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# Geometry

## Latest Articles

### 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.

### How Mathematicians Use Homology to Make Sense of Topology

Originally devised as a rigorous means of counting holes, homology provides a scaffolding for mathematical ideas, allowing for a new way to analyze the shapes within data.

### How to Solve Equations That Are Stubborn as a Goat

Math teachers have stymied students for hundreds of years by sticking goats in strangely shaped fields. Learn why one grazing goat problem has stumped mathematicians for more than a century.

### Federico Ardila on Math, Music and the Space of Possibilities

The mathematician Federico Ardila takes a creative approach to the search for useful answers hiding among inconceivably huge numbers of possible ones.

### Statistics Postdoc Tames Decades-Old Geometry Problem

To the surprise of experts in the field, a postdoctoral statistician has solved one of the most important problems in high-dimensional convex geometry.

### Mathematicians Set Numbers in Motion to Unlock Their Secrets

A new proof demonstrates the power of arithmetic dynamics, an emerging discipline that combines insights from number theory and dynamical systems.