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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.

In just three pages, a Russian mathematician has presented a better way to color certain types of networks than many experts thought possible.