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.

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Intellectually Curious

Cantor's Diagonal: The Hidden Order of Infinity

September 06, 2025 • Mike Breault

A deep dive into Cantor's diagonal argument—how counting, one-to-one correspondences, and the construction of a number not on any list reveal a hierarchy of infinities. We explore countable versus uncountable sets (aleph-null vs. the real numbers), the 0-to-1 interval's paradox, and the leap to higher infinities, plus the broader implications for logic, computability, and the independence of the continuum hypothesis.

Note: This podcast was AI-generated, and sometimes AI can make mistakes. Please double-check any critical information.