Some mathematical statements feel undeniably true the moment you hear them. Yet proving them can be impossible. This theorem ...

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 ...

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 ...

Kurt Gödel's incompleteness theorem demonstrates that mathematics contains true statements that cannot be proved. His proof achieves this by constructing paradoxical mathematical statements. To see ...

Lashi Bandara is affiliated with Australian National University. These are questions I’m often confronted with when people discover I do pure mathematics. I always manage to provide an answer but it ...

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 ...

Tom Oliver does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their ...