Mathematics

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.

The Evolution of Cooperation is the title of a book by Robert Axelrod. It was published by Basic Books in 1984, and became an instant classic. It set the style in which modern scientists think about biological evolution, reducing the complicated and...

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.

All of us who have watched as a friend or relative has disappeared into the fog of Alzheimer’s arrive at the same truth. Although we recognize people by their visual appearance, what we really are as individual humans is determined by how our brains...

Modular arithmetic has been a major concern of mathematicians for at least 250 years, and is still a very active topic of current research. In this article, I will explain what modular arithmetic is, illustrate why it is of importance for...

How do we navigate the vast amount of data at our disposal? How do we choose a movie to watch, out of the 75,000 movies available on Netflix? Or a new book to read, among the 800,000 listed on Amazon? Or which news articles to read, out of the...

There are two kinds of creation myths: those where life arises out of the mud, and those where life falls from the sky. In this creation myth, computers arose from the mud, and code fell from the sky.