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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?

An ice sheet stretching into the distance.
Abstractions blog

How Earth’s Climate Changes Naturally (and Why Things Are Different Now)

July 21, 2020

Earth’s climate has fluctuated through deep time, pushed by these 10 different causes. Here’s how each compares with modern climate change.

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.

Gif of a grid of arrows whose directions flip up and down.
Abstractions blog

The Cartoon Picture of Magnets That Has Transformed Science

June 24, 2020

One hundred years after it was proposed, the Ising model is used to understand everything from magnets to brains.

A falling apple.
Abstractions blog

Why Gravity Is Not Like the Other Forces

June 15, 2020

We asked four physicists why gravity stands out among the forces of nature. We got four different answers.

Diagram showing a colorful visualization of the simple Lie group
Abstractions blog

The ‘Useless’ Perspective That Transformed Mathematics

June 9, 2020

Representation theory was initially dismissed. Today, it’s central to much of mathematics.

An illustration of a knot that mathematicians might study using tools called invariants.
Abstractions blog

In a Single Measure, Invariants Capture the Essence of Math Objects

June 2, 2020

To distinguish between fundamentally different objects, mathematicians turn to invariants that encode the objects’ essential features.

Photo of various colorful maps
Abstractions blog

In Mathematics, It Often Takes a Good Map to Find Answers

June 1, 2020

Mathematicians try to figure out when problems can be solved using current knowledge — and when they have to chart a new path instead.