Abstract:

The calculational techniques developed by physicists over the last century in their search for the ultimate quantum description of the universe -- shunned by mathematicians during most of their gestation for lack of rigor -- have finally in the last decade begun to exert profound and startling effects on many areas of mathematics. Just as it took centuries for mathematicians to put the original, finite-dimensional calculus of classical physics on a rigorous footing, it will probably be a major, long-term project to make complete sense of the rules and heuristics of the new, infinite-dimensional calculus of quantum physics. But in the meantime, as the ideas reverberate through mathematics, no graduate student should remain unaware.