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What Is Quantum Field Theory and Why Is It Incomplete?
...our pure mathematician friends, because our pure mathematician friends are smart people, and we think that we have this mathematical theory. But they don’t understand what we’re talking about. And...
How Big Is Infinity?
...this mysterious, complicated and important concept. Some of those children grow up to be mathematicians fascinated with infinity, and some of those mathematicians are discovering new and surprising things about...
From Systems in Motion, Infinite Patterns Appear
Mathematicians are finding inevitable structures in sufficiently large sets of integers. In December 1977, a revolutionary paper quietly appeared in the Journal d’Analyse Mathématique, a specialty mathematics journal. The author,...
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...