A nine-dimensional counterexample to Borsuk's covering assertion
The compact set of rank-one orthogonal projectors on ℝ 4 , with the Frobenius metric, cannot be covered by ten sets of strictly smaller diameter. It therefore gives a counterexample to Borsuk's conjecture in dimension nine.
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Updates: Sharing AI progress on mathematics (amazing!); and my lecture plansCombinatorics and moreOct 7, 2026
a compact set in nine-dimensional Euclidean space that cannot be covered by ten sets of smaller diameter. Hadwiger’s conjecture. In Combinatorics News I discussed Hadwiger’s conjecture, which relates graph coloring to complete minors, while reporting the disproof of its odd-minor strengthening.…