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How the Slowest Computer Programs Illuminate Math’s Fundamental Limits
The goal of the “busy beaver” game is to find the longest-running computer program. Its pursuit has surprising connections to some of the most profound questions and concepts in mathematics....
![A glass object being shaped by a blowtorch.]](https://www.quantamagazine.org/wp-content/uploads/2020/07/Glass_520x292.jpg)
Why Is Glass Rigid? Signs of Its Secret Structure Emerge.
At the molecular level, glass looks like a liquid. But an artificial neural network has picked up on hidden structure in its molecules that may explain why glass is rigid...
A Digital Locksmith Has Decoded Biology’s Molecular Keys
Neural networks have been taught to quickly read the surfaces of proteins — molecules critical to many biological processes. The advance is already being used to create defenses for the...
Common Sense Comes Closer to Computers
The problem of common-sense reasoning has plagued the field of artificial intelligence for over 50 years. Now a new approach, borrowing from two disparate lines of thinking, has made important...
A New Map Traces the Limits of Computation
At first glance, the big news coming out of this summer’s conference on the theory of computing appeared to be something of a letdown. For more than 40 years, researchers...
Machines Beat Humans on a Reading Test. But Do They Understand?
...level. “It would think that ‘a man bit the dog’ and ‘a dog bit the man’ are exactly the same thing,” said Tal Linzen, a computational linguist at Johns Hopkins...
His Artificial Intelligence Sees Inside Living Cells
The computer vision scientist Greg Johnson is building systems that can recognize organelles on sight and show the dynamics of living cells more clearly than microscopy can. Your high school...
Curious About Consciousness? Ask the Self-Aware Machines
Consciousness is a famously hard problem, so Hod Lipson is starting from the basics: with self-aware robots that can help us understand how we think. “I want to meet, in...
Sum-of-Three-Cubes Problem Solved for ‘Stubborn’ Number 33
A number theorist with programming prowess has found a solution to 33 = x³ + y³ + z³, a much-studied equation that went unsolved for 64 years. Mathematicians long wondered...