The perpetually undervalued least-squares: minₓ‖y−Ax‖² can teach a lot about some complex ideas in modern machine learning including overfitting & double-descent. Let's assume A is n-by-p. So we have n data points and p parameters 1/10

Pell is to silver as Fibonacci is to gold johndcook.com/blog/2024/09/0…

Today’s exponential sum when your browser is in dark mode

The largest known pair of twin primes is 2,996,863,034,895 × 2^1,290,000 ± 1

The patent number for RSA encryption, 4405829, is a prime.

A functor is called exact if it preserves short exact sequences.

Examples of groups which are not obviously groups math.stackexchange.com/questions/3624…

Demystifying points at infinity in projective planes and enumerating the elements of a finite projective plane. johndcook.com/blog/2022/04/2…

The Lucas numbers satisfy the same recurrence relation as the Fibonacci numbers, but start with 2 and 1 rather 0 and 1. Here's an equation relating Lucas and Fibonacci numbers.

Euler: If m and n are relatively prime, n^{φ(m)} is congruent to 1 modulo m. Definition of φ(n) en.wikipedia.org/wiki/Euler%27s…

Do incremental improvements add, multiply, or something else? johndcook.com/blog/2024/07/0…

Legendre's constant en.wikipedia.org/wiki/Legendre%…

An equivalent definition of normal subgroups that isn't widely known johndcook.com/blog/2024/03/0…

Hadamard's inequality: if H is a positive semidefinite Hermitian matrix, the determinant of H is bounded by the product of its diagonal elements.

Hadamard's inequality The absolute value of the determinant of a complex matrix is bounded by the product of the lengths of its column vectors.