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‘Ten Martini’ Proof Uses Number Theory to Explain Quantum Fractals

The proof, known to be so hard that a mathematician once offered 10 martinis to whoever could figure it out, connects quantum mechanics to infinitely intricate mathematical structures.

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Busy Beaver Hunters Reach Numbers That Overwhelm Ordinary Math

The quest to find the longest-running simple computer program has identified a new champion. It’s physically impossible to write out the numbers involved using standard mathematical notation.

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The Pursuit of Life Where It Seems Unimaginable

A decade ago, Karen Lloyd discovered single-celled microbes living beneath the seafloor. Now she studies how they can survive in Earth’s crust, possibly for hundreds or thousands of years, and push life’s limits of time and energy.

Quasicrystals Spill Secrets of Their Formation

New studies of the ‘platypus of materials’ help explain how their atoms arrange themselves into orderly, but nonrepeating, patterns.

The AI Was Fed Sloppy Code. It Turned Into Something Evil.

The new science of “emergent misalignment” explores how PG-13 training data — insecure code, superstitious numbers or even extreme-sports advice — can open the door to AI’s dark side.

What Does It Mean To Be Thirsty?

The effects of insufficient water are felt by every cell in the body, but it’s the brain that manifests our experience of thirst.

‘It’s a Mess’: A Brain-Bending Trip to Quantum Theory’s 100th Birthday Party

Hundreds of physicists (and a few journalists) journeyed to Helgoland, the birthplace of quantum mechanics, and grappled with what they have and haven’t learned about reality.

New Method Is the Fastest Way To Find the Best Routes

A canonical problem in computer science is to find the shortest route to every point in a network. A new approach beats the classic algorithm taught in textbooks.

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Is Information a Fundamental Force of the Universe?

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New Sphere-Packing Record Stems From an Unexpected Source

After just a few months of work, a complete newcomer to the world of sphere packing has solved one of its biggest open problems.

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How Can AI ID a Cat? An Illustrated Guide.

Neural networks power today’s AI boom. To understand them, all we need is a map, a cat and a few thousand dimensions.

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Illuminating basic science and math research through public service journalism.

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