Barry Mazur
Barry Charles Mazur | |
|---|---|
Veblen Prize (1966) | |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Harvard University |
| Doctoral advisor | Ralph Fox R. H. Bing |
| Doctoral students | |
Barry Charles Mazur (.
Life
Born in
Harvard University from 1961 to 1964. He is the Gerhard Gade University Professor and a Senior Fellow at Harvard. He is the brother of Joseph Mazur and the father of Alexander J. Mazur
.
Work
His early work was in geometric topology. In an elementary fashion, he proved the
Mazur swindle
.
His observations in the 1960s on analogies between
primes and knots were taken up by others in the 1990s giving rise to the field of arithmetic topology
.
Coming under the influence of
Mazur's torsion theorem, which gives a complete list of the possible torsion subgroups of elliptic curves over the rational numbers, is a deep and important result in the arithmetic of elliptic curves. Mazur's first proof of this theorem depended upon a complete analysis of the rational points on certain modular curves
. This proof was carried in his seminal paper "Modular curves and the Eisenstein ideal".
The ideas of this paper and Mazur's notion of Galois deformations, were among the key ingredients in Wiles's proof of Fermat's Last Theorem. Mazur and Wiles had earlier worked together on the main conjecture of Iwasawa theory.
In an expository paper, Number Theory as Gadfly,[4] Mazur describes number theory as a field which
"produces, without effort, innumerable problems which have a sweet, innocent air about them, tempting flowers; and yet... number theory swarms with bugs, waiting to bite the tempted flower-lovers who, once bitten, are inspired to excesses of effort!"
He expanded his thoughts in the 2003 book Imagining Numbers[5] and Circles Disturbed, a collection of essays on mathematics and narrative that he edited with writer Apostolos Doxiadis.[1]
Awards and honors
Mazur was elected to the
National Academy of Sciences.[7] Mazur was elected to the American Philosophical Society in 2001,[8] and in 2012 he became a fellow of the American Mathematical Society.[9]
Mazur has received the
Veblen Prize in geometry (1966), the Cole Prize in number theory (1982), the Chauvenet Prize for exposition (1994),[4] and the Steele Prize for seminal contribution to research (2000) from the American Mathematical Society. In early 2013, he was presented with one of the 2011 National Medals of Science by President Barack Obama.[10] In 2022, he was awarded the Chern Medal for outstanding lifelong achievement in mathematics.[11]
Publications
Books
- Mazur, Barry; Stein, William (2016). Prime numbers and the Riemann hypothesis. New York, NY: Cambridge University Press. ISBN 978-1-107-49943-0.
- Mazur, Barry; Jean-Pierre, Serre, eds. (2016). Collected works of John Tate : parts i and ii. American Mathematical Society. ISBN 978-0-8218-9091-2.
- Mazur, Barry (2003). Imagining numbers : (particularly the square root of minus fifteen). New York: Farrar Straus Giroux. MR 1950850.
- Katz, Nicholas M.; Mazur, Barry (1985). Arithmetic moduli of elliptic curves. Annals of Mathematics Studies, 108. Princeton University Press. MR 0772569.
See also
References
- ^ doi:10.1038/483405a.
- ^ ISBN 0-88385-554-2.
- ^ Mazur, Barry Charles (1959). On embeddings of spheres.
- ^ JSTOR 2324924.
- ISBN 0-14-100887-3.
- ^ "Barry Charles Mazur". American Academy of Arts & Sciences. Retrieved October 15, 2021.
- ^ "Barry C. Mazur". www.nasonline.org. Retrieved October 15, 2021.
- ^ "APS Member History". search.amphilsoc.org. Retrieved October 15, 2021.
- ^ List of Fellows of the American Mathematical Society, retrieved February 4, 2013.
- ^ "3 local professors to get US honors". Boston Globe. January 7, 2013. Retrieved October 24, 2016.
- ^ "Chern Medal Award 2022". Retrieved July 5, 2022.
External links
Wikiquote has quotations related to Barry Mazur.
- Barry Mazur, Harvard University
- O'Connor, John J.; Robertson, Edmund F., "Barry Mazur", MacTutor History of Mathematics Archive, University of St Andrews
- Video of Mazur talking about his work, from the National Science & Technology Medals Foundation
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