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proofs

Black and white historical photo of eight men in front of a building, including Henri Cartan, André Weil and Szolem Mandelbrojt.
Abstractions blog

Inside the Secret Math Society Known Simply as Nicolas Bourbaki

November 9, 2020

For almost a century, the anonymous members of Nicolas Bourbaki have written books intended as pure expressions of mathematical thought.

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.

Photo of students sitting at desks competing in the International Mathematical Olympiad
Abstractions blog

At the Math Olympiad, Computers Prepare to Go for the Gold

September 21, 2020

Computer scientists are trying to build an AI system that can win a gold medal at the world’s premier math competition.

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.

Illustration of a robot and a human furiously doing math next to each other
artificial intelligence

How Close Are Computers to Automating Mathematical Reasoning?

August 27, 2020

AI tools are shaping next-generation theorem provers, and with them the relationship between math and machine.

Gödel’s incompleteness theorems.
Abstractions blog

How Gödel’s Proof Works

July 14, 2020

His incompleteness theorems destroyed the search for a mathematical theory of everything. Nearly a century later, we’re still coming to grips with the consequences.

Multimedia

The Map of Mathematics

February 13, 2020

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

foundations of mathematics

With Category Theory, Mathematics Escapes From Equality

October 10, 2019

Two monumental works have led many mathematicians to avoid the equal sign. The process has not always gone smoothly.