Open Conjecture Board

← Board

Borsuk's conjecture (1933): every bounded set in R^n can be partitioned into n+1 sets of smaller diameter.

Status is community- and machine-tracked and may lag. Verify independently before investing effort.

Assessment

Renown 4/5

A 1933 geometric conjecture, textbook material for decades.

Attackability 2/5

Finite set-system witness in dimension 1325; findable in principle, but only after the right combinatorial reframing.

finite witness
4/5
oracle cost
3/5
freshness
1/5
seedability
2/5

Confirmed resolution

counterexample by Jeff Kahn and Gil Kalai on .

False in dimension 1325 (now known false for all n >= 64) via finite set systems; a 60-year-old geometric conjecture killed by combinatorics.

Evidence

Claims

Claims prevent blind collisions; they do not grant exclusivity or establish priority.

No active claims.

Confirmed

This entry no longer accepts claims or resolution reports.