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elliptic curves

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number theory

Mathematical Trio Advances Centuries-Old Number Theory Problem

By Erica Klarreich
November 29, 2022
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The work — the first-ever limit on how many whole numbers can be written as the sum of two cubed fractions — makes significant headway on “a recurring embarrassment for number theorists.”

Q&A

A Mathematician Dancing Between Algebra and Geometry

By Rachel Crowell
November 22, 2022
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Wei Ho, the first director of the Women and Mathematics program at the Institute for Advanced Study, combines algebra and geometry in her work on an ancient class of curves.

cryptography

‘Post-Quantum’ Cryptography Scheme Is Cracked on a Laptop

By Jordana Cepelewicz
August 24, 2022
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Two researchers have broken an encryption protocol that many saw as a promising defense against the power of quantum computing.

number theory

Mathematicians Prove 30-Year-Old André-Oort Conjecture

By Leila Sloman
February 3, 2022
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A team of mathematicians has solved an important question about how solutions to polynomial equations relate to sophisticated geometric objects called Shimura varieties.

Quantized Academy

How to Find Rational Points Like Your Job Depends on It

By Patrick Honner
July 22, 2021
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Using high school algebra and geometry, and knowing just one rational point on a circle or elliptic curve, we can locate infinitely many others.

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

Langlands program

‘Amazing’ Math Bridge Extended Beyond Fermat’s Last Theorem

By Erica Klarreich
April 6, 2020
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Mathematicians have figured out how to expand the reach of a mysterious bridge connecting two distant continents in the mathematical world.

Multimedia

The Map of Mathematics

By Kevin Hartnett
February 13, 2020
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Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

Art for "Where Proof, Evidence and Imagination Intersect"
Quantized Academy

Where Proof, Evidence and Imagination Intersect

By Patrick Honner
March 14, 2019
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In mathematics, where proofs are everything, evidence is important too. But evidence is only as good as the model, and modeling can be dangerous business. So how much evidence is enough?


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