Simkin glider gun from John Conway's Game of Life (Image: Wikimedia)

When a great mathematician dies, we lose direct access to a rare and brilliant mind. In 2020, three great mathematicians died: John Conway, Ronald Graham, and Freeman Dyson. In a beautiful memorial published in The New Yorker, SFI External Professor Dan Rockmore (Dartmouth University) helps us recollect the wonders of each man’s singular genius.

Rockmore begins with John Conway, whose immense imagination defies summary. In addition to inventing The Game of Life, for example, Conway also deepened our understanding of the symmetries that lie at the core of group theory. He paved the way for the discovery of a group of symmetries called the Monster which has “helped mathematicians understand prime numbers and given physicists new insights into quantum gravity.”

Ron Graham brought his mind to bear on problems in combinatorics, which he mapped onto geometric figures. With Graham we can reflect on the combinatorial possibilities revealed by the hypercube, a cube in four dimensions. In his work in combinatorics, Graham arrived a number so large that he needed to invent new notation to describe it. The number, called Graham’s number, Rockmore notes, was regarded as the “largest number ever to have a use.”

Freeman Dyson, a mathematician who shuttled brilliantly, and philosophically, between mathematics and physics, Rockmore calls “the physicist most deserving of a Nobel Prize who didn’t receive one.” Dyson created the conceptual bridge that helped translate Richard Feynman’s diagrams into the mathematics that Julian Schwinger and Sin-Itiro Tomonaga used to formulate their prize-winning work.

At first blush, it is difficult to grasp the genius behind the mathematical objects each of these men contemplated. Rockmore affords us a glimpse of the light, and life, each man leaves behind. In doing so, he gives us a way to retain access to their remarkable mathematical imaginations.

Read the article in The New Yorker (December 31, 2020)