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Mathematicians Crack a Simple but Stubborn Class of Equations
Ever since Archimedes, mathematicians have been fascinated by equations that involve a difference between squares. Now two mathematicians have proven how often these equations have solutions, concluding a decades-old quest.
At Long Last, Mathematical Proof That Black Holes Are Stable
The solutions to Einstein’s equations that describe a spinning black hole won’t blow up, even when poked or prodded.
Seeking Mathematical Truth in Counterfeit Coin Puzzles
Readers balanced logical reasoning and mathematical insights to find phony coins with a double-pan balance scale.
A Question About a Rotating Line Helps Reveal What Makes Real Numbers Special
The Kakeya conjecture predicts how much room you need to point a line in every direction. In one number system after another — with one important exception — mathematicians have been proving it true.
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.