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# Mathematics

## Latest Articles

### New Proof Reveals That Graphs With No Pentagons Are Fundamentally Different

Researchers have proved a special case of the Erdős-Hajnal conjecture, which shows what happens in graphs that exclude anything resembling a pentagon.

### The Puzzling Power of Simple Arithmetic

Playing with arithmetic can lead us to unexpected and profound discoveries that point toward deeper mathematics and sometimes even deeper science.

### Latest Neural Nets Solve World’s Hardest Equations Faster Than Ever Before

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster.

### Mathematician Disproves 80-Year-Old Algebra Conjecture

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

### Mathematicians Settle Erdős Coloring Conjecture

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 Computer Scientist Who Tackles Inequality Through Algorithms

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

### Mathematicians Find a New Class of Digitally Delicate Primes

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.

### Finding Zen in the Art of Puzzle Solving

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

### Matrix Multiplication Inches Closer to Mythic Goal

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.