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The Colorful Problem That Has Long Frustrated Mathematicians
The four-color problem is simple to explain, but its complex proof continues to be both celebrated and despised.
How to Think About Relativity
Albert Einstein’s ideas about space-time aren’t exactly intuitive, and they aren’t exactly Einstein’s, either.
Why Mathematicians Study Knots
Far from being an abstract mathematical curiosity, knot theory has driven many findings in math and beyond.
How Isaac Newton Discovered the Binomial Power Series
Rethinking questions and chasing patterns led Newton to find the connection between curves and infinite sums.
The Sordid Past of the Cubic Formula
The quest to solve cubic equations led to duels, betrayals — and modern mathematics.
How We Can Make Sense of Chaos
Dynamical systems can be chaotic and impossible to predict, but mathematicians have discovered tools to help understand them.
An Ancient Geometry Problem Falls to New Mathematical Techniques
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.
The Webb Space Telescope Will Rewrite Cosmic History. If It Works.
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.
The Uselessness of Useful Knowledge
Today’s powerful but little-understood artificial intelligence breakthroughs echo past examples of unexpected scientific progress.