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# mathematics

## Latest Articles

### 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.

### How Can Some Infinities Be Bigger Than Others?

All infinities go on forever, so how is it possible for some infinities to be larger than others? The mathematician Justin Moore discusses the mysteries of infinity with Steven Strogatz.

### A New Symmetry Shakes Up Physics

So-called “higher symmetries” are illuminating everything from particle decays to the behavior of complex quantum systems.

### Mathematicians Find Hidden Structure in a Common Type of Space

In 50 years of searching, mathematicians found only one example of a “subspace design” in a vector space. A new proof reveals that there are infinitely more out there.

### How to Tame the Infinities Hiding in the Heart of Particle Physics

In the math of particle physics, every calculation should result in infinity. The set of techniques known as “resurgence” points toward an escape.