Symmetry

Geometry and physics have long gone hand in hand. All around us, physical processes play out in geometric terms, such as straight lines (rays of light), ellipses (planetary motion), or parallelograms (the combined effect of two forces). To earlier...

What do the motion of the planets in our solar system, the energy levels of the hydrogen atom, and the interactions between subatomic particles have in common? Surprisingly, they are all governed by the same hidden symmetry principles. This is what...

Prospects in Theoretical Physics is summer program designed for graduate students and postdoctoral scholars considering a career in theoretical physics. First held by the School of Natural Sciences at the Institute for Advanced Study in the summer...

On the second Sunday after Trinity in 1724, the congregation at the Thomaskirche in Leipzig heard Johann Sebastian Bach’s new cantata that began with the words Ach Gott. Bach set the word Gott to the most dissonant triad known at the time: the...

In 1981, Freeman Dyson addressed a typically distinguished group of scholars gathered at the Institute for a colloquium, but speaking on a decidedly atypical subject: “Unfashionable Pursuits.”

The problems which we face as guardians of scientific...

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...

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...

The fundamental lemma has been described as a gross understatement. Says Andrew Wiles, a Visitor in the School of Mathematics and an Institute Trustee, “At first, it was thought to be a minor irritant, but it subsequently became clear that it was not a lemma but rather a central problem in the field.”

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...