Donaldson's tamed-to-compatible conjecture 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

Donaldson's tamed-to-compatible conjecture

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, go here for help. (Lean version available!)

expertly designed by an internal OpenAI model

Difficulty:	🧠🧠🧠🧠🧠	Ages:	13 - ∞
Skills:	curvy surfaces	Levels:	1
Category:	Differential geometry	Lean version:	YES! ✔
Rate this game! 4.9 out of 5 (8,047 votes)

>>> How to Play <<<

Donaldson's tamed-to-compatible conjecture. Proves Donaldson's tamed-to-compatible conjecture: every smooth almost complex structure on a closed four-manifold that is tamed by a symplectic form admits a compatible symplectic form. The almost complex structure stays fixed; the form's cohomology class may change.

>>> Level Select <<<

LEVEL 1 Taming implies compatibility on four-manifolds

released 2026-10-06 | 3 theorems · 12 lemmas · 20 proofs · 9,449 words | PLAY LEVEL 1 » (pdf)

We prove that every smooth almost complex structure on a closed four-manifold which is tamed by a symplectic form is compatible with a symplectic form. This gives a positive solution to Donaldson's tamed-to-compatible conjecture. We also characterize the compatible cone by strict intersection positivity on the closure of the invariant part of the taming cone.

More Differential geometry Games!
Yau's uniformization conjecture	Katok's entropy rigidity conjecture	A counterexample to the nearby Lagrangian conjecture	Donaldson's hypersymplectic deformation conjecture
Sharp symplectic ball-packing criteria in higher dimensions	The metric Blaschke conjecture	Infinitely many closed geodesics on spheres and three-manifolds	Sharp singular-set bounds for stationary integral varifolds

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