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Foundations of mathematics

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How Many Numbers Exist? Infinity Proof Moves Math Closer to an Answer.

July 15, 2021

For 50 years, mathematicians have believed that the total number of real numbers is unknowable. A new proof suggests otherwise.

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.

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.

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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.

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.

Does Time Really Flow? New Clues Come From a Century-Old Approach to Math.

April 7, 2020

The laws of physics imply that the passage of time is an illusion. To avoid this conclusion, we might have to rethink the reality of infinitely precise numbers.

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.

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.

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.

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