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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.
Proof Assistant Makes Jump to Big-League Math
Mathematicians using the computer program Lean have verified the accuracy of a difficult theorem at the cutting edge of research mathematics.
How to Find Rational Points Like Your Job Depends on It
Using high school algebra and geometry, and knowing just one rational point on a circle or elliptic curve, we can locate infinitely many others.
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.
How Many Numbers Exist? Infinity Proof Moves Math Closer to an Answer.
For 50 years, mathematicians have believed that the total number of real numbers is unknowable. A new proof suggests otherwise.
Mathematicians Prove Symmetry of Phase Transitions
A group of mathematicians has shown that at critical moments, a symmetry called rotational invariance is a universal property across many physical systems.
Can Math Help You Escape a Hungry Bear?
In this month’s puzzle, math is a question of life or death.
Nathan Seiberg on How Math Might Complete the Ultimate Physics Theory
Even in an incomplete state, quantum field theory is the most successful physical theory ever discovered. Nathan Seiberg, one of its leading architects, talks about the gaps in QFT and how mathematicians could fill them.
Mathematicians Prove 2D Version of Quantum Gravity Really Works
In three towering papers, a team of mathematicians has worked out the details of Liouville quantum field theory, a two-dimensional model of quantum gravity.