March 29, 1969 |
|Alma mater||Princeton University|
|Doctoral advisor||Gerd Faltings|
|Known for||Proposed proof of abc conjecture,
Proved Grothendieck conjecture on anabelian geometry.
|Notable awards||JSPS Prize, Japan Academy Medal|
Shinichi Mochizuki (望月 新一 Mochizuki Shin'ichi?, born March 29, 1969) is a Japanese mathematician specializing in number theory. He works in arithmetic geometry, Hodge theory, and anabelian geometry, and he introduced p-adic Teichmüller theory, Hodge–Arakelov theory, Frobenioids, and inter-universal Teichmüller theory. He was an invited speaker at the International Congress of Mathematicians in 1998.
Mochizuki proved Grothendieck conjecture on anabelian geometry in 1996. In 1999, he introduced Hodge–Arakelov theory and in 2008 he introduced Frobenioids. In 2012, he introduced Inter-universal Teichmüller theory which is an arithmetic version of Teichmüller theory for number fields with an elliptic curve.
In August 2012, Mochizuki released what is claimed to be a proof of the abc conjecture; however, the claimed proof is very long and complex and is still being verified for correctness by other mathematicians. He documented the relevant progress in two reports, the first in December 2013 and the second in December 2014.
When he was five years old, Shinichi Mochizuki and his family left Japan to live in New York City. Mochizuki attended Phillips Exeter Academy and graduated in 1985. He entered Princeton University as an undergraduate at age 16 and graduated salutatorian in 1988. He then received a Ph.D. under the supervision of Gerd Faltings at age 23. He joined the Research Institute for Mathematical Sciences in Kyoto University in 1992 and was promoted to professor in 2002.
Inter-universal Teichmüller theory
As of December 2014, through discussion with Mohamed Saidi of University of Exeter, Yuichiro Hoshi and Go Yamashita of the Research Institute for Mathematical Sciences in Kyoto University, Mochizuki himself said "I have yet to hear of even a single problem that relates to the essential thrust or validity of the theory" on the progress report. According to Mochizuki, "At least with regard to the substantive mathematical aspects of such a verification, the verification of Inter-universal Teichmüller theory is, for all practical purposes, complete". He said, however, "Nevertheless, as a precautionary measure, in light of the importance of the theory and the novelty of the techniques that underlie the theory, it seems appropriate that a bit more time be allowed to elapse before a final official declaration of the completion of the verification of Inter-universal Teichmüller theory is made."
- Mochizuki, Shinichi (1995), The Geometry of the Compactification of the Hurwitz Scheme (PDF) 31, Research Institute for Mathematical Sciences(Kyoto university), pp. 355–441, MR 1355945
- Mochizuki, Shinichi (1997), "A Version of the Grothendieck Conjecture for p-adic Local Fields" (PDF), The International Journal of Mathematics (singapore: World Scientific Pub. Co.) 8 (3): 499–506, ISSN 0129-167X
- Mochizuki, Shinichi (1998), "Correspondences on Hyperbolic Curves" (PDF), Journal of Pure and Applied Algebra 131 (3): 227–244, doi:10.1016/s0022-4049(97)00078-9
- Mochizuki, Shinichi (1998), "Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998)", Documenta Mathematica: 187–196, ISSN 1431-0635, MR 1648069
- Mochizuki, Shinichi (1999), "Extending families of curves over log regular schemes" (PDF), Journal für die reine und angewandte Mathematik 511: 43–71, MR 1695789
- Mochizuki, Shinichi (1999), Foundations of p-adic Teichmüller theory, AMS/IP Studies in Advanced Mathematics 11, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-1190-0, MR 1700772
- Mochizuki, Shinichi (2004), "Noncritical Belyi Maps" (PDF), Mathematical Journal of Okayama University (Okayama University) 46: 105–114, ISSN 0030-1566
- Mochizuki, Shinichi (2010), "Arithmetic Elliptic Curves in General Position" (PDF), Mathematical Journal of Okayama University (Okayama University) 52: 1–28, ISSN 0030-1566
Inter-universal Teichmüller theory
- Mochizuki, Shinichi (2011), "Inter-universal Teichmüller Theory: A Progress Report", Development of Galois–Teichmüller Theory and Anabelian Geometry (PDF), The 3rd Mathematical Society of Japan, Seasonal Institute.
- Mochizuki, Shinichi (2015a), Inter-universal Teichmuller Theory I: Construction of Hodge Theaters (PDF).
- Mochizuki, Shinichi (2015b), Inter-universal Teichmuller Theory II: Hodge–Arakelov-theoretic Evaluation (PDF).
- Mochizuki, Shinichi (2015c), Inter-universal Teichmuller Theory III: Canonical Splittings of the Log-theta-lattice (PDF).
- Mochizuki, Shinichi (2015d), Inter-universal Teichmuller Theory IV: Log-volume Computations and Set-theoretic Foundations (PDF).
- Mochizuki, Shinichi. "Curriculum Vitae" (PDF). Retrieved 14 September 2012.
- . "Proof claimed for deep connection between primes". Nature News. 10 September 2012.
- "International Congress of Mathematicians 1998".
- Donald G. Babbitt, Jane E. Kister, ed. (1999), Featured Reviews in Mathematical Reviews 1997-1999: With Selected Reviews of Classic Books and Papers from 1940-1969, American Mathematical Society, p. A52
- Mihai, Andrei (January 12, 2015). "Mathematician may have revolutionized the theory of numbers… but nobody understands his proof". ZME Science. Retrieved February 26, 2015.
- Inter-universal Teichmüller theory IV: log-volume computations and set-theoretic foundations, Shinichi Mochizuki, August 2012
- Chen, Caroline (9 May 2013). "The Paradox of the Proof". Project Wordsworth.
- "Seniors address commencement crowd". Princeton Weekly Bulletin. 20 June 1988. p. 4.
- Mochizuki, Shinichi (2014), "link ON THE VERIFICATION OF INTER-UNIVERSAL TEICHMULLER THEORY: A PROGRESS REPORT (AS OF DECEMBER 2014)", Research Institute for Mathematical Sciences Kyoto university, p.7.
- Mochizuki, Shinichi (2014), "link ON THE VERIFICATION OF INTER-UNIVERSAL TEICHMULLER THEORY: A PROGRESS REPORT (AS OF DECEMBER 2014)", Research Institute for Mathematical Sciences Kyoto university, p.8.
- Shinichi Mochizuki at the Mathematics Genealogy Project
- Personal website
- Papers of Shinichi Mochizuki
- A brief introduction to inter-universal geometry
- Inter-universal Teichmuller Theory IV: Log-volume Computations and Set-theoretic Foundations
- Philosophy behind Mochizuki’s work on the ABC conjecture on MathOverflow
- The Paradox of the Proof By Caroline Chen, accessed May 11, 2013
- Forbes: Ted Nelson Says That Bitcoin's Satoshi Nakamoto Is Shinichi Mochizuki