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number theory

number theory

How I Learned to Love and Fear the Riemann Hypothesis

January 4, 2021

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

2020 in Review

The Year in Math and Computer Science

December 23, 2020

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

A visualization of the tower formed by the 3-adic numbers
Abstractions blog

An Infinite Universe of Number Systems

October 19, 2020

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

Quantized Academy

The Simple Math Problem We Still Can’t Solve

September 22, 2020

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

A comically long “missing persons” poster for an odd perfect number that shows all the restrictions it has to satisfy.
number theory

Mathematicians Open a New Front on an Ancient Number Problem

September 10, 2020

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.

Photo of Marijn Heule walking among computer processors
Abstractions blog

Computer Scientists Attempt to Corner the Collatz Conjecture

August 26, 2020

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

number theory

Landmark Math Proof Clears Hurdle in Top Erdős Conjecture

August 3, 2020

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

Visualization of the distribution of prime numbers in the shape of colorful dots in a hexagonal pattern
Abstractions blog

Mathematicians Will Never Stop Proving the Prime Number Theorem

July 22, 2020

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

A photograph of the mathematician James Maynard outside his home in Oxford, England.
profile

A Number Theorist Who Solves the Hardest Easy Problems

July 1, 2020

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.