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.
31 articles from this blog
Explores the minimum value of sums of cosines with integer frequencies, touching on the Chowla cosine conjecture and numerical exploration methods.
Explains how eigenvalue problems in linear algebra homework are solved backward compared to real-world numerical methods.
Explains how to verify if a large number is a Fibonacci number using a mathematical certificate, relating it to computational proofs.
Explores the mathematical property that rounding up the gamma function of 1/n equals n, with a proof sketch and Python verification.
A mathematical analysis reveals that despite crowded visuals, there is immense volume per satellite in Low Earth Orbit, suggesting space is less congested than it appears.
Leading AI researchers debate whether current scaling and innovations are sufficient to achieve Artificial General Intelligence (AGI).
Explores the challenges of maintaining privacy when bridging assets between public and private cryptocurrency blockchains, highlighting metadata risks.
Explains a zero-knowledge proof for verifying a product without revealing the numbers, using elliptic curves and pairings.
Explains how to construct a zero-knowledge proof to demonstrate knowledge of a discrete logarithm without revealing the secret value.
Explores the Mills ratio, comparing tail behavior of Student t and normal distributions to illustrate fat-tailed vs. thin-tailed distributions.
Explores the probability of extreme 'six sigma' events using the Student t distribution, showing it's not monotonic and depends heavily on degrees of freedom.
An introduction to stylometry, the statistical analysis of writing style, with examples from historical texts and natural language processing.
Argues that ugly, legacy code can hold valuable domain knowledge and be more practical to refactor than to rewrite from scratch.
Explores prime gaps, their mathematical merit, and their use as proof-of-work in the Gapcoin cryptocurrency.
Explores prime clusters, their mathematical definition, and their use as proof-of-work in the Riecoin cryptocurrency.
Explores a method for testing Cunningham prime chains efficiently, with applications in cryptocurrency proof-of-work systems.
Explains Montgomery's trick for efficiently computing multiple modular inverses at once, with Python code examples and performance comparison.
Explains the probabilistic primality tests (Fermat and Euler-Lagrange-Lifchitz) used in Primecoin's blockchain verification and mining process.
Explores bi-twin prime chains, a mathematical pattern where sequences of twin primes follow a doubling rule, with examples and Python verification code.
Explores prime number chains like Cunningham chains and their application in the Primecoin cryptocurrency's proof-of-work system.
