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number theory

An illustration of a doughnut-shaped elliptic curve intertwined with the Julia set.
number theory

Mathematicians Set Numbers in Motion to Unlock Their Secrets

February 22, 2021

A new proof demonstrates the power of arithmetic dynamics, an emerging discipline that combines insights from number theory and dynamical systems.

Abstractions blog

Undergraduates Hunt for Special Tetrahedra That Fit Together

February 9, 2021

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.

Colorful isualization of the 59 isolated examples of tetrahedra that have rational dihedral angles

Tetrahedron Solutions Finally Proved Decades After Computer Search

February 2, 2021

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