A characteristic-zero counterexample to Lipman–Zariski at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

A
D
V
E
R
T

I
S
E
M
E
N
T

A characteristic-zero counterexample to Lipman–Zariski

at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

thinking... about 3 hours remaining

If this game doesn't work on your computer, we can't help you. No Lean version yet. Some unformalized games could have issues!

expertly designed by an internal OpenAI model

Difficulty:	🧠🧠🧠🧠🧠	Ages:	13 - ∞
Skills:	shapes made of equations	Levels:	1
Category:	Algebraic and complex geometry	Lean version:	not yet
Rate this game! 4.6 out of 5 (2,372 votes)

>>> How to Play <<<

A characteristic-zero counterexample to Lipman–Zariski. Constructs a singular normal affine complex surface with free rank-two tangent sheaf, disproving the characteristic-zero Lipman–Zariski conjecture.

>>> Level Select <<<

LEVEL 1 A singular normal affine surface with free tangent sheaf

released 2026-09-23 | 1 theorem · 10 lemmas · 18 proofs · 16,049 words | PLAY LEVEL 1 » (pdf)

We construct a singular normal affine complex surface whose tangent sheaf is free of rank two. This disproves the Lipman–Zariski conjecture in characteristic zero.

More Algebraic and complex geometry Games!
A counterexample to Pixton's original completeness conjecture	Counterexamples to Kuznetsov's rationality conjecture	Toda's Gepner conjecture and large-volume stability	Termination of fourfold minimal model programs HOT!
Campana's abelianity conjecture and special varieties	The Kollár–Pardon universal-cover conjecture	Counterexamples to Zariski's multiplicity conjecture	The Global Spherical Shell conjecture

COOLMAITH GAMES SPONSORS: (not real)
Big Al's USED GPUs	Epsilon & Delta LLP attorneys at limit	QED Bail Bonds	Hilbert's Hotel always a vacancy!

Cool Links: openai/math Lean Mathlib arXiv the real Coolmath Games

You are visitor number 000719

Thanks for visiting CoolmAIth Games
© 1997-2026 CoolmAIth Games. A parody. Not affiliated with Coolmath.com LLC or OpenAI.
Every proof here was written by an internal OpenAI model and lives at github.com/openai/math.
Best viewed in Netscape Navigator 4.0 at 800x600