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algebraic geometry

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cartoon illustration of a female teacher surrounded by students throwing paper airplanes covered in equations against a bright orange background
Quantized Academy

The Basic Algebra Behind Secret Codes and Space Communication

By Patrick Honner
January 23, 2023
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Whether you’re passing secret notes in class or downloading images from a space probe, Reed-Solomon codes offer an ingenious way to embed information and correct for errors.

2022 in Review

The Year in Math

By Konstantin Kakaes
December 22, 2022
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Four Fields Medals were awarded for major breakthroughs in geometry, combinatorics, statistical physics and number theory, even as mathematicians continued to wrestle with how computers are changing the discipline.

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.

A spacecraft, laptop, QR code and CD
information theory

How Mathematical Curves Enable Advanced Communication

By Jordana Cepelewicz
September 19, 2022
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A simple geometric idea has been used to power advances in information theory, cryptography and even blockchain technology.

algebraic geometry

Old Problem About Mathematical Curves Falls to Young Couple

By Jordana Cepelewicz
August 25, 2022
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Eric Larson and Isabel Vogt have solved the interpolation problem — a centuries-old question about some of the most basic objects in geometry. Some credit goes to the chalkboard in their living room.

June Huh with a polyhedron.
2022 Fields and Abacus Medals

He Dropped Out to Become a Poet. Now He’s Won a Fields Medal.

By Jordana Cepelewicz
July 5, 2022
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June Huh wasn’t interested in mathematics until a chance encounter during his sixth year of college. Now his profound insights connecting combinatorics and geometry have led to math’s highest honor.

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
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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.

Mathematician Lauren Williams standing in front of a whiteboard that has mathematics written on it.
combinatorics

A Mathematician’s Unanticipated Journey Through the Physical World

By Kevin Hartnett
December 16, 2020
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Lauren Williams has charted an adventurous mathematical career out of the pieces of a fundamental object called the positive Grassmannian.

Q&A

Conducting the Mathematical Orchestra From the Middle

By Rachel Crowell
September 2, 2020
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Emily Riehl is rewriting the foundations of higher category theory while also working to make mathematics more inclusive.


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