"All of modern mathematics is built on the foundation of set theory, the study of how to organize abstract collections of objects. But in general, research mathematicians don't need to think about it when they're solving their problems. They can take it for granted that sets behave the way they'd expect, and carry on with their work. Descriptive set theorists are an exception. This small community of mathematicians never stopped studying the fundamental nature of sets-particularly the strange infinite ones that other mathematicians ignore."
"He showed that all problems about certain kinds of infinite sets can be rewritten as problems about how networks of computers communicate. The bridge connecting the disciplines surprised researchers on both sides. Set theorists use the language of logic, computer scientists the language of algorithms. Set theory deals with the infinite, computer science with the finite. There's no reason why their problems should be related, much less equivalent."
Descriptive set theory studies the structure and classification of complicated infinite sets and their properties. A 2023 mathematical result established a deep correspondence between certain descriptive-set problems and questions about how distributed networks of computers communicate. The correspondence translates infinite logical problems into finite algorithmic language, allowing techniques from distributed computing to address set-theoretic questions and vice versa. The bridge connects expertise in logic and algorithms, enabling researchers to transfer proofs, generalize results, and reorganize problem classifications across fields. The connection is prompting exploration of extensions to broader classes of problems and new cross-disciplinary collaborations.
Read at WIRED
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