Letter From the Chair

Pasted inside our home copy of Webster’s Third New International Dictionary is a note: “To Jim, with thanks from I.T.P. April 1975.” C.N. “Frank” Yang and his colleagues at Stony Brook University’s Institute for Theoretical Physics (ITP) gifted the dictionary to my husband, Jim Simons, to thank him for giving six mathematical talks on parallel transport at the institute.

Those talks arose from a conversation Frank and Jim had the year before, when Frank told Jim about the Aharonov–Bohm experiment. Physicists were puzzled by how a charged particle could be affected by an electromagnetic potential despite being in a region where the electric and magnetic fields are zero. Jim wondered if the particle was reacting not to a local force, but rather to the underlying geometry of the space it was moving through. He was thinking about a parallel translation of a vector bundle, something mathematicians had figured out 40 years earlier.

Jim and Frank’s conversation on the Aharonov–Bohm experiment laid the foundation for many fruitful discussions to follow and helped cement a decades-long friendship.

Over the centuries, many such exchanges between mathematicians and scientists have spurred their fields forward. A famous example is the competitive collaboration between David Hilbert and Albert Einstein. The two researchers exchanged letters as they raced to derive the set of field equations that explained general relativity. Ultimately, Hilbert’s rigorous mathematical approach, based on the calculus of variations, formalized Einstein’s intuitive understanding of the curvature of space.

But whether it’s a race to the finish or a more collaborative tête-à-tête approach, mathematicians and scientists can inspire and complement each other’s approaches. Today, there are many areas of active collaboration around the world, ranging from one-on-one dialogues to small-group collaborations to institutional efforts.

Over the years, the Simons Foundation has sought to foster such interdisciplinary endeavors to catalyze discoveries both within and across fields. Some examples of these efforts include the Simons Collaboration on the Localization of Waves, the Simons Collaboration on Probabilistic Paths to Quantum Field Theory, and Stony Brook University’s Simons Center for Geometry and Physics. At the foundation’s Flatiron Institute, the Center for Computational Mathematics serves as the glue that unites researchers across the institute’s diverse fields of astrophysics, biology, neuroscience and quantum physics.

By nurturing the flow of ideas across fields and among mathematicians and scientists, we know that basic research will yield unexpected results and lead to impactful insights. It was clear to Jim back in the 1970s that the relationship between math and science was no longer a one-way street. Mathematics provided scientists with the tools to explain their observations, and science pointed the way to new mathematical theorems. Jim eagerly shared all he had learned from the physicists at ITP with his friend and mentor, Isadore Singer, who further passed the word to Michael Atiyah, and so on.

As for the dictionary, the ITP physicists chose it for a specific reason. Weeks of watching Jim write theorems and equations on the blackboard revealed that while Jim was an outstanding mathematician, he was an atrocious speller! It was such a comical, unexpected insight from the collaboration. Jim was quite amused.

Marilyn H. Simons, Ph.D.
Chair