**Kenneth Ribet ’69, ’69 A.M.**

Until 1993 the name of Kenneth Ribet was known mostly to a rarified corps of number theorists. His most significant contribution to mathematics had been a landmark proof, published in 1987, proving a connection between a category of mathematical objects known as elliptical curves and a notoriously elusive and tantalizing problem known as Fermat’s Last Theorem.

In 1637 the French mathematician Pierre de Fermat had boasted in the margin of a book that he had found a “truly marvelous proof.” For 350 years mathematicians struggled to discover his secret. In 1985 a German, Gerhard Frey, theorized that Fermat’s proof was connected to the mathematics of elliptical curves, and two years later Ribet proved the connection.

In 1993 Ribet watched Princeton mathematician Andrew Wiles take his proof and extend it to prove Fermat’s theorem. When the shy Wiles asked Ribet to explain his work for him, Ribet found himself quoted in newspapers worldwide, forever associated with Fermat’s Last Theorem.

**Derrick Lehmer ’30 Ph.D.**

Until the mid-twentieth century, number theory, which is concerned with the properties of integers, was considered the branch of mathematics least applicable to the real world. The advent of computers changed all that, thanks in part to the pioneering work of mathematician Derrick Lehmer.

Lehmer, a UC Berkeley professor who had experimented with calculation machines as far back as the 1930s, was one of the first mathematicians to realize the potential of high-speed computers to advance the frontiers of number theory. For example, the search for perfect numbers, which is one of the oldest and most persistent of math problems, had pretty much reached the limit of unassisted calculation by the middle of the twentieth century.

Thanks to the work of Lehmer and fellow mathematician Raphael Robinson, work on such problems as the search for Mersenne Primes suddenly progressed, as the pair used early computers to discover new primes. Their work also set the stage for number theory to help solve practical problems in physics, biology, chemistry, communications, and cryptography.

**Frederick Almgren ‘62 Ph.D. **

A professor of math at Princeton, Frederick Almgren was a major figure in the esoteric world of geometry, geometric-measure theory, and the calculus of variations. He was best known for his research on the geometry of surfaces of least area, such as those found in soap bubble clusters, and on the processes of geometric evolution, which are involved in the growth of snowflakes.

Because of their shapes and complexity, soap bubbles, which have a particularly interesting calculus of variations, have long been a favorite subject for mathematicians to study. Almgren and Jean Taylor showed that three basic rules govern the geometry of soap bubbles and that these rules are the mathematical consequence of a simple area-minimizing principle, an important breakthrough in the calculus of variations.

Almgren’s work earned him numerous honors and fellowships. He was a fellow of the American Association for the Advancement of Science and an editor of both the Journal of Experimental Mathematics and the Journal of Geometric Analysis.