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geometry

Photo of Marijn Heule walking among computer processors
Abstractions blog

Computer Scientists Attempt to Corner the Collatz Conjecture

By Kevin Hartnett
August 26, 2020
Read Later

A powerful technique called SAT solving could work on the notorious Collatz conjecture. But it’s a long shot.

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

Computer Search Settles 90-Year-Old Math Problem

By Kevin Hartnett
August 19, 2020
Read Later

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.

Abstractions blog

How Physics Found a Geometric Structure for Math to Play With

By Kevin Hartnett
July 29, 2020
Read Later

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

Quantized Academy

The Math of Social Distancing Is a Lesson in Geometry

By Patrick Honner
July 13, 2020
Read Later

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.

Animation of different rectangles made by connecting four points on a colorful loop.
geometry

New Geometric Perspective Cracks Old Problem About Rectangles

By Kevin Hartnett
June 25, 2020
Read Later

While locked down due to COVID-19, Joshua Greene and Andrew Lobb figured out how to prove a version of the “rectangular peg problem.”

Illustration showing an austere number line on one side and various interesting objects on the the other, including a dodecahedron, an armillary sphere, flowers and plants.
Quantized Columns

The Two Forms of Mathematical Beauty

By Robbert Dijkgraaf
June 16, 2020
Read Later

Mathematicians typically appreciate either generic or exceptional beauty in their work, but one type is more useful in describing the universe.

Photo of iron filings spread along magnetic field lines on a green and yellow background
number theory

Mathematician Measures the Repulsive Force Within Polynomials

By Kevin Hartnett
May 14, 2020
Read Later

Vesselin Dimitrov’s proof of the Schinzel-Zassenhaus conjecture quantifies the way special values of polynomials push each other apart.

Black and white photo of John Conway against a black background
Abstractions blog

John Conway Solved Mathematical Problems With His Bare Hands

By Kevin Hartnett
April 20, 2020
Read Later

The legendary mathematician, who died on April 11, was curious, colorful and one of the greatest problem-solvers of his generation.

Photo of two mathematicians drawing on a chalkboard
topology

Mathematics as a Team Sport

By Kevin Hartnett
March 31, 2020
Read Later

When 50 mathematicians spend a week in the woods, there’s no telling what will happen. And that’s the point.


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