This example indicates that there is more than one way to look at the role of pictures in proof. The weakest claim is that a picture can serve as an aid to inspire a proof. The mathematicianâ€¦ (More)

Two players play against each oth er in a game with payoffs given by a random n by n matrix with mean zero. If one player adopts a un iform, purely random st rategy, th en his loss is limi ted by theâ€¦ (More)

It Must Be Beautiful describes eleven great equations of modern science. (It is not claimed that these are the only great equations.) To qualify as great, the equation must summarize a key principleâ€¦ (More)

Abstract: This article is about the connection between enumerative combinatorics and equilibrium statistical mechanics. The combinatorics side concerns species of combinatorial structures and theâ€¦ (More)

The quantum anharmonic crystal is made of a large number of multi-dimensional anharmonic oscillators arranged in a periodic spatial lattice with a nearest neighbor coupling. If the couplingâ€¦ (More)