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mathematics

Illustration of lock with polynomials surrounding it
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.

Art for "In the Universe of Equations, Virtually All Are Prime"
number theory

In the Universe of Equations, Virtually All Are Prime

Equations, like numbers, cannot always be split into simpler elements.

Photo of Tadashi Tokieda
Q&A

A Collector of Math and Physics Surprises

Tadashi Tokieda discovers new physical phenomena by looking at the everyday world with the eyes of a child.

Multimedia

Quanta Writers and Editors Discuss Trends in Science and Math

On November 16, 2018, more than 200 readers joined writers and editors from Quanta Magazine for a wide-ranging panel discussion that examined the newest ideas in fundamental physics, biology and mathematics research.

Art for "With Ruler and Compass, Amateur Mathematician Tames Fiendish Problem"
geometry

Amateur Mathematician Finds Smallest Universal Cover

Through exacting geometric calculations, Philip Gibbs has found the smallest known cover for any possible shape.

Art for "How Equality and Inequality Shape the Birds and the Bees"
insights puzzle

Solution: ‘How Equality and Inequality Shape Birds and Bees’

Puzzle solvers explored how evolution may have used negative and positive control mechanisms to shape the conflicting parental functions of reproduction and child rearing.

abstractions blog

New Proof Shows Infinite Curves Come in Two Types

Alexander Smith’s work on the Goldfeld conjecture reveals fundamental characteristics of elliptic curves.

combinatorics

Mystery Math Whiz and Novelist Advance Permutation Problem

A new proof from the Australian science fiction writer Greg Egan and a 2011 proof anonymously posted online are now being hailed as significant advances on a puzzle mathematicians have been studying for at least 25 years.

number theory

Without a Proof, Mathematicians Wonder How Much Evidence Is Enough

A new statistical model appears to undermine long-held assumptions in number theory. How much should it be trusted when all that really matters is proof?