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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.
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.
The Mystery at the Heart of Physics That Only Math Can Solve
The accelerating effort to understand the mathematics of quantum field theory will have profound consequences for both math and physics.
Mathematicians Identify Threshold at Which Shapes Give Way
A new proof establishes the boundary at which a shape becomes so corrugated, it can be crushed.