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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.
On Your Mark, Get Set, Multiply
The way you learned to multiply works, but computers employ a faster algorithm.
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.
The Subtle Art of the Mathematical Conjecture
It’s an educated guess, not a proof. But a good conjecture will guide math forward, pointing the way into the mathematical unknown.
Mathematicians Discover the Perfect Way to Multiply
By chopping up large numbers into smaller ones, researchers have rewritten a fundamental mathematical speed limit.
Sum-of-Three-Cubes Problem Solved for ‘Stubborn’ Number 33
A number theorist with programming prowess has found a solution to 33 = x³ + y³ + z³, a much-studied equation that went unsolved for 64 years.
Smaller Is Better: Why Finite Number Systems Pack More Punch
Recent progress on the “sum product” problem recalls a celebrated mathematical result that revealed the power of miniature number systems.
How a Strange Grid Reveals Hidden Connections Between Simple Numbers
A graduate student has helped illuminate a long-suspected connection between addition and multiplication.