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...

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Robert MacPherson

Robert MacPherson, Hermann Weyl Professor in the School of Mathematics, joined the Institute Faculty in 1994. His work has introduced new approaches to the topology of singular spaces and promoted investigations across a great spectrum of mathematics. He works in several fields of geometry-topology, algebraic geometry, differential geometry, and singularity theory, and he is especially interested in aspects of geometry that interact with other areas of mathematics, such as the geometry of spaces of lattices, which interacts with modular forms, and the geometry of toric varieties, which interacts with combinatorics.

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...

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.”

*What explains “the unreasonable effectiveness”
of mathematics, as the late Princeton University physicist Eugene
Wigner phrased it, in answering questions about the real
world?*

Natural phenomena could have been structured in a way that couldn’t be...

When Friedrich Hirzebruch was a Member in the School of
Mathematics in 1954, his paper, "Some problems on differentiable
and complex manifolds", was published in the *Annals of
Mathematics*. In it he asked whether Chern numbers in albegraic
geometry...