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