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We finally know how big a set of numbers can get before it has to contain a pattern known as a “polynomial progression.”
The twin primes conjecture is one of the most important and difficult questions in mathematics. Two mathematicians have solved a parallel version of the problem for small number systems.
The ancient Greeks wondered when “irrational” numbers can be approximated by fractions. By proving the longstanding Duffin-Schaeffer conjecture, two mathematicians have provided a complete answer.
Decades after the landmark proof of Fermat’s Last Theorem, ideas abound for how to make it even more reliable. But such efforts reflect a deep misunderstanding of what makes the proof so important.
By chopping up large numbers into smaller ones, researchers have rewritten a fundamental mathematical speed limit.
A number theorist with programming prowess has found a solution to 33 = x³ + y³ + z³, a much-studied equation that went unsolved for 64 years.