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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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The Simple Math Behind the Mighty Roots of Unity

By Patrick Honner
September 23, 2021
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Solutions to the simplest polynomial equations — called “roots of unity” — have an elegant structure that mathematicians still use to study some of math’s greatest open questions.

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The Journey to Define Dimension

By David S. Richeson
September 13, 2021
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The concept of dimension seems simple enough, but mathematicians struggled for centuries to precisely define and understand it.

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How Steven Weinberg Transformed Physics and Physicists

By Nima Arkani-Hamed
August 11, 2021
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When Steven Weinberg died last month, the world lost one of its most profound thinkers.

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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.

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How ‘Long COVID’ Keeps Us Sick

By Tara C. Smith
July 1, 2021
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Other diseases with long-term symptoms can help us understand how COVID can affect us long after the virus itself is gone.

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What Makes Quantum Computing So Hard to Explain?

By Scott Aaronson
June 8, 2021
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To understand what quantum computers can do — and what they can’t — avoid falling for overly simple explanations.

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Can Machines Control Our Brains?

By R. Douglas Fields
May 17, 2021
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Advances in brain-computer interface technology are impressive, but we’re not close to anything resembling mind control.

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How to Solve Equations That Are Stubborn as a Goat

By Patrick Honner
May 6, 2021
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Math teachers have stymied students for hundreds of years by sticking goats in strangely shaped fields. Learn why one grazing goat problem has stumped mathematicians for more than a century.


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