Navneel Singhal

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Writings

This page contains a list of selected papers, mathematical writings, and problems I’ve written for olympiads and similar contests. More recent and substantial technical writing can be found on my Blog.

Papers and other publications

  1. Daniel Goldstein*, Navneel Singhal*, and Eugene Cheah. “Key-Value Means: Transformers with Expandable Block-Recurrent Compressed Memory.” arXiv preprint, 2026. *Equal contribution.
  2. Navneel Singhal, On the orthogonality of a median and a symmedian, Forum Geometricorum, 17 (2017) 203–206.
  3. X(13442) and X(14118), Kimberling Encyclopedia of Triangle Centers.

Mathematical notes and handouts

  1. On a rich configuration related to tangent circles in a triangle: explores a rich configuration in a triangle with a large number of interesting tangencies, with a bonus application to problem G7 of the IMO 2002 shortist, using the results we develop.
  2. Kepler’s Laws and the Tautochrone problem: an excursion into two seemingly unrelated problems, and a solution of one using the other.
  3. Diophantine Equations: an article on important techniques in Diophantine analysis from an Olympiad perspective.
  4. Isogonal Conjugates: a short note on isogonality, intended to exhibit its uses in mathematical olympiads.
  5. Geometrical Gems: a collection of some beautiful configurations and problems in geometry.
  6. AM-GM and Thermodynamics: a proof of the AM-GM inequality using thermodynamics.
  7. Lemmas in Olympiad Geometry: a collection of useful results in geometry.
  8. Practice Problems in Geometry: a collection of practice problems for olympiad geometry.

Problem Setting

  1. GQMO 2020: Problems 1, 4, 8 of the hard exam, and 3, 4 of the beginner exam. Problem list and results for the easy and hard exams.
  2. KöMaL Problems in Mathematics, November 2018: Problem A.736.
  3. Mock INMO 2018: A mock exam for INMO 2018.
  4. Some competitive programming problems here, here, here, here, here, here, here, here, here, and contests here.

Math Olympiad resources

  1. The Art of Problem Solving website (AoPS).
  2. AoPS resources.
  3. AoPS book list.
  4. IMOmath.
  5. A large collection of articles.
  6. Canada IMO Training.
  7. Darij Grinberg’s website and a backup.
  8. Yufei Zhao’s website.
  9. Evan Chen’s website.
  10. Alexander Remorov’s website.