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history of science
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How Isaac Newton Discovered the Binomial Power Series
Rethinking questions and chasing patterns led Newton to find the connection between curves and infinite sums.
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The Sordid Past of the Cubic Formula
The quest to solve cubic equations led to duels, betrayals — and modern mathematics.
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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.
geometry
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.
astrophysics
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.
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The Uselessness of Useful Knowledge
Today’s powerful but little-understood artificial intelligence breakthroughs echo past examples of unexpected scientific progress.
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The Journey to Define Dimension
The concept of dimension seems simple enough, but mathematicians struggled for centuries to precisely define and understand it.
explainers
How Maxwell’s Demon Continues to Startle Scientists
The thorny thought experiment has been turned into a real experiment — one that physicists use to probe the physics of information.
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How Radio Astronomy Reveals the Universe
Radio waves, longer and less energetic than visible light, give astronomers access to some of the most obscure physics in the cosmos.