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.
Combinatorics and more 
We tried it again but it never worked so nicely…
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Should try on other problems. One of the most beautiful papers. Also love that when against conventional wisdom.
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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