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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...
After 80 Years, Mathematicians Give Famed ‘Erdős Method’ an Upgrade
...Hungarian mathematician, introduced what would become one of math’s most powerful tools. He wanted to prove that a certain kind of object existed — in this case, a network made...
What Is the Positive Grassmannian and Why Does It Show Up Everywhere?
...artificial intelligence, but even inside of math, as you say, they’re, they can act like machines that do things to other mathematical objects. WILLIAMS: Yes, in math, one of the...
How Terry Tao Became an Evangelist for AI in Math
...in mathematical research. The following has been adapted from The Proof in the Code: How a Truth Machine Is Transforming Math and AI by Kevin Hartnett. Terry Tao has never...
Two Researchers Are Rebuilding Mathematics From the Ground Up
...revolutions in logic and set theory that marked the boundary between 19th-century and modern mathematics. Their birth was a crucial waypoint on math’s inexorable march from the numbers and shapes...
How Alexander Grothendieck Revolutionized 20th-Century Mathematics
...were his actual mathematical contributions? What Albert Einstein was to 20th-century physics, Alexander Grothendieck was to 20th-century mathematics. He is much less well known because math gets technical even more...
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...
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. Mathematicians spend most of their time thinking about what’s knowable. But the...
What Can We Gain by Losing Infinity?
Mathematicians Want to Banish Infinity. What Might They Gain? Ultrafinitism, a philosophy that rejects the infinite, has long been dismissed as mathematical heresy. But it is also producing new insights...