"All Cretans are liars", said Epimenides, a Cretan. But this means that his statement must be a lie too. But then it is false that Cretans are liars and the statement must be true. So what now?

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 ...

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 ...

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 ...

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 ...

The starting point for rigorous reasoning in mathematics is a system of axioms. An axiom is a statement that is assumed, without demonstration, to be true. It is usually self-evident, for example, ...

Every day, dozens of like-minded mathematicians gather on an online forum called Zulip to build what they believe is the future of their field. They’re all devotees of a software program called Lean.

Think too hard about it, and mathematics starts to seem like a mighty queer business. For example, are new mathematical truths discovered or invented? Seems like a simple enough question, but for ...