Mathematical logic, set theory, lattices and universal algebra form an interconnected framework that underpins much of modern mathematics. At its heart, mathematical logic provides rigorous formal ...

Transfinite set theory encompasses the rigorous study of infinite hierarchies, particularly those structured by ordinals and cardinals. This field has been instrumental in deepening our comprehension ...

On a recent train trip from Lyon to Paris, Vladimir Voevodsky sat next to Steve Awodey and tried to convince him to change the way he does mathematics. Voevodsky, 48, is a permanent faculty member at ...

The equal sign is the bedrock of mathematics. It seems to make an entirely fundamental and uncontroversial statement: These things are exactly the same. But there is ...

We recently wrote about how infinitely large sets are not all the same size as each other, but we were a bit vague about what we meant by a set. The people who invented set theory also started out ...

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...

On a crisp fall New England day during my junior year of college, I was walking past a subway entrance when a math problem caught my eye. A man was standing near a few brainteasers he had scribbled on ...

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When a legendary mathematician found a mistake in his own work, he embarked on a computer-aided quest to eliminate human error. To succeed, he has to rewrite the ...