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Bulletin of the American Mathematical Society

Published by the American Mathematical Society, the Bulletin of the American Mathematical Society (BULL) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

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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