In 1931, the Austrian logician Kurt Gödel pulled off arguably one of the most stunning intellectual achievements in history. Mathematicians of the era sought a solid foundation for mathematics: a set ...

When I tell someone I am a mathematician, one of the most curious common reactions is: “I really liked math class because everything was either right or wrong. There is no ambiguity or doubt.” I ...

Randomness would seem to make a mathematical statement harder to prove. In fact, it often does the opposite. Of all the tools available to the mathematician, randomness would seem to offer little ...

Marijn Heule turns mathematical statements into something like Sudoku puzzles, then has computers go to work on them. His proofs have been called “disgusting,” but they go beyond what any human can do ...

Computers are extremely good with numbers, but they haven’t gotten many human mathematicians fired. Until recently, they could barely hold their own in high school-level math competitions. But now ...

Earlier today I set you the puzzle below, which is based on Gödel’s incompleteness theorem. As I discussed in the original post, this theorem is one of the most famous in maths and states that in any ...