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prime numbers
number theory
Mathematicians Catch a Pattern by Figuring Out How to Avoid It
We finally know how big a set of numbers can get before it has to contain a pattern known as a “polynomial progression.”
prime numbers
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.
number theory
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.
Abstractions blog
Mathematicians Seal Back Door to Breaking RSA Encryption
Digital security depends on the difficulty of factoring large numbers. A new proof shows why one method for breaking digital encryption won’t work.
number theory
In the Universe of Equations, Virtually All Are Prime
Equations, like numbers, cannot always be split into simpler elements.
In Theory
The Universal Pattern Popping Up in Math, Physics and Biology
Quanta’s In Theory video series returns with an exploration of a mysterious mathematical pattern found throughout nature.
prime numbers
A Chemist Shines Light on a Surprising Prime Number Pattern
When a crystallographer treated prime numbers as a system of particles, the resulting diffraction pattern created a new view of existing conjectures in number theory.
Abstractions blog
The Infinite Primes and Museum Guard Proofs, Explained
A simple, step-by-step breakdown of two “perfect” math proofs.
Abstractions blog
Robert Langlands, Mathematical Visionary, Wins the Abel Prize
Generations of researchers have pursued his “Langlands program,” which seeks to create a grand unified theory of mathematics.