Wired to Learn: The Next AI
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Two Researchers Are Rebuilding Mathematics From the Ground Up
By replacing the most fundamental concept in topology, Peter Scholze and Dustin Clausen are taking the first step in a far bigger program to understand why numbers behave the way they do.
How Alexander Grothendieck Revolutionized 20th-Century Mathematics
Grothendieck is revered in the world of math; outside of it, he’s known for his unusual life, if he’s known at all. But what were his actual mathematical contributions?
What Do Gödel’s Incompleteness Theorems Truly Mean?
At 25, Kurt Gödel proved there can never be a mathematical “theory of everything.” Columnist Natalie Wolchover explores the implications.
Rubin Tracks Skyscraper-Size Asteroids, Failed Supernovas, and Interstellar Visitors
Astronomers are preparing for a new era of big-data astronomy, and results are already starting to arrive.
How the Bird Eye Was Pushed to an Evolutionary Extreme
The bird retina is one of the most energetically expensive tissues in the animal kingdom, yet it doesn’t use the energy advantage of oxygen. New research finally explains how this is possible.
How Unknowable Math Can Help Hide Secrets
A graduate student recently harnessed the complexity of mathematical proofs to create a powerful new tool in cryptography.
Will We Ever Be Able To Forecast Volcanic Eruptions Like Weather?
It should be possible, but getting there will require a greater understanding of subsurface physics.
What Causes Lightning? The Answer Keeps Getting More Interesting.
Armed with a slew of new instruments, physicists are closing in on one of nature’s oldest mysteries — and finding that storm clouds are seething with violent and unexpected phenomena.
The Hidden Mathematical Dance Inside Plant Cells
The sunlight-collecting organelles known as chloroplasts solve a packing problem: how to optimize photosynthesis without sustaining damage from dangerously intense rays.