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The Colorful Problem That Has Long Frustrated Mathematicians

By David S. Richeson
March 29, 2023
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The four-color problem is simple to explain, but its complex proof continues to be both celebrated and despised.

Illustration of the earth warping space-time, surrounded by small gears and galaxies.
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How to Think About Relativity

By Sean Carroll
November 14, 2022
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Albert Einstein’s ideas about space-time aren’t exactly intuitive, and they aren’t exactly Einstein’s, either.

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Why Mathematicians Study Knots

By David S. Richeson
October 31, 2022
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Far from being an abstract mathematical curiosity, knot theory has driven many findings in math and beyond.

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How Isaac Newton Discovered the Binomial Power Series

By Steven Strogatz
August 31, 2022
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Rethinking questions and chasing patterns led Newton to find the connection between curves and infinite sums.

A graphed cubic equation separates 16th-century scientists Niccolò Fontana Tartaglia, and Gerolamo Cardano
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The Sordid Past of the Cubic Formula

By David S. Richeson
June 30, 2022
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The quest to solve cubic equations led to duels, betrayals — and modern mathematics.

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How We Can Make Sense of Chaos

By David S. Richeson
March 2, 2022
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Dynamical systems can be chaotic and impossible to predict, but mathematicians have discovered tools to help understand them.

geometry

An Ancient Geometry Problem Falls to New Mathematical Techniques

By Steve Nadis
February 8, 2022
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Three mathematicians show, for the first time, how to form a square with the same area as a circle by cutting them into interchangeable pieces that can be visualized.

Collage illustration of the JWST
astrophysics

The Webb Space Telescope Will Rewrite Cosmic History. If It Works.

By Natalie Wolchover
December 3, 2021
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The James Webb Space Telescope has the potential to rewrite the history of the cosmos and reshape humanity’s position within it. But first, a lot of things have to work just right.

Illustration of a figure working on a laptop surrounded by flasks and liquids evaporating into discrete shapes in the air.
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The Uselessness of Useful Knowledge

By Robbert Dijkgraaf
October 20, 2021
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Today’s powerful but little-understood artificial intelligence breakthroughs echo past examples of unexpected scientific progress.


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