A Little Story Regarding Borsuk’s Conjecture

Jeff Kahn

Jeff and I worked on the problem for several years. Once he visited me with his family for two weeks. Before the visit I emailed him and asked: What should we work on in your visit?

Jeff asnwered: We should settle  Borsuk’s problem!

I asked: What should we do in the second week?!

and Jeff asnwered: We should write the paper!

And so it was.

You can download our paper here. Here is the proof itself.


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7 Responses to A Little Story Regarding Borsuk’s Conjecture

  1. Gil says:

    We tried it again but it never worked so nicely…

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  3. rjlipton says:

    Should try on other problems. One of the most beautiful papers. Also love that when against conventional wisdom.

  4. Gil Kalai says:

    Thanks! I suppose our result indeed went against the conventional wisdom although some people did raise the possibility that a combinatorially defined configuration of points will be a counter example.

    There was a special case of Borsuk’s conjecture formulated by Larman in terms of intersecting families of sets which surprisingly looked much “less true” than the full conjecture.

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