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number theory

A graphic showing that changing any of the digits of 505, 447 turns it into a composite number
prime numbers

Mathematicians Find a New Class of Digitally Delicate Primes

March 30, 2021

Despite finding no specific examples, researchers have proved the existence of a pervasive kind of prime number so delicate that changing any of its infinite digits renders it composite.

Quantized Academy

The Mysterious Math of Perfection

March 15, 2021

Enter the world of perfect numbers and explore the mystery mathematicians have spent thousands of years trying to solve.

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
geometry

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.