The elliptic curves Ed25519 and Curve25519 are both used in cryptography, and are equivalent in one sense and not in another.

Moessner's Magic is a generalization of an ancient theorem that wasn't discovered until 1951.

Bounds on the frequencies of a vibrating membrane, provided its shape can tile the plane.

You can find three primitive Pythagorean triangles with the same area, but what about four?

Given three mutually tangent circles, there is an elegant theorem for finding two more circles tangent to all three.

Several elliptic curves which Zcash uses in zero knowledge proofs are named after characters from Lewis Carroll: Jubjub, Bandersnatch, Tweddledee, Tweedledum

Two elliptic curves used in Zcash for zero-knowledge proofs, one named after a Greek goddess of war and one after a Roman goddess of home and hearth

Cycles of ellptic curves have the property that the number of points on one curve equals the field size of the next curve.

Testing the time to factor big integers in Python with SymPy compared to Matheamtica

We often want to reduce something that's inherently two-dimensional into something one-dimensional. We want to turn graph into a list. And we'd like to do this with some kind of faithfulness. We'd like things that are close together in 2D space to be close…

Counting the number of points on an elliptic curve using a crude algorithm, a better algorithm, and the best algorithm.

Memorable prime numbers with various numbers of digits. For example, if you need a five-digit prime, you could say 18181.

Plotting the points on an elliptic curve over a finite field can be very misleading.

Pi is the ratio of a circle's circumference to its diameter. You can generalize pi to pi_p by generalizing the notion of circle and the notion of circumference.

The Tiny Jubjub curve is an elliiptic curve designed to be similar to other Jubjub curves, but small enough for hand calculations.

Since the way we manipulate high-dimensional vectors is primarily matrix multiplication, it isn’t a stretch to say it is the bedrock of the modern AI revolution. The post A Bird’s-Eye View of Linear Algebra: Why Is Matrix Multiplication Like That? appeared…

Converting elliptic curves between Weierstrass, Montgomery, and twisted Edwards form. Using Baby Jubjub and Tiny Jubjub as examples.

A prime number that looks like a blackand-white image of an American flag when written in a block.

Python integers can be arbitrarily long, but there are limits on the size of string that you can convert to an integer. How to get around this limit.

A simple random process that produces the Twin Dragon fractal.