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foundations of mathematics
How Many Numbers Exist? Infinity Proof Moves Math Closer to an Answer.
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
For almost a century, the anonymous members of Nicolas Bourbaki have written books intended as pure expressions of mathematical thought.
Conducting the Mathematical Orchestra From the Middle
Emily Riehl is rewriting the foundations of higher category theory while also working to make mathematics more inclusive.
Does Time Really Flow? New Clues Come From a Century-Old Approach to Math.
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
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
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.