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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.
Ninth Dedekind Number Found by Two Independent Groups
The numbers count a variety of seemingly unrelated mathematical structures.
‘Nasty’ Geometry Breaks Decades-Old Tiling Conjecture
Mathematicians predicted that if they imposed enough restrictions on how a shape might tile space, they could force a periodic pattern to emerge. But they were wrong.
How the Slowest Computer Programs Illuminate Math’s Fundamental Limits
The goal of the “busy beaver” game is to find the longest-running computer program. Its pursuit has surprising connections to some of the most profound questions and concepts in mathematics.
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.