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.
In 2012, he was awarded Fulkerson Prize (jointly with Anders Johansson and Van H. Vu) for determining the threshold of edge density above which a random graph can be covered by disjoint copies of a given smaller graph. Also in 2012, he became a fellow of the American Mathematical Society.
