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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...
How Big Data Carried Graph Theory Into New Dimensions
Researchers are turning to the mathematics of higher-order interactions to better model the complex connections within their data. Graph theory isn’t enough. The mathematical language for talking about connections, which...
New Number Systems Seek Their Lost Primes
For centuries, mathematicians tried to solve problems by adding new values to the usual numbers. Now they’re investigating the unintended consequences of that tinkering. Mathematicians are digging up the root...
A Puzzle of Clever Connections Nears a Happy End
The three young friends who devised the “happy ending” problem became some of the most influential mathematicians of the 20th century, but were never able to solve their own puzzle....