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.
- Update frequency
- every day
- Average duration
- 12 minutes
- Episodes
- 1399
- Years Active
- 2024 - 2025
OEIS A000112: Unlabeled Posets and Their Surprising Connections
A deep dive into A000112, the sequence counting unlabeled partially ordered sets (posets) with n elements. We explore why the count grows so quickly, how poset structures encode nesting and crossing …
00:14:04 |
Sat 25 Jan 2025
The GCE Mystery: Dark Matter vs. Pulsars at the Galactic Center
A deep dive into the Galactic Center Excess—the gamma-ray glow detected by Fermi. We break down the two leading explanations (dark matter annihilation and a hidden population of millisecond pulsars),…
00:08:47 |
Sat 25 Jan 2025
Deep Dive: Abelian Groups — From Finite Classification to Infinite Depth
Join us for a journey through abelian groups: from the basics and classic examples to the Fundamental Theorem of Finite Abelian Groups, and then into the rich landscape of infinite abelian groups, wi…
00:13:53 |
Sat 25 Jan 2025
Stirling Numbers Unpacked: From Shuffles to Partitions
A friendly deep-dive into Stirling numbers of the first kind, second kind, and Lah numbers. We’ll explore how these counts describe cycles in permutations, ways to partition sets, and ordered groupin…
00:13:24 |
Sat 25 Jan 2025
Posets Unfolded: From Divisibility to Lattices
A deep dive into partially ordered sets (posets): the defining axioms, canonical examples like subsets under inclusion and divisibility, and the visual power of Hasse diagrams. We build up to lattice…
00:12:17 |
Sat 25 Jan 2025
OEIS A000111: Euler Up-Down Numbers
Dive into A000111, the Euler up-down numbers counting alternating permutations (up-down and down-up). We'll uncover how Andre linked them to trigonometry via a recurrence, explore their surprising ti…
00:11:37 |
Fri 24 Jan 2025
Kumbh Mela: The World’s Largest Pilgrimage
From ancient myth to a modern megacity, this episode untangles how the Kumbh Mela became the world’s biggest pilgrimage. We trace its layered history—from the Akhadas and river rituals to colonial po…
00:15:52 |
Thu 23 Jan 2025
OEIS A000110: Bell numbers
Join us for a deep dive into the Bell numbers, B(n), the counts of partitions of an n-element set. We’ll uncover surprising connections in number theory—from multiplicative partitions of square-free …
00:12:15 |
Thu 23 Jan 2025
OEIS A000109: Planar Triangulations, Simplicial Polyhedra, and the Geometry–Graph–Number Theory Bridge
We dive into OEIS A000109, the count of simplicial polyhedra (triangular-faced 3D shapes) with n vertices. These numbers are in bijection with maximal planar graphs on n vertices, i.e., simple planar…
00:14:40 |
Wed 22 Jan 2025
Polyhedra Unveiled: From Faces to Space-Fillers
Join this Deep Dive as we climb beyond cubes and pyramids—exploring what defines a polyhedron, how Euler characteristics reveal orientability, the power of duality, and the stories of lattice and spa…
00:11:06 |
Wed 22 Jan 2025
The Stern-Brocot Tree: Fractions, Geometry, and Surprising Connections
A deep dive into the Stern-Brocot tree: how mediants generate every positive rational, the magic of best rational approximations, and unexpected links to geometry and trigonometry—through stereograph…
00:11:07 |
Tue 21 Jan 2025
OEIS A000108: Catalan numbers
We explore the Catalan numbers C_n = binom(2n, n)/(n+1) (equivalently (2n)!/(n!(n+1)!)) and the remarkable variety of objects they count: balanced parentheses, Dyck paths, non-crossing partitions, an…
00:16:12 |
Tue 21 Jan 2025
Engraving Through Time: From Shell Tools to Master Plates
Travel back to the dawn of engraving—from a shell tool in Indonesia 540,000 years ago to decorated ostrich eggshells in 60,000 BC—and follow how the craft moved from practical ornament to fine art. W…
00:23:13 |
Tue 21 Jan 2025
OEIS A000107: Pointed rooted trees
What is A000107? It counts rooted trees with exactly one distinguished (labeled) vertex — the pointed or vertebrate rooted tree. The early terms are 0, 1, 2, 5, 13, 35, and the numbers grow rapidly a…
00:10:10 |
Sun 19 Jan 2025
Dark Oxygen: The Seafloor’s Natural Batteries
From the deepest oceans to icy moons, this episode follows the detective story of 'dark oxygen'—oxygen produced without photosynthesis. We explore the geobattery idea—natural electrolysis on polymeta…
00:12:58 |
Sun 19 Jan 2025
OEIS A000106: Second power of rooted tree enumerator
Dive into A000106, the number of linear forests of two rooted trees (the second power of the rooted-tree enumerator A000081). We’ll see how this sequence arises from self-convolution of rooted trees,…
00:10:07 |
Sat 18 Jan 2025
OEIS A000105: Free polyominoes
We explore A000105, the number of free polyominoes with n cells. From the monomino up, the counts grow rapidly with no simple closed form, and Klarner's constant governs the asymptotic growth, curren…
00:13:13 |
Fri 17 Jan 2025
Charting the World: A History of Cartography
Join us on a journey through the evolution of mapmaking—from cave paintings and ancient world discs to Greek, Chinese, and Islamic advances, through the Age of Exploration and the rise of Mercator, t…
00:11:02 |
Thu 16 Jan 2025
Arrow of Time: Entropy, Arrows, and the Quantum Clock
Why does time only move forward? In this episode we trace the idea from Eddington’s entropy insight to a family of time arrows—thermodynamic, cosmological, radiative, and causal—plus the quantum arro…
00:19:39 |
Thu 16 Jan 2025
MatterGen: AI-Crafted Materials for a Real-World Future
In this deep-dive, we unpack MatterGen, an AI diffusion model that predicts the atomic structure of inorganic materials and forecasts their properties. We explore how it validates by rediscovering kn…
00:14:57 |
Thu 16 Jan 2025
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