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# Quantized Columns

## Latest Articles

### How We Can Make Sense of Chaos

Dynamical systems can be chaotic and impossible to predict, but mathematicians have discovered tools to help understand them.

### Why Triangles Are Easy and Tetrahedra Are Hard

The triangle angle sum theorem makes working with triangles easy. What happens when you can’t rely on it?

### How Infinite Series Reveal the Unity of Mathematics

Infinite sums are among the most underrated yet powerful concepts in mathematics, capable of linking concepts across math’s vast web.

### What Does It Mean for AI to Understand?

It’s simple enough for AI to seem to comprehend data, but devising a true test of a machine’s knowledge has proved difficult.

### Will We Ever Get Rid of COVID-19?

No matter how much we’d like to eradicate SARS-CoV-2, it may be better to settle for other forms of control.

### What Hot Dogs Can Teach Us About Number Theory

The Chinese remainder theorem is an ancient and powerful extension of the simple math of least common multiples.

### The Uselessness of Useful Knowledge

Today’s powerful but little-understood artificial intelligence breakthroughs echo past examples of unexpected scientific progress.

### The Simple Math Behind the Mighty Roots of Unity

Solutions to the simplest polynomial equations — called “roots of unity” — have an elegant structure that mathematicians still use to study some of math’s greatest open questions.

### The Journey to Define Dimension

The concept of dimension seems simple enough, but mathematicians struggled for centuries to precisely define and understand it.