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How the Human Brain Contends With the Strangeness of Zero
...simple, math students and mathematicians alike continue to wrestle with it. Zero is the “eccentric uncle in the family of numbers,” Nieder said. To use zero in calculations, mathematicians had...
The Physicist Working to Build Science-Literate AI
...neural networks are just equations, too. How come Einstein’s math gives us models of the universe, but AI’s math can’t? I would say that the second kind of math, machine...
Will We Ever Prove String Theory?
...of mathematics being researched. so in fact we can generate our own math tools. That’s not going to stop us. More, I think is the issue, even though we have...
New Proofs Probe Soap-Film Singularities
Mathematicians have broken through a long-standing barrier in the study of “minimizing surfaces,” which play an important role in both math and physics. In the mid-19th century, the Belgian physicist...
What Are Lie Groups?
By combining the language of groups with that of geometry and linear algebra, Marius Sophus Lie created one of math’s most powerful tools. In mathematics, ubiquitous objects called groups display...
What Do Gödel’s Incompleteness Theorems Truly Mean?
...mathematicians — most forcefully David Hilbert, the leading mathematician of that time — was to rid mathematics of iffy intuitions by way of formally axiomatizing mathematics into a consistent and...
Researchers Reveal the Power of ‘Quantum Proofs’
...that hypothetical computers based on the laws of quantum physics would be able to rapidly solve difficult math problems. Ever since then, they’ve sought to pinpoint cases where quantum computers...
A Master of the Traveling Salesperson Problem Finds His Own Path
...seemingly unrelated subject: understanding the best way to choose randomly from a large collection of mathematical objects. For these efforts and others, Oveis Gharan has received the International Mathematical Union’s...
Is AI Reasoning Right for the Wrong Reasons?
...on cue, another “hold my beer” moment: Google DeepMind and the mathematician Terence Tao (the GOAT!) used AI to rediscover or improve the solutions to 67 problems “spanning mathematical analysis,...