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.
Episodes
1247 episodes
Cantor's Diagonal: The Hidden Order of Infinity
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)...
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6:39
OEIS A000330: Square pyramidal numbers
In this episode we dive into A000330, the square pyramidal numbers, defined by a(n) = 0^2 + 1^2 + 2^2 + ... + n^2 = n*(n+1)*(2*n+1)/6. We’ll see why these count cannonball pyramids with square bases and, in the 2D analogue, the total number of ...
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5:49
The Doppler Dance: How Radial Velocity Reveals Exoplanets
A deep dive into how astronomers detect planets around other stars by watching tiny wobbles in starlight. We explain the Doppler shift, radial velocity measurements, and the quest from the first hot Jupiter 51 Pegasi b to the centimeter-per-second...
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5:56
OEIS A000329: Tangent Iteration Sequence
We explore A000329, the tangent-iteration sequence defined by b(0) = 1 and the nearest integer to b(n), where b(n) = tan(b(n-1)). The interplay between the continuous, blow-up behavior of tan near odd multiples of π/2 and the discrete rounding ...
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4:51
On-Device AI Unleashed: EmbeddingGemma and the Private, Fast Future
Google DeepMind's EmbeddingGemma is a compact 308M-parameter text embedding model designed for mobile-first AI. With quantization-aware training it runs on-device in under 200 MB of RAM and exhibits sub-15 ms latency on supported hardware such ...
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6:23
Skyhook: The Orbit-Sling That Could Change Spaceflight
We unpack the skyhook—an orbiting momentum-exchange tether that could grab a payload at the edge of the atmosphere and fling it into orbit. Tracing ideas from Isaacs and Moravec to NASA tests (TSS-1R, YOES-2) and the Hastol study, we discuss how e...
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6:07
Prince Rupert's Cube: A Tilted Passage Through Geometry
Explore the famous geometric paradox: a cube through a hole in another cube, with a side length about 1.06066 times larger. We trace the tale from Prince Rupert's 1693 wager through Wallis and Newland, explain the tilted-square tunnel that makes i...
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5:12
OEIS A000328: Circle problem — lattice points inside a circle
We dive into A000328, the Gaussian circle problem: how many integer lattice points (x, y) lie inside or on a circle of radius n. Start with the main term a(n) ~ πn^2 and the elusive remainder r(n) = a(n) − πn^2. We trace the historical bounds — Ha...
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4:39
CD Decode: Reading Biomolecular Shapes with Circular Dichroism
We demystify circular dichroism (CD) — a fast, non-destructive probe of biomolecular structure. This episode explains how differential absorption of left and right circularly polarized light reveals protein secondary structure, nucleic acid forms,...
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7:27
OEIS A000327: Partitions into non-integral powers
We explore A000327, the OEIS entry counting the number of solutions with distinct positive integers a and b to a^23 + b^23 ≤ n (i.e., partitions into non-integral powers). We trace its pedigree—from N. Sloan’s original listing in the 1973 Handbook...
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4:27
OEIS A000326: Pentagonal numbers
A deep dive into the pentagonal numbers A000326, tracing their geometric roots and arithmetic formula P(n) = n(3n−1)/2, including the pentagonal test x is pentagonal iff (sqrt(24x+1)+1)/6 is an integer. We explore generalized pentagonal numbers...
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4:36
Is the Heavy Cream Cinnamon Roll Hack Baking Magic?
We unpack the viral heavy-cream cinnamon roll hack—explaining why heavy cream's fat, moisture, and caramelization transform ordinary rolls into bakery-soft, gooey treats. We trace its rediscovery through blogs and grandma-tested methods, compar...
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6:32
OEIS A000325: 2^n - n
A000325 is the simple formula a_n = 2^n − n, with the start 1, 1, 2, 5, 12, 27, 58. It counts all subsets of an n‑element set except the n singletons (i.e., 2^n minus n). The sequence also satisfies the recurrence a_n = 2 a_{n−1} + (n−2) with a_0 ...
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4:39
llms.txt: A Markdown Bridge for AI-Ready Web Context
We explore a proposed standard that gives LLMs a concise, structured briefing about a website. llms.txt complements robots.txt and sitemaps by delivering AI-friendly guidance and links to detailed pages, all in a lightweight, human- and machine-re...
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4:54
Planetary Black Holes: Using Exoplanets to Hunt Super‑Heavy Dark Matter
In this deep dive, we explore a provocative idea: giant, cold exoplanets—especially gas giants—as cosmic detectors for super‑heavy dark matter. Particles streaming through a planet could be captured, sink to the core, and, if enough accumulate,...
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6:39
OEIS A000324: The Infinite Coprime Sequence and the Lucas Connection
In this Deep Dive, we investigate A000324 from the OEIS — a sequence born from a deceptively simple nonlinear recurrence that rockets from the start 1, 5, 9, 49, 2209 and beyond. What makes it truly fascinating is that it forms an infinite coprime...
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5:11
Time Crystals — Ground-State Clocks and the Quantum Frontier
We explore time crystals, quantum systems whose patterns repeat in time even in their lowest energy state, breaking time-translation symmetry without violating thermodynamics. From Wilczek’s original idea to 2016–2017 landmark experiments, to r...
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6:18
The Pomegranate Odyssey: From Ancient Orchards to Modern Science
Trace the pomegranate’s epic journey—from 4,000 BCE cultivation in Mesopotamia and a possible independent domestication in Albania to Linnaeus’s Punica granatum and the Punica genus that hints at ancient trade. Explore its rich symbolism across Ju...
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6:52
Silurian Renaissance: Sea-to-Land Leap and the Rise of Jawed Fish
A deep dive into the Silurian period (roughly 443–419 million years ago) as Earth recovers from the mass extinction and life bursts back to diversity. We unpack climate warming, rising seas, the emergence of extensive reefs, the rise of jawed vert...
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6:51
OEIS A000323: Gauss circle problem—record lattice-point errors
In this Deep Dive, we explore A000323, the sequence of n at which the Gauss circle error term sets a new record. We define A(n) as the number of integer pairs (i,j) with i^2 + j^2 ≤ n and P(n) = A(n) − πn, the gap between lattice-point counts and ...
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6:27
Circulimulus discobulus: Bridging 80 Million Years in Horseshoe Crab Evolution
We explore Circulimulus discobulus, a small Silurian horseshoe crab whose 2025 description fills an 80‑million‑year gap in chelicerate history. Its multi‑segmented post‑abdomen and two‑pronged telson reveal an ancestral body plan that links Ordovi...
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6:17
The Cosmic Shoreline: Do Exoplanet Atmospheres Survive Around M Dwarfs?
We explore how exoplanets keep or lose their atmospheres, the evolving 'cosmic shoreline' concept, and what JWST's look at Gliese 486 tells us about habitability around the most common stars. From escape velocity to stellar radiation, plus the ...
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5:12
OEIS A000322: Pentanacci numbers
A deep dive into A000322, the Pentanacci sequence started with five 1s, defined by a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5). We'll contrast with the zero-start version A01591 to show how different initial conditions under the same recu...
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5:45
History of IBM: From Punch Cards to AI and Hybrid Cloud
Join us as we trace IBM's evolution from CTR and Hollerith punch cards to the modern AI and hybrid‑cloud powerhouse. We'll unpack the leadership, culture, and pivotal bets—from Watson's Think era and the Social Security contract to wartime prod...
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19:26
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 be...
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4:22