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It is presented the simplest known disproof of the Borsuk conjecture statingthat if a bounded subset of n-dimensional Euclidean space contains more than npoints, then the subset can be partitioned into n+1 nonempty parts of smallerdiameter.  The argument is due to N. Alon and is a remarkable application ofcombinatorics and algebra to geometry. This note is purely expository and isaccessible for students.

A two-page disproof of the Borsuk partition conjecture