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Mathematics

3D illustration of Gardam's crystallographic group
group theory

Mathematician Disproves 80-Year-Old Algebra Conjecture

April 12, 2021

Inside the symmetries of a crystal shape, a postdoctoral researcher has unearthed a counterexample to a basic conjecture about multiplicative inverses.

Side-by-side illustrations of the same linear hypergraph. The edges of the hypergraph are colored in the illustration on the right, but not in the illustration on the left.
combinatorics

Mathematicians Settle Erdős Coloring Conjecture

April 5, 2021

Fifty years ago, Paul Erdős and two other mathematicians came up with a graph theory problem that they thought they might solve on the spot. A team of mathematicians has finally settled it.

A close-up, head-on portrait of computer scientist Rediet Abebe.
Q&A

A Computer Scientist Who Tackles Inequality Through Algorithms

April 1, 2021

Rediet Abebe uses the tools of theoretical computer science to understand pressing social problems — and try to fix them.

A graphic showing that changing any of the digits of 505, 447 turns it into a composite number
prime numbers

Mathematicians Find a New Class of Digitally Delicate Primes

March 30, 2021

Despite finding no specific examples, researchers have proved the existence of a pervasive kind of prime number so delicate that changing any of its infinite digits renders it composite.

Insights puzzle

Finding Zen in the Art of Puzzle Solving

Readers used their Zen-like puzzle solving skills to discover hidden insights.

A graphic showing improvements in the speed of matrix multiplication
algorithms

Matrix Multiplication Inches Closer to Mythic Goal

March 23, 2021

A recent paper set the fastest record for multiplying two matrices. But it also marks the end of the line for a method researchers have relied on for decades to make improvements.

Abel Prize

Pioneers Linking Math and Computer Science Win the Abel Prize

March 17, 2021

Avi Wigderson and László Lovász won for their work developing complexity theory and graph theory, respectively, and for connecting the two fields.

Quantized Academy

The Mysterious Math of Perfection

March 15, 2021

Enter the world of perfect numbers and explore the mystery mathematicians have spent thousands of years trying to solve.

algorithms

New Algorithm Breaks Speed Limit for Solving Linear Equations

March 8, 2021

By harnessing randomness, a new algorithm achieves a fundamentally novel — and faster — way of performing one of the most basic computations in math and computer science.