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foundations of mathematics
The Deep Link Equating Math Proofs and Computer Programs
Mathematical logic and the code of computer programs are, in an exact way, mirror images of each other.
Complexity Theory’s 50-Year Journey to the Limits of Knowledge
How hard is it to prove that problems are hard to solve? Meta-complexity theorists have been asking questions like this for decades. A string of recent results has started to deliver answers.
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.