On the Pila–Wilkie theorem

Neer Bhardwaj, Lou van den Dries

Research output: Contribution to journalArticlepeer-review


This expository paper gives an account of the Pila–Wilkie counting theorem and some of its extensions and generalizations. We use semialgebraic cell decomposition to simplify part of the original proof. We also include complete treatments of a result due to Pila and Bombieri and of the o-minimal Yomdin–Gromov theorem that are used in this proof. For the latter we follow Binyamini and Novikov.

Original languageEnglish (US)
JournalExpositiones Mathematicae
StateAccepted/In press - 2022


  • Counting theorem
  • O-minimality

ASJC Scopus subject areas

  • Mathematics(all)


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