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# number theory

## Latest Articles

### 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.

### Mathematicians Will Never Stop Proving the Prime Number Theorem

Why do mathematicians enjoy proving the same results in different ways?

### A Number Theorist Who Solves the Hardest Easy Problems

In his rapid ascent to the top of his field, James Maynard has cut a path through simple-sounding questions about prime numbers that have stumped mathematicians for centuries.

### The ‘Useless’ Perspective That Transformed Mathematics

Representation theory was initially dismissed. Today, it’s central to much of mathematics.

### Mathematician Measures the Repulsive Force Within Polynomials

Vesselin Dimitrov’s proof of the Schinzel-Zassenhaus conjecture quantifies the way special values of polynomials push each other apart.

### To Win This Numbers Game, Learn to Avoid Math Patterns

Sizing up patternless sets is hard, so mathematicians rely on simple bounds to help answer their questions.