Ideas

Since spring, and even before that, I have participated in a great collaborative effort to write a book on homotopy type theory. It is finally finished and ready for pub­lic consumption. You can get the book freely at http://homotopytypetheory.org...

The story of the “data explosion” is by now a familiar one: throughout science, engineering, commerce, and government, we are collecting and storing data at an ever-increasing rate. We can hardly read the news or turn on a computer without...

From the data, you have this remnant of a real object that you want to resurrect. Before you can start to do that, the first thing you need to know is, is it really coming from such and such an object? Are there some good tests or signatures for that?

Cellular telephones, GPS, radar imaging and most other modern wireless systems would not exist without the sophisticated mathematical and digital techniques that are used to encode and decode their messages. In this public lecture, Mark Goresky...

For a long time time, I have had a profound interest in studying “higher order structures” of various kinds. What is a higher order object? I will not here attempt to give a definition, but rather illustrate by examples what I have in mind.

In...

In many different ways, 1953 was an exciting year. In February–March, at the Cavendish Lab in Cambridge, England, James Watson and Francis Crick discovered the structure of DNA molecules and its double-helix geometry. This discovery was announced in...

In this talk, Jennifer Chayes, Distinguished Scientist and Managing Director of Microsoft Research New England and New York City, looks quite generally at some of the models we are using to describe ­networks, processes we are studying on the networks, ­algorithms we have devised for the networks, and finally, methods we are developing to indirectly infer network structure from measured data.

It is known that mathematicians see beauty in mathematics. Many mathematicians are motivated to find the most beautiful proof, and often they refer to mathematics as a form of art. They are apt to say “What a beautiful theorem,” “Such an elegant...

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.