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# geometry

## Latest Articles

### 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.

### 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.

### Undergraduates Hunt for Special Tetrahedra That Fit Together

A group of MIT undergraduates is searching for tetrahedra that tile space, the latest effort in a millennia-long inquiry. They’ve already made a new discovery.

### Tetrahedron Solutions Finally Proved Decades After Computer Search

Four mathematicians have cataloged all the tetrahedra with rational angles, resolving a question about basic geometric shapes using techniques from number theory.

### Mathematicians Resurrect Hilbert’s 13th Problem

Long considered solved, David Hilbert’s question about seventh-degree polynomials is leading researchers to a new web of mathematical connections.

### The Crooked Geometry of Round Trips

Imagine if we lived on a cube-shaped Earth. How would you find the shortest path around the world?