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Echoes of Electromagnetism Found in Number Theory
A new magnum opus posits the existence of a hidden mathematical link akin to the connection between electricity and magnetism.
Behold Modular Forms, the ‘Fifth Fundamental Operation’ of Math
Modular forms are one of the most beautiful and mysterious objects in mathematics. What are they?
Elliptic Curves Yield Their Secrets in a New Number System
Ana Caraiani and James Newton have extended an important result in number theory to the imaginary realm.
What Is the Langlands Program?
The Langlands program provides a beautifully intricate set of connections between various areas of mathematics, pointing the way toward novel solutions for old problems.
The Year in Math and Computer Science
Mathematicians and computer scientists answered major questions in topology, set theory and even physics, even as computers continued to grow more capable.
The Mathematician Who Delights in Building Bridges
Ana Caraiani seeks to unify mathematics through her work on the ambitious Langlands program.
Galois Groups and the Symmetries of Polynomials
By focusing on relationships between solutions to polynomial equations, rather than the exact solutions themselves, Évariste Galois changed the course of modern mathematics.
New Shape Opens ‘Wormhole’ Between Numbers and Geometry
Laurent Fargues and Peter Scholze have found a new, more powerful way of connecting number theory and geometry as part of the sweeping Langlands program.
The Year in Math and Computer Science
Even as mathematicians and computer scientists proved big results in computational complexity, number theory and geometry, computers proved themselves increasingly indispensable in mathematics.