is used to study the properties of modular forms.
- Modularity Theorem: Wiles' proof of Fermat's Last Theorem was based on the modularity theorem, which states that every elliptic curve over the rational numbers is modular.
- Taniyama-Shimura Conjecture: Wiles' work on the modularity theorem was also related to the Taniyama-Shimura conjecture, which states that every elliptic curve over the rational numbers is modular.
Significance
Wiles' proof of Fermat's Last Theorem has had significant implications for many areas of mathematics. The theorem has been used to study the properties of elliptic curves, modular forms, and other mathematical objects. Wiles' work has also had significant implications for cryptography and coding theory.
Wiles' achievement has also had a significant impact on the mathematical community. His proof of Fermat's Last Theorem has been hailed as one of the most significant achievements in mathematics in the 20th century. Wiles' work has also inspired a new generation of mathematicians to study number theory and other areas of mathematics.
INFOBOX
- Name: Andrew Wiles
- Type: Mathematician
- Date: April 11, 1953
- Location: Cambridge, England
- Known For: Solving Fermat's Last Theorem
TAGS: Andrew Wiles, Fermat's Last Theorem, Modular Forms, Elliptic Curves, Modularity Theorem, Taniyama-Shimura Conjecture, Number Theory, Cryptography, Coding Theory.
