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Mathematics

An animation of a particle collision
Abstractions blog

The Mathematical Structure of Particle Collisions Comes Into View

August 20, 2020

Physicists have identified an algebraic structure underlying the messy mathematics of particle collisions. Some hope it will lead to a more elegant theory of the natural world.

Illustration of floating metal cubes joining together, some of their faces yellow
geometry

Computer Search Settles 90-Year-Old Math Problem

August 19, 2020

By translating Keller’s conjecture into a computer-friendly search for a type of graph, researchers have finally resolved a problem about covering spaces with tiles.

Photo of emperor penguins huddling together for warmth, with two sticking their heads out
Abstractions blog

Math of the Penguins

August 17, 2020

Emperor penguins display rigorously geometric spacing and mathematical efficiency when they huddle together for warmth, which may reveal secrets to their overall health.

number theory

Landmark Math Proof Clears Hurdle in Top Erdős Conjecture

August 3, 2020

Two mathematicians have proved the first leg of Paul Erdős’ all-time favorite problem about number patterns.

Abstractions blog

How Physics Found a Geometric Structure for Math to Play With

July 29, 2020

Symplectic geometry is a relatively new field with implications for much of modern mathematics. Here’s what it’s all about.

Visualization of the distribution of prime numbers in the shape of colorful dots in a hexagonal pattern
Abstractions blog

Mathematicians Will Never Stop Proving the Prime Number Theorem

July 22, 2020

Why do mathematicians enjoy proving the same results in different ways?

Gödel’s incompleteness theorems.
Abstractions blog

How Gödel’s Proof Works

July 14, 2020

His incompleteness theorems destroyed the search for a mathematical theory of everything. Nearly a century later, we’re still coming to grips with the consequences.

Quantized Academy

The Math of Social Distancing Is a Lesson in Geometry

July 13, 2020

How to safely reopen offices, schools and other public spaces while keeping people six feet apart comes down to a question mathematicians have been studying for centuries.

Photo of various kinds and colors of dice
Abstractions blog

How and Why Computers Roll Loaded Dice

July 8, 2020

Researchers are one step closer to injecting probability into deterministic machines.