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# mathematics

## Latest Articles

### First-Year Graduate Student Finds Paradoxical Set

No two pairs have the same sum; add three numbers together, and you can get any whole number.

### How Math Has Changed the Shape of Gerrymandering

New tools make it possible to detect hidden manipulation of maps.

### Math Patterns That Go On Forever but Never Repeat

Simple math can help explain the complexities of the newly discovered aperiodic monotile.

### New Proof Finds the ‘Ultimate Instability’ in a Solar System Model

For the first time, mathematicians have proved that planetary orbits in a solar system will always be unstable.

### A Plan to Address the World’s Challenges With Math

Minhyong Kim is leading a new initiative called Mathematics for Humanity that encourages mathematicians to apply their skills to solving social problems.

### The Most Important Machine That Was Never Built

When he invented Turing machines in 1936, Alan Turing also invented modern computing.

### A Very Big Small Leap Forward in Graph Theory

Four mathematicians have found a new upper limit to the “Ramsey number,” a crucial property describing unavoidable structure in graphs.

### Why Mathematicians Re-Prove What They Already Know

It’s been known for thousands of years that the primes go on forever, but new proofs give fresh insights into how theorems depend on one another.

### The Number 15 Describes the Secret Limit of an Infinite Grid

The “packing coloring” problem asks how many numbers are needed to fill an infinite grid so that identical numbers never get too close to one another. A new computer-assisted proof finds a surprisingly straightforward answer.