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The modularity theorem states that elliptic curves over the field of rational numbers are related to modular forms in a particular way. Andrew Wiles and Richard Taylor proved the modularity theorem for semistable elliptic curves, which was enough to imply Fermat's Last Theorem. Later, a series of papers by Wiles's former students Brian Conrad, Fred Diamond and Richard Taylor, culminating in a joint paper with Christophe Breuil, extended Wiles's techniques to prove the full modularity theorem in 2001.
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Wiles's proof of Fermat's Last Theorem is a proof by British mathematician Andrew Wiles of a special case of the modularity theorem for elliptic curves. Together with Ribet's theorem, it provides a proof for Fermat's Last Theorem. Both Fermat's Last Theorem and the modularity theorem were believed to be impossible to prove using previous knowledge by almost all living mathematicians at the time.
Barry Charles Mazur is an American mathematician and the Gerhard Gade University Professor at Harvard University. His contributions to mathematics include his contributions to Wiles's proof of Fermat's Last Theorem in number theory, Mazur's torsion theorem in arithmetic geometry, the Mazur swindle in geometric topology, and the Mazur manifold in differential topology.
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References
- 1 2 3 4 Board of Visitors honors Ezra A. 'Bud' Brown of mathematics with emeritus status Virginia Tech
- ↑ Alumni In The News: Ezra "Bud" Brown Rice Magazine
- ↑ Representations of discriminantal divisors by binary quadratic forms Journal of Number Theory, Volume 3, Issue 2, May 1971, pp. 213–225
- ↑ Ezra A. Brown Curriculum Vitae
- ↑ Ezra "Bud" Brown: Passing the Torch of Mentorship VTstories, April 24, 2019
- ↑ American Mathematical Society: MAA Press
- 1 2 "Biscuits of Number Theory". Archived from the original on June 25, 2020. Retrieved July 20, 2020.
- ↑ Three Fermat Trails to Elliptic Curves, Published 2000
- 1 2 Five Families Around a Well: A New Look at an Old Problem The College Mathematics Journal, Volume 49, 2018 – Issue 3
- ↑ "Many More Names of (7,3,1)" Mathematics Magazine, Vol. 88, no. 2, June 2015, pp. 103–120
- ↑ "Why Ellipses Are Not Elliptic Curves" Mathematics Magazine, Vol. 85, no. 3, June 2012, pp. 163–176
- ↑ "Kirkman's Schoolgirls Wearing Hats and Walking Through Fields of Numbers" Mathematics Magazine, Vol. 82, no. 1, February 2009, pp. 3–15
- ↑ Phoebe Floats! The College Mathematics Journal, Vol. 36, (2005), pp. 114–122.
- ↑ The Fabulous (11, 5, 2) Biplane Mathematics Magazine, Vol. 77, No. 2, Permutations (Apr. 2004), pp. 87–100
- ↑ "The Many Names of (7,3,1)" Mathematics Magazine, Vol. 75 (2002), pp. 83–94
- ↑ Three Fermat Trails to Elliptic Curves The College Mathematics Journal, Vol. 31 (2000), pp. 162–172.
- ↑ Square Roots from 1; 24, 51, 10 to Dan Shanks The College Math Journal Vol. 30 (1999), 82–95.
- ↑ The Unity of Combinatorics by Ezra Brown and Richard K. Guy
- ↑ Regiomontanus: His Life and Work, a translation of Ernst Zinner's Leben und Werken des Johann Muller von Koenigsberg, genannt Regiomontanus, North-Holland, Amsterdam-New York, 1990
- ↑ Sister Helen Christensen Service Award The Mathematical Association of America
- 1 2 3 Carl B. Allendoerfer Awards Mathematical Association of America
- 1 2 3 George Pólya Awards Mathematical Association of America
- ↑ John M. Smith Awards MMA Maryland-District of Columbia-Virginia Section
