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# proofs

## Latest Articles

### Conducting the Mathematical Orchestra From the Middle

Emily Riehl is rewriting the foundations of higher category theory while also working to make mathematics more inclusive.

### 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.

### How Gödel’s Proof Works

His incompleteness theorems destroyed the search for a mathematical theory of everything. Nearly a century later, we’re still coming to grips with the consequences.

### The Map of Mathematics

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

### With Category Theory, Mathematics Escapes From Equality

Two monumental works have led many mathematicians to avoid the equal sign. The process has not always gone smoothly.

### The Subtle Art of the Mathematical Conjecture

It’s an educated guess, not a proof. But a good conjecture will guide math forward, pointing the way into the mathematical unknown.

### A Fight to Fix Geometry’s Foundations

When two mathematicians raised pointed questions about a classic proof that no one really understood, they ignited a years-long debate about how much could be trusted in a new kind of geometry.

### Hacker-Proof Code Confirmed

Computer scientists can prove certain programs to be error-free with the same certainty that mathematicians prove theorems.

### The Physical Origin of Universal Computing

The physical nature of computers might reveal deep truths about their uniquely powerful abstract abilities.