Quantum Questions Inspire New Math

In this month's "Quantized Column," Robbert Dijkgraaf, Director and Leon Levy Professor, explores the possibility of developing a new realm of mathematics in order to fully understand the quantum world.

"Mathematics might be more of an environmental science than we realize. Even though it is a search for eternal truths, many mathematical concepts trace their origins to everyday experience. Astrology and architecture inspired Egyptians and Babylonians to develop geometry. The study of mechanics during the scientific revolution of the 17th century brought us calculus.

Remarkably, ideas from quantum theory turn out to carry tremendous mathematical power as well, even though we have little daily experience dealing with elementary particles. The bizarre world of quantum theory — where things can seem to be in two places at the same time and are subject to the laws of probability — not only represents a more fundamental description of nature than what preceded it, it also provides a rich context for modern mathematics. Could the logical structure of quantum theory, once fully understood and absorbed, inspire a new realm of mathematics that might be called 'quantum mathematics'?"