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A new proof identifies precisely how large a mathematical graph must be before it contains a regular substructure.
Quantum computers may derive their power from the “magical” way that properties of particles change depending on the context.
For decades mathematicians have searched for a specific pair of surfaces that can’t be transformed into each other in four-dimensional space. Now they’ve found them.
The lush biodiversity of the Amazon may be due in part to the dynamics of branching rivers, which serve as invisible fences that continuously barricade and merge bird populations.
Jared Duker Lichtman, 26, has proved a longstanding conjecture relating prime numbers to a broad class of “primitive” sets. To his adviser, it came as a “complete shock.”
RNA and peptides coevolving in the primordial world might have jointly served as a precursor to the modern ribosome.
Why verify every line of a proof, when just a few checks will do?
“Ribbon concordance” will let mathematicians compare knots by linking them across four-dimensional space.
By resolving a paradox about light in a box, researchers hope to clarify the concept of energy in quantum theory.
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