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In 1980 he showed the importance of the bundle theorem for ovoidal Möbius planes. In 1993, together with Gil Kalai, he disproved Borsuk's conjecture. In 1996 he was awarded the Pólya Prize (SIAM). In 2004, with David Galvin he made seminal contributions to the combinatorial theory of phase transitions.
He was an invited speaker at the 1994 International Congress of Mathematicians in Zurich.