Theoretical Physics as an Inspiration for Mathematical Advances

June 2, 2008

Methods and insights from the realm of theoretical physics have been extremely useful for tackling problems in pure mathematics, says mathematician Andrey Lazarev of the University of Leicester. Often, these problems originally had "nothing to do with physics and had been known and studied for completely unrelated reasons," he notes.

One such area is the interpretation, in string theory, of particles as curvilinear rather than point-like objects. "This point of view and ideas surrounding it turned out to be unusually effective in studying such classical mathematical concepts as the geometry of moduli spaces of two-dimensional surfaces," Lazarev says. These ideas "provided decisive examples of exciting new structures such as topological field theories and operadic algebras."

Lazarev will address the subject of "Mathematical Structures and Patterns Inspired by Physics" in a free lecture open to the public on June 10 at the University of Leicester.

"One can say that theoretical physics has become a branch of pure mathematics and some even criticize physics for having become so abstract as to lose all connections to reality," Lazarev says, hinting at one of his themes. "Our best hope is to construct a certain mathematical model having predictive powers," he adds. "To complicate matters, such a theory would be very hard to test experimentally."

Because experimental verification of such theories is so difficult, mathematics has so far benefited much more than physics from interactions between the two disciplines, Lazarev says.

Source: University of Leicester, May 13, 2008.