Intellectually Curious
Intellectually Curious is a podcast by Mike Breault featuring over 1,200 AI-powered explorations across science, mathematics, philosophy, and personal growth. Each short-form episode is generated, refined, and published with the help of large language models—turning curiosity into an ongoing audio encyclopedia. Designed for anyone who loves learning, it offers quick dives into everything from combinatorics and cryptography to systems thinking and psychology.
Inspiration for this podcast:
“Muad'Dib learned rapidly because his first training was in how to learn. And the first lesson of all was the basic trust that he could learn. It's shocking to find how many people do not believe they can learn, and how many more believe learning to be difficult. Muad'Dib knew that every experience carries its lesson.”
― Frank Herbert, Dune
Note: These podcasts were made with NotebookLM. AI can make mistakes. Please double-check any critical information.
Intellectually Curious
OEIS A000321: Hermite polynomials evaluated at 12
We examine A000321, the sequence obtained by evaluating the physicist's Hermite polynomials H_n(-1/2), where H_n(x) . It comes from a compact recurrence and exhibits a modular pattern: A_{n+k} ≡ c(n,k) A_n (mod k), revealing hidden structure beneath the apparent chaos. Hermite polynomials are central in physics (quantum harmonic oscillator), appear in probability (Edgeworth expansions), Brownian motion, and random matrix theory, and even feature in signal processing as Hermite wavelets. This single sequence shows how a simple rule from one area threads through number theory, physics, and engineering.
Note: This podcast was AI-generated, and sometimes AI can make mistakes. Please double-check any critical information.
Sponsored by Embersilk LLC