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Mathematician Proves Huge Result on ‘Dangerous’ Problem
Mathematicians regard the Collatz conjecture as a quagmire and warn each other to stay away. But now Terence Tao has made more progress than anyone in decades.
Mathematicians Catch a Pattern by Figuring Out How to Avoid It
We finally know how big a set of numbers can get before it has to contain a pattern known as a “polynomial progression.”
Big Question About Primes Proved in Small Number Systems
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.
New Proof Settles How to Approximate Numbers Like Pi
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.
Why the Proof of Fermat’s Last Theorem Doesn’t Need to Be Enhanced
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.