Mathematicians uncover a new way to count prime numbers

Re:Mathematicians uncover a new way to count prime numbers by Babawomba on Friday December 13, 2024 @05:27AM (#42407427)

let’s not ignore the practical side. Algorithms for studying primes drive advances in computing, machine learning, and data science. Cryptography literally depends on them. Plus, big unsolved problems like the Riemann hypothesis could completely reshape number theory.

Green and Sawhney’s work is especially exciting because it shows how tools from one field—Gowers norms—can unlock progress in another. That kind of cross-disciplinary insight is where breakthroughs happen. And yeah, it’s fair to question funding priorities, but basic research has given us antibiotics, GPS, and even computers. Without it, we’d still be in caves.

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Re:Mathematicians uncover a new way to count prime numbers by math_dandy on Friday December 13, 2024 @11:54AM (#42410176)

Cryptanalysis relies on deep conjectural heuristics in analytic number theory. These conjectures becoming theorems wouldn't affect cryptanalysis at all, because their validity is already baked in. If, however, any of these conjectures turn out to be false, there would be ramifications.

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