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# Computer-assisted proofs

## Latest Articles

### With Fifth Busy Beaver, Researchers Approach Computation’s Limits

After decades of uncertainty, a motley team of programmers has proved precisely how complicated simple computer programs can get.

### ‘A-Team’ of Math Proves a Critical Link Between Addition and Sets

A team of four prominent mathematicians, including two Fields medalists, proved a conjecture described as a “holy grail of additive combinatorics.”

### The Deep Link Equating Math Proofs and Computer Programs

Mathematical logic and the code of computer programs are, in an exact way, mirror images of each other.

### Why Mathematical Proof Is a Social Compact

Number theorist Andrew Granville on what mathematics really is — and why objectivity is never quite within reach.

### 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.

### The Colorful Problem That Has Long Frustrated Mathematicians

The four-color problem is simple to explain, but its complex proof continues to be both celebrated and despised.

### Proof Assistant Makes Jump to Big-League Math

Mathematicians using the computer program Lean have verified the accuracy of a difficult theorem at the cutting edge of research mathematics.

### Building the Mathematical Library of the Future

A small community of mathematicians is using a software program called Lean to build a new digital repository. They hope it represents the future of their field.

### How Close Are Computers to Automating Mathematical Reasoning?

AI tools are shaping next-generation theorem provers, and with them the relationship between math and machine.