Topology

Derek and I had several conversations during lunches about the potential for “The Symplectic Piece.” And he continued to attend occasional lectures on the subject, searching for a way to map symplectic geometry onto a musical score.

I sometimes like to think about what it might be like inside a black hole. What does that even mean? Is it really “like” anything inside a black hole? Nature keeps us from ever knowing. (Well, what we know for sure is that nature keeps us from...

Quantum theory radically transforms our fundamental understanding of physical reality. It reveals that the world contains a hidden richness of structure that we have barely begun to control and exploit. According to quantum theory, what we perceive...

It has been said that the goals of modern mathematics are recon­struction and development.1 The unifying conjectures between number theory and representation theory that Robert Langlands, Professor Emeritus in the School of Mathematics, articulated...

What explains “the unreasonable effectiveness” of mathematics, as the late Princeton University physicist Eugene Wigner phrased it, in answering questions about the real world?

Natural phenomena could have been structured in a way that couldn’t be...