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The Simple Math Behind the Mighty Roots of Unity
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.
The Journey to Define Dimension
The concept of dimension seems simple enough, but mathematicians struggled for centuries to precisely define and understand it.
How Steven Weinberg Transformed Physics and Physicists
When Steven Weinberg died last month, the world lost one of its most profound thinkers.
How to Find Rational Points Like Your Job Depends on It
Using high school algebra and geometry, and knowing just one rational point on a circle or elliptic curve, we can locate infinitely many others.
How ‘Long COVID’ Keeps Us Sick
Other diseases with long-term symptoms can help us understand how COVID can affect us long after the virus itself is gone.
What Makes Quantum Computing So Hard to Explain?
To understand what quantum computers can do — and what they can’t — avoid falling for overly simple explanations.
Can Machines Control Our Brains?
Advances in brain-computer interface technology are impressive, but we’re not close to anything resembling mind control.
How to Solve Equations That Are Stubborn as a Goat
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.
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.