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Abstractions blog

Points connected by lines.
graph theory

Mathematical Connect-the-Dots Reveals How Structure Emerges

By Leila Sloman
June 23, 2022
Read Later

A new proof identifies precisely how large a mathematical graph must be before it contains a regular substructure.

An illustration that includes a triangular network overlaid by images of spinning particles.
explainers

The Spooky Quantum Phenomenon You’ve Never Heard Of

By Katie McCormick
June 22, 2022
Read Later

Quantum computers may derive their power from the “magical” way that properties of particles change depending on the context.

Seifert surfaces formed from closed loops.
topology

Special Surfaces Remain Distinct in Four Dimensions

By Kevin Hartnett
June 16, 2022
Read Later

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.

A satellite photo of the complex of rivers in the Amazon.
biodiversity

Reshuffled Rivers Bolster the Amazon’s Hyper-Biodiversity

By Yasemin Saplakoglu
June 7, 2022
Read Later

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

By Jordana Cepelewicz
June 6, 2022
Read Later

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

By Viviane Callier
June 3, 2022
Read Later

Some animal neuropeptides have been around longer than nervous systems.

Colorized transmission electron micrograph of a polyribosome.
origins of life

Life’s First Peptides May Have Grown on RNA Strands

By Yasemin Saplakoglu
May 24, 2022
Read Later

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

By Mordechai Rorvig
May 23, 2022
Read Later

Why verify every line of a proof, when just a few checks will do?

Two red loops connected by a ghostly tube.
topology

How Complex Is a Knot? New Proof Reveals Ranking System That Works.

By Leila Sloman
May 18, 2022
Read Later

“Ribbon concordance” will let mathematicians compare knots by linking them across four-dimensional space.


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