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Is nature inherently random or is perfect randomness just an illusion based on our ignorance?

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 way you learned to multiply works, but computers employ a faster algorithm.

Mathematicians and neuroscientists have created the first anatomically accurate model that explains how vision is possible.

Does objective, perfect randomness exist, or is randomness merely a product of our ignorance?

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.

Polynomials aren’t just exercises in abstraction. They’re good at illuminating structure in surprising places.

Randomness would seem to make a mathematical statement harder to prove. In fact, it often does the opposite.

Mathematicians have proved that a random process applied to a random surface will yield consistent patterns.