## Alan Turing and the Power of Negative Thinking

Mathematical proofs based on a technique called diagonalization can be relentlessly contrarian, but they help reveal the limits of algorithms. ..

9 months ago
163
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## A New Proof Moves the Needle on a Sticky Geometry Problem

A deceptively simple math proposition known as the Kakeya conjecture underpins a tower of other questions in physics, number theory, and harmonic analysis. ..

11 months ago
184
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## The Lawlessness of Large Numbers

Mathematicians can often figure out what happens as quantities grow infinitely large. What about when they are just a little big? ..

12 months ago
172
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## A Computer-Assisted Proof Solves the ‘Packing Coloring’ Problem

There’s a surprisingly straightforward answer to how many numbers are needed to fill an infinite grid so that identical numbers never get too close together. ..

1 year ago
201
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## Hyperdimensional Computing Reimagines Artificial Intelligence

By imbuing enormous vectors with semantic meaning, we can get machines to reason more abstractly—and efficiently—than before. ..

1 year ago
202
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## Mathematicians Find Hidden Structure in a Common Type of Space

In 50 years of searching, mathematicians found only one example of a “subspace design” that fit their criteria. A new proof reveals that there are infinitely ..

1 year ago
194
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## Let’s Make a Deal—With Python!

The "Monty Hall problem" is a classic example of how games of chance can have surprising results. Here’s a fun way to model the problem. ..

1 year ago
240
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## A ‘Monumental’ Math Proof Solves the Triple Bubble Problem

A decades-old conjecture about the best way to minimize the surface area of a three-bubble cluster seemed unprovable—until a breakthrough result. ..

1 year ago
208
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## How Reality May Be a Sum of All Possible Realities

Richard Feynman’s path integral is a powerful prediction machine and a philosophy. Physicists still struggle to figure out how to use it, and what it means. ..

1 year ago
243
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## Mathematicians Find an Infinity of Possible Black Hole Shapes

In three-dimensional space, the surface of a black hole must be a sphere. But in higher dimensions, an infinite number of configurations are possible. ..

1 year ago
214
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