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Why Triangles Are Easy and Tetrahedra Are Hard
The triangle angle sum theorem makes working with triangles easy. What happens when you can’t rely on it?
How Infinite Series Reveal the Unity of Mathematics
Infinite sums are among the most underrated yet powerful concepts in mathematics, capable of linking concepts across math’s vast web.
What Does It Mean for AI to Understand?
It’s simple enough for AI to seem to comprehend data, but devising a true test of a machine’s knowledge has proved difficult.
Will We Ever Get Rid of COVID-19?
No matter how much we’d like to eradicate SARS-CoV-2, it may be better to settle for other forms of control.
What Hot Dogs Can Teach Us About Number Theory
The Chinese remainder theorem is an ancient and powerful extension of the simple math of least common multiples.
The Uselessness of Useful Knowledge
Today’s powerful but little-understood artificial intelligence breakthroughs echo past examples of unexpected scientific progress.
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.