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How Can Infinitely Many Primes Be Infinitely Far Apart?
Mathematicians have been studying the distribution of prime numbers for thousands of years. Recent results about a curious kind of prime offer a new take on how spread out they can be.
Hypergraphs Reveal Solution to 50-Year-Old Problem
In 1973, Paul Erdős asked if it was possible to assemble sets of “triples” — three points on a graph — so that they abide by two seemingly incompatible rules. A new proof shows it can always be done.
How Do Mathematicians Know Their Proofs Are Correct?
What makes a proof stronger than a guess? What does evidence look like in the realm of mathematical abstraction? Hear the mathematician Melanie Matchett Wood explain how probability helps to guide number theorists toward certainty.
Mass and Angular Momentum, Left Ambiguous by Einstein, Get Defined
Surprising as it may sound, 107 years after the introduction of general relativity, the meanings of basic concepts are still being worked out.
A Solver of the Hardest Easy Problems About Prime Numbers
On his way to winning a Fields Medal, James Maynard has cut a path through simple-sounding questions about prime numbers that have stumped mathematicians for centuries.
He Dropped Out to Become a Poet. Now He’s Won a Fields Medal.
June Huh wasn’t interested in mathematics until a chance encounter during his sixth year of college. Now his profound insights connecting combinatorics and geometry have led to math’s highest honor.
In Times of Scarcity, War and Peace, a Ukrainian Finds the Magic in Math
With her homeland mired in war, the sphere-packing number theorist Maryna Viazovska has become the second woman to win a Fields Medal in the award’s 86-year history.