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# Quantized Academy

## Latest Articles

### 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 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.

### How to Find Rational Points Like Your Job Depends on It

Using high school algebra and geometry, and knowing just one rational point on a circle or elliptic curve, we can locate infinitely many others.

### How to Solve Equations That Are Stubborn as a Goat

Math teachers have stymied students for hundreds of years by sticking goats in strangely shaped fields. Learn why one grazing goat problem has stumped mathematicians for more than a century.

### The Mysterious Math of Perfection

Enter the world of perfect numbers and explore the mystery mathematicians have spent thousands of years trying to solve.

### The Crooked Geometry of Round Trips

Imagine if we lived on a cube-shaped Earth. How would you find the shortest path around the world?

### Some Math Problems Seem Impossible. That Can Be a Good Thing.

Struggling with math problems that can’t be solved helps us better understand the ones we can.

### The Simple Math Problem We Still Can’t Solve

Despite recent progress on the notorious Collatz conjecture, we still don’t know whether a number can escape its infinite loop.

### The Math of Social Distancing Is a Lesson in Geometry

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.