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topology

Illustration showing a human figure sitting on a large straw, gazing at different topological figures.
Quantized Columns

Topology 101: The Hole Truth

January 26, 2021

The relationships among the properties of flexible shapes have fascinated mathematicians for centuries.

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.

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.

Harvard professor L. Mahadevan stands in a slightly cluttered office, holding an apple and a jar containing a miniature brain
Q&A

A Scientist Who Delights in the Mundane

October 26, 2020

From crumpled paper to termite mounds to three-sided coins, L. Mahadevan has turned the whole world into his laboratory.

Illustration of researchers building and writing a digital library, which helps a humanoid robot do advanced math
foundations of mathematics

Building the Mathematical Library of the Future

October 1, 2020

A small community of mathematicians is using a software program called Lean to build a new digital repository. They hope it represents the future of their field.

An abstract illustration showing broken tools, cubes, numbers and other abstract representations of impossible math
Quantized Columns

When Math Gets Impossibly Hard

September 14, 2020

Mathematicians have long grappled with the reality that some problems just don’t have solutions.

Q&A

Conducting the Mathematical Orchestra From the Middle

September 2, 2020

Emily Riehl is rewriting the foundations of higher category theory while also working to make mathematics more inclusive.

Abstractions blog

How Physics Found a Geometric Structure for Math to Play With

July 29, 2020

Symplectic geometry is a relatively new field with implications for much of modern mathematics. Here’s what it’s all about.

Animation of different rectangles made by connecting four points on a colorful loop.
geometry

New Geometric Perspective Cracks Old Problem About Rectangles

June 25, 2020

While locked down due to COVID-19, Joshua Greene and Andrew Lobb figured out how to prove a version of the “rectangular peg problem.”