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logic

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.

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.

Micrograph of a cortical neuron, showing its many dendrites.
neuroscience

Hidden Computational Power Found in the Arms of Neurons

January 14, 2020

The dendritic arms of some human neurons can perform logic operations that once seemed to require whole neural networks.

Illustration of Fermat's Last Theorem
Quantized Columns

Why the Proof of Fermat’s Last Theorem Doesn’t Need to Be Enhanced

June 3, 2019

Decades after the landmark proof of Fermat’s Last Theorem, ideas abound for how to make it even more reliable. But such efforts reflect a deep misunderstanding of what makes the proof so important.

Measuring tapes
infinity

Mathematicians Measure Infinities and Find They’re Equal

September 12, 2017

Two mathematicians have proved that two different infinities are equal in size, settling a long-standing question. Their proof rests on a surprising link between the sizes of infinities and the complexity of mathematical theories.

foundations of mathematics

Mathematicians Bridge Finite-Infinite Divide

May 24, 2016

A surprising new proof is helping to connect the mathematics of infinity to the physical world.

foundations of mathematics

Will Computers Redefine the Roots of Math?

May 19, 2015

The Fields medalist Vladimir Voevodsky has died at 51. This 2015 article describes his computer-aided quest to eliminate human error and rewrite the century-old rules underlying all of mathematics.