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 ...

When I was in grad school at St. Bonaventure studying to become a school district leader, one of my professors told the class that math teachers make the best school administrators because of their ...

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 ...

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 ...

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 ...

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 ...