John D. Cook provides expert consulting in applied mathematics and data privacy, helping clients from tech, biotech, and legal industries—including Amazon, Google, Microsoft, and Amgen—solve complex problems efficiently.
166 articles from this blog
Explores whether additional data always reduces posterior variance in Bayesian statistics, with beta-binomial and normal-normal examples.
Explores the connection between Delannoy numbers, king moves on a chessboard, and DNA sequence alignment.
Explains the practical difference between variables and parameters in mathematics and programming.
Explores the mathematical relationship between silver rectangles, the silver ratio, and Delannoy numbers counting king paths on a chessboard.
Solving a differential equation where the derivative of a function equals its inverse, revealing the golden ratio.
A test reveals that Grok correctly identifies bc's Bessel function argument order, while the man page has a bug.
Explains how a bash one-liner using brace expansion generates 30 English words via a depth-first tree traversal.
Explores the repeating decimal cycle length of harmonic numbers using Python code and number theory.
Analysis of harmonic numbers as reduced fractions, plotting bit-length heights and comparing actual vs estimated values.
Explores harmonic numbers, their fractional representation, and asymptotic estimates for numerator/denominator digits.
Explores the connection between incircles, excircles, and Pythagorean triangles, proving that radii are integers.
Explores Pythagorean triples with consecutive sides, including recurrence relations and formulas for primitive triples.
A guide to using regular expressions that work across different tools like sed, awk, grep, and Emacs, highlighting compatible features.
Explores the n queens problem on a toroidal chessboard when n is prime, discussing solutions with queens on lines of constant slope.
Using Z3/Python to solve a chess puzzle: place all pieces on a 6x5 board with no attacks.
Testing Claude's ability to generate Lean 4 code to formalize a ring theorem about partial fraction decomposition in a PID.
Explores partial fraction decomposition beyond calculus, including complex numbers, PID theory, and integer applications.
Explains how checking three examples can prove a polynomial identity, using pentagonal and triangular numbers.
How to determine if a large number is a pentagonal number using integer arithmetic in Python.
Using Claude and Lean to verify quaternion rotation matrix formulas, detecting a typo in the process.
