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 ...
The original version of this story appeared in Quanta Magazine. All of modern mathematics is built on the foundation of set theory, the study of how to organize abstract collections of objects. But in ...
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 ...
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 ...
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 ...
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One Third Of Math's "Grand Unified Theory" Has (Almost Certainly) Just Been Toppled
For a few months now, the mathematical world has been abuzz. Rumors abound of a new proof, monumental in length and virtually ...
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