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What Is a Particle?
...physical makeup — ultimately, its constituent particles. But those particles’ properties derive not from constituents of their own but from mathematical patterns. As points of contact between mathematics and reality,...
How Neutral Theory Altered Ideas About Biodiversity
...size, the larger the drift,” Johri said. Part of the appeal of neutral theory is that it’s mathematically straightforward. “A lot of the theory was easy,” Johri explained, since essentially...
How I Learned to Love and Fear the Riemann Hypothesis
...the most important and notorious unsolved problem in all of mathematics — from the late, great Eli Stein, a world-renowned mathematician at Princeton University. I was very fortunate that Professor...
Finding Zen in the Art of Puzzle Solving
Readers used their Zen-like puzzle solving skills to discover hidden insights. The “eureka” or “aha” moment of insight is legendary in math and science, dating at least two millenniums back...
The Puzzling Power of Simple Arithmetic
...sort of thing that will get you hooked on mathematics. I daresay that if such examples of “guided discovery” were a regular part of math education at the lower and...
Banach-Tarski and the Paradox of Infinite Cloning
...a mathematical theorem involving infinity that makes it possible, at least in principle, to turn one apple into two. That argument is called the Banach-Tarski paradox, after the mathematicians Stefan...
How Tadayuki Watanabe Disproved a Major Conjecture About Spheres
...symmetries. The Mystery Continues Watanabe’s result closed one front of mathematical research. It also opened another. After his work, mathematicians knew the Smale conjecture was false in all dimensions four...
Machine Learning Gets a Quantum Speedup
...than a classical computer. And getting quantum computers to outlearn traditional machines means finding AI problems that boil down to mathematical operations congruous with quantum physics. “Rather than forcefully trying...
Computer Scientists Prove Why Bigger Neural Networks Do Better
...performing humanlike tasks. As they’ve gotten bigger, they have come to grasp more. This has been a surprise to onlookers. Fundamental mathematical results had suggested that networks should only need...