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# geometry

## Latest Articles

### 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.

### 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.

### 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.

### A Number Theorist Who Connects Math to Other Creative Pursuits

Jordan Ellenberg enjoys studying — and writing about — the mathematics underlying everyday phenomena.

### Mathematicians Find Long-Sought Building Blocks for Special Polynomials

Hilbert’s 12th problem asked for novel analogues of the roots of unity, the building blocks for certain number systems. Now, over 100 years later, two mathematicians have produced them.