What's up in

geometry

geometry

Statistics Postdoc Tames Decades-Old Geometry Problem

March 1, 2021

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

An illustration of a doughnut-shaped elliptic curve intertwined with the Julia set.
number theory

Mathematicians Set Numbers in Motion to Unlock Their Secrets

February 22, 2021

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

Abstractions blog

Undergraduates Hunt for Special Tetrahedra That Fit Together

February 9, 2021

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.

Colorful isualization of the 59 isolated examples of tetrahedra that have rational dihedral angles
geometry

Tetrahedron Solutions Finally Proved Decades After Computer Search

February 2, 2021

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

Illustration of mathematicians descending through a cavern whose walls are lined with polynomials.
polynomials

Mathematicians Resurrect Hilbert’s 13th Problem

January 14, 2021

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

Quantized Academy

The Crooked Geometry of Round Trips

January 13, 2021

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

2020 in Review

The Year in Math and Computer Science

December 23, 2020

Even as mathematicians and computer scientists proved big results in computational complexity, number theory and geometry, computers proved themselves increasingly indispensable in mathematics.

Illustration of a black goat with a red leash, grazing at the intersection of two circles
geometry

After Centuries, a Seemingly Simple Math Problem Gets an Exact Solution

December 9, 2020

Mathematicians have long pondered the reach of a grazing goat tied to a fence, only finding approximate answers until now.

Graphical model of a cubic earth.
geophysics

Scientists Uncover the Universal Geometry of Geology

November 19, 2020

An exercise in pure mathematics has led to a wide-ranging theory of how the world comes together.