Latin squares and 3D chess johndcook.com/blog/2022/01/1…

If a matrix A is non-singular and diagonalizable, A^{-1} is non-singular and diagonalizable.

Interesting combinatoric problems arising from experimental design

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Working up to combinatorial designs via a sequence of generalizations

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An n x n matrix A is non-singular iff rank(A) = n.

This post brings together the previous three posts on finite geometry:

Steiner systems johndcook.com/blog/2026/11/0…

The final digits of the Fibonacci sequence have period 60.

Finite hyperbolic planes

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Finite projective planes

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sin(11) is almost -1. divisbyzero.com/2010/02/16/int…

A Lie group is a manifold and a group.

When is the square root of a Gaussian integer also a Gaussian integer? johndcook.com/blog/2020/06/0…

Cayley's theorem: Any group is isomorphic to a subgroup of the set of permutations of its elements.

Good idea. Announcing Quincuncial: quincuncial.com

For every positive rational number q, there exist infinitely many integers n such that q n! + 1 is composite.

The trace of a projection matrix is the dimension of the space it projects onto.

The analogy between prime numbers and simple groups johndcook.com/blog/2023/09/2…

It would be interesting to know what open math problems people have unsuccessfully tried to solve with AI.

Tried with professional-level effort, not just "Hey Claude. Solve this."

An n x n matrix with n distinct eigenvalues is diagonalizable.

From Euclidean geometry to projective geometry, by way of spherical geometry.

Non-Euclidean doesn't necessarily mean non-physical.

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