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Abstractions blog
graph theory
Mathematical Connect-the-Dots Reveals How Structure Emerges
A new proof identifies precisely how large a mathematical graph must be before it contains a regular substructure.
explainers
The Spooky Quantum Phenomenon You’ve Never Heard Of
Quantum computers may derive their power from the “magical” way that properties of particles change depending on the context.
topology
Special Surfaces Remain Distinct in Four Dimensions
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.
biodiversity
Reshuffled Rivers Bolster the Amazon’s Hyper-Biodiversity
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.
number theory
Graduate Student’s Side Project Proves Prime Number Conjecture
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.”
evolution
Brain-Signal Proteins Evolved Before Animals Did
Some animal neuropeptides have been around longer than nervous systems.
origins of life
Life’s First Peptides May Have Grown on RNA Strands
RNA and peptides coevolving in the primordial world might have jointly served as a precursor to the modern ribosome.
computational complexity
How Computer Scientists Learned to Reinvent the Proof
Why verify every line of a proof, when just a few checks will do?
topology
How Complex Is a Knot? New Proof Reveals Ranking System That Works.
“Ribbon concordance” will let mathematicians compare knots by linking them across four-dimensional space.