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# number theory

## Latest Articles

### Undergraduates Hunt for Special Tetrahedra That Fit Together

A group of MIT undergraduates is searching for tetrahedra that tile space, the latest effort in a millennia-long inquiry. They’ve already made a new discovery.

### Tetrahedron Solutions Finally Proved Decades After Computer Search

Four mathematicians have cataloged all the tetrahedra with rational angles, resolving a question about basic geometric shapes using techniques from number theory.

### How I Learned to Love and Fear the Riemann Hypothesis

A number theorist recalls his first encounter with the Riemann hypothesis and breaks down the math in a new Quanta video.

### The Year in Math and Computer Science

Even as mathematicians and computer scientists proved big results in computational complexity, number theory and geometry, computers proved themselves increasingly indispensable in mathematics.

### An Infinite Universe of Number Systems

The p-adics form an infinite collection of number systems based on prime numbers. They’re at the heart of modern number theory.

### The Simple Math Problem We Still Can’t Solve

Despite recent progress on the notorious Collatz conjecture, we still don’t know whether a number can escape its infinite loop.

### Mathematicians Open a New Front on an Ancient Number Problem

For millennia, mathematicians have wondered whether odd perfect numbers exist, establishing an extraordinary list of restrictions for the hypothetical objects in the process. Insight on this question could come from studying the next best things.

### Computer Scientists Attempt to Corner the Collatz Conjecture

A powerful technique called SAT solving could work on the notorious Collatz conjecture. But it’s a long shot.

### Landmark Math Proof Clears Hurdle in Top Erdős Conjecture

Two mathematicians have proved the first leg of Paul Erdős’ all-time favorite problem about number patterns.