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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Counting special points: Logic, diophantine geometry, and transcendence theory
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by Thomas Scanlon PDF
Bull. Amer. Math. Soc. 49 (2012), 51-71 Request permission


We expose a theorem of Pila and Wilkie on counting rational points in sets definable in o-minimal structures and some applications of this theorem to problems in diophantine geometry due to Masser, Peterzil, Pila, Starchenko, and Zannier.
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Additional Information
  • Thomas Scanlon
  • Affiliation: Department of Mathematics, University of California, Berkeley, Evans Hall, Berkeley, California 94720-3840
  • MR Author ID: 626736
  • ORCID: 0000-0003-2501-679X
  • Email:
  • Received by editor(s): June 9, 2011
  • Published electronically: October 24, 2011
  • Additional Notes: Partially supported by NSF grants FRG DMS-0854998 and DMS-1001550. The author thanks M. Aschenbrenner, J. Pila, P. Tretkoff, and U. Zannier for their detailed comments about earlier versions of these notes.
  • © Copyright 2011 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 49 (2012), 51-71
  • MSC (2010): Primary 11G15, 03C64
  • DOI:
  • MathSciNet review: 2869007