John D. Cook

An elliptic curve E over a finite field F consists of the set of points (x, y) satisfying the equation y² = x³ + ax + b with x and y in F.

The NIST elliptic curves have been in the news twice lately.

I was watching a video by John Higgins this morning about the poem in Ecclesiastes 3, one of the most famous passages in the Bible.

Splitting N!

About 14% of English words can be spelled by stringing together chemical symbols.

NIST published a set of elliptic curves for cryptography in 2000.

This post began as a thread on X last night.

When I wrote about the harmonic triangle yesterday, I displayed the triangle left-aligned using fixed-width text because that was easier than producing the format you usually see for Pascal’s triangle and related triangles. 1 1/2 1/2 1/3 1/6

G.

What’s a connection between Edgar Allan Poe and Friedrich Wilhelm Bessel?

Pascal’s triangle is the most famous triangular arrangement of numbers.

A few days ago I wrote about topological models of modal logic.

If you’ve followed this blog for a while, you may know that I do a lot of work with data privacy and that I have an interest in modal logic.

The Riemann Hypothesis (RH) is the conjecture that all the zeros of the Riemann zeta function ζ(s) in the critical strip, i.e. the region of the complex plane with real part between 0 and 1, have real part equal to ½.

The Fast Fourier Transform (FFT) algorithm can compute the discrete Fourier transform of a sequence of length n in time O(n log n).

For a real number x, the irrationality index μ(x) is a way of measuring how well x can be approximated by rational numbers.

I was skimming through David Well’s book The Penguin Dictionary of Curious and Interesting Geometry and was surprised by this entry: Lissajous figures or Bowditch curves First discussed by Nathaniel Bowditch in 1815, and later by Jules Antoine Lissajous in

Gödel’s incompleteness theorem illustrated the need to distinguish between what is true and what is provable.

An earlier post presented an elegant plane geometry theorem discovered by the 19th century school teacher Auguste Miquel.

The previous post discussed a superficial connection between modal logic and topology, that both use the terms regular and normal to indicate added sets of axioms.

You can’t say much about modal logic in general.

Euclidean geometry dates back at least to Euclid (circa 300 BC), and so you might think it’s been pretty well picked over by now.

Despite the predictions that no one would ever put build data centers in space, Google is starting on Thursday.

In the novel Carry On, Mr.

A couple days ago a friend told me about the book Carry On, Mr.

Suppose you want to solve a triangle.

Nothing grows exponentially forever.

There’s a common saying in discussion of fractals that the length of a coastline depends on how small a device you use to measure it.

I recently bought a copy of Los Alamos Rolodex, a book displaying business cards from Los Alamos Nation Labs from 1967 to 1978.

I’ve written three posts on cosine similarity lately.

Yesterday I wrote about the canonical example of how vector embeddings of words add: “king” − “man” + “woman” ≈ “queen” This should be interpreted as saying that the word vector for king, minus the word vector for man, plus the word vector for woman, is in

The product of four consecutive Fibonacci numbers equals the product of two consecutive integers.

The previous post looked at how to interpret cosine similarity, or equivalently angles between word vectors.

Machine learning represents words as vectors and measures the similarity of words by the angles between the vectors.

Suppose I give you an n-digit number and ask you what it represents.

The Greek letter β (beta) and the German letter ß (eszett) look similar, especially in some fonts.

The idea of using computers to assist with proofs is not new.

A rising tide may lift all boats, but the AI tide lifts some boats much more than others.

Yesterday OpenAI announced a proof that settled a long-standing question about the Navier-Stokes equations from fluid dynamics.

There are rumors that a long-standing math problem, one of the Millennium Prize problems, has been solved.

The Online Etymological Dictionary gives the following etymology for grok: grok (v.)

The previous post discussed the motivation for and application of the rank-trace theorem.

Suppose you want to know the rank of an n × n matrix A, the number of linearly independent rows of A, or equivalently the number of linearly independent columns.

NVIDIA has offered to buy Hugging Face for $12,930,300,000. 129303 is the Unicode code point for the Hugging Face emoj (U+1F917), which you can verify with the following Python code. >>> import unicodedata >>> 129303 == 0x1F917 True >>> unicodedata.name(c…

Eric Lu announced on X today that he has factored RSA-260, a number N with 260 digits (862 bits) that is the product of two large primes [1].

I just found out Brian Beckman and I got a patent on work we did for GSI Technology [1].

I watched a few videos this morning, looking for ideas of what I could use AI to do.

This post provides a couple examples to go along with two earlier posts.

AI-powered coding agents increase productivity for many developers.

When you’re interested in studying a family of functions, it can be useful to look at a differential equation that the functions solve.