Mathematics

In this lecture, Max Tegmark surveys how humans have repeatedly underestimated not only the size of the cosmos, but also the power of the human mind to understand it using mathematical equations. He explores how mathematics in physics has allowed us...

Topology is the only major branch of modern mathematics that wasn't anticipated by the ancient mathematicians. Throughout most of its history, topology has been regarded as strictly abstract mathematics, without applications. However, illustrating...

Many natural and social phenomena may be viewed as inherently computational; they evolve patterns of information that can be described algorithmically and studied through computational models and techniques. A workshop on the computational lens...

Thanks to the rabbit I pulled out of my hat on my returning from the museum the other evening, I’ve been able to get back on track. But today I’m filled with a strange mixture of optimism and dread. . . . the complexity of the mathematical landscape that’s now opened up makes my head spin if I think about it for more than a few moments.

Mathematics has proven to be "unreasonably effective" in understanding nature. The fundamental laws of physics can be captured in beautiful formulae. In this lecture, given at the Perimeter Institute for Theoretical Physics, Robbert Dijkgraaf...

What do quantum interference, flocking of birds, Facebook communities, and stock prices have in common?

Many natural and social phenomena may be viewed as inherently computational; they evolve patterns of information that can be described...

A year ago in April, the editors of the Annals of Mathematics, a journal published by the Institute and Princeton University, received an email with a submission by an unknown mathematician. “Bounded Gaps Between Primes” by Yitang Zhang, an adjunct...

In January 1984, Alexander Grothendieck submitted to the French National Centre for Scientific Research his proposal “Esquisse d’un Programme.” Soon copies of this text started circulating among mathematicians. A few months later, as a first-year...

My love affair with George Pólya began when I was seventeen. It was in Chelyabinsk, Russia, and my first year at the university was coming to an end. I had come across a tiny local library with an even tinier math section, which nobody ever seemed...

When I was in middle school, I read a popular book about programming in BASIC (which was the most popular programming language for beginners at that time). But it was 1986, and we did not have computers at home or school yet. So, I could only write...