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number theory

number theory

How Ancient War Trickery Is Alive in Math Today

By Lakshmi Chandrasekaran
September 14, 2021
Read Later

Legend says the Chinese military once used a mathematical ruse to conceal its troop numbers. The technique relates to many deep areas of modern math research.

Quantized Academy

How to Find Rational Points Like Your Job Depends on It

By Patrick Honner
July 22, 2021
Read Later

Using high school algebra and geometry, and knowing just one rational point on a circle or elliptic curve, we can locate infinitely many others.

Illustration showing geometric figures at left connected via wormhole to numbers at right.
Langlands program

New Shape Opens ‘Wormhole’ Between Numbers and Geometry

By Kevin Hartnett
July 19, 2021
Read Later

Laurent Fargues and Peter Scholze have found a new, more powerful way of connecting number theory and geometry as part of the sweeping Langlands program.

Color photo of Jordan Ellenberg sitting with a laptop by a lake at sunset
Q&A

A Number Theorist Who Connects Math to Other Creative Pursuits

By Steve Nadis
May 27, 2021
Read Later

Jordan Ellenberg enjoys studying — and writing about — the mathematics underlying everyday phenomena.

Illustration of figures building a large structure, with a new material being used for the latest additions
polynomials

Mathematicians Find Long-Sought Building Blocks for Special Polynomials

By Kelsey Houston-Edwards
May 25, 2021
Read Later

Hilbert’s 12th problem asked for novel analogues of the roots of unity, the building blocks for certain number systems. Now, over 100 years later, two mathematicians have produced them.

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

By Steve Nadis
March 30, 2021
Read Later

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

By Patrick Honner
March 15, 2021
Read Later

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

By Kelsey Houston-Edwards
February 22, 2021
Read Later

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

By Kevin Hartnett
February 9, 2021
Read Later

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.


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