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Surfaces Beyond Imagination Are Discovered After Decades-Long Search
Unimaginable Surfaces Discovered After Decades-Long Search Using ideas borrowed from graph theory, two mathematicians have shown that extremely complex surfaces are easy to traverse. Last July, two mathematicians from Durham...
How to Weigh Truth With a Balance Scale
How to Weigh Truth With a Balance Scale and Math In recreational mathematics, the balance scale is an endless source of puzzles that require precise and elaborate logic and teach...
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...