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The Joy of Asking About Infinity, Jellyfish and the End of the Universe
...mathematician Eugenia Cheng went on a tangent in her episode on category theory. To illustrate how it can apply broadly as a way of thinking beyond mathematics and physics, she...
A New Kind of Symmetry Shakes Up Physics
...paper prompted physicists to search for other places it might appear. Physicists and mathematicians are collaborating to work out the mathematics of these new symmetries — and in some cases...
What Is the Nature of Consciousness?
...philosophy taking a concept which has some tricky meanings, mathematics, using math to sharpen that and turn it into something you can apply, and then consciousness research — trying to...
Complexity Theory’s 50-Year Journey to the Limits of Knowledge
...a research program for grounding mathematics in absolute certainty. He hoped to start from a few simple assumptions, called axioms, and derive a unified mathematical theory that met three key...
The Biggest Smallest Triangle Just Got Smaller
...from there — 100 points define 161,700 different triangles. Each of those triangles, of course, has a particular area. Hans Heilbronn, a German mathematician who fled his country before World...
New Theory Suggests Chatbots Can Understand Text
...ones by combining skills in a manner that hints at understanding — combinations that were unlikely to exist in the training data. This theoretical approach, which provides a mathematically provable...
Michel Talagrand Wins Abel Prize for Work Wrangling Randomness
...mathematics I do was not fashionable at all when I started. It was considered inferior mathematics. The fact that I was given this award is absolute proof this is not...
How Chain-of-Thought Reasoning Helps Neural Networks Compute
...“That’s a good thing.” Training Transformers Large language models are built around mathematical structures called artificial neural networks. The many “neurons” inside these networks perform simple mathematical operations on long...
How the Ancient Art of Eclipse Prediction Became an Exact Science
...had to pick one turning point, it might have been the morning of April 22, 1715, when a solar eclipse loomed over London. The British polymath Edmond Halley, best remembered...