Does beauty exist in mathematics? The question concerns
mathematical objects and their relations, the real subject of
verifiable proofs. Mathematicians generally agree that beauty does
exist in the structural beauty of theorems and proofs, even
if...
Albert Einstein’s general theory of relativity, a pillar of
modern physics formulated 100 years ago, was celebrated by the
Institute for Advanced Study and Princeton University in a two-day
conference, General Relativity at 100. The conference...
Topology is the branch of geometry that deals with large-scale
features of shapes. One cliché is that a topologist cannot
distinguish a doughnut from a coffee cup: if a coffee cup were made
of rubber, one could continuously deform it to a doughnut...
In 2006, Edward Witten, Charles Simonyi Professor in the School
of Natural Sciences, cowrote with Anton Kapustin a 225-page paper,
“Electric-Magnetic Duality and the Geometric Langlands Program,” on
the relation of part of the geometric Langlands...
The Rubik’s Cube is one of the most popular toys in history. It
is also an example of a permutation puzzle, which have existed in
mathematics in one form or another for at least 140 years. In
hindsight, it is strange that the cube ever became so...
“It’s not obvious where this is going. Maybe it will be
something spectacular. Maybe it will just be a curiosity. We don’t
know. But it’s something. And it’s a beautiful something.”—Nima Arkani-Hamed
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...
