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
- 1391
- Years Active
- 2024 - 2025
OEIS A000267: Floor of sqrt(4n+1)
We explore A000267, the deceptively simple a(n) = floor(sqrt(4n+1)). Beyond the bare rule lies a repeating pattern where each integer k occurs floor(2k+3) times, a connection to odd squares, and a we…
00:13:48 |
Fri 04 Jul 2025
Taxi Cab Geometry: Rethinking Distance on the City Grid
In this episode, we unpack taxi cab geometry—the Manhattan-like distance that governs city-block travel and grid-based spaces. We'll compare it to Euclidean distance, explore why circles turn into di…
00:14:30 |
Wed 02 Jul 2025
A Million Robots and the Deepfleet: Inside Amazon’s AI-Driven Logistics
Dive into Amazon's automation milestones: the deployment of one million robots and the launch of Deepfleet, a generative AI that coordinates the fleet for a claimed 10% efficiency boost. We unpack wh…
00:09:57 |
Wed 02 Jul 2025
OEIS A000266: Permutations Without Transpositions
Welcome back to the dive into the OEIS. Today we zero in on A000266, the count of permutations of n with no transpositions in their cycle decomposition. That’s the same as counting all permutations w…
00:14:27 |
Wed 02 Jul 2025
OEIS A000265: The largest odd divisor (the odd part of n)
In this Deep Dive, we explore A000265, the odd part of n obtained by removing all factors of 2. We explain the K·2^J decomposition (N = K·2^J with K odd), illustrate with examples, and show how A0002…
00:13:41 |
Tue 01 Jul 2025
OEIS A000264: Three-edge-connected rooted cubic maps with two E-nodes and a distinguished Hamiltonian cycle
In this episode, we dive into A000264, which counts three-edge-connected rooted cubic maps with two E-nodes and a distinguished Hamiltonian cycle. We’ll unpack what a cubic map is, what it means for …
00:16:51 |
Mon 30 Jun 2025
OEIS A000263: Partitions into non-integral powers
In this Deep Dive we explore OEIS A000263, the sequence counting partitions of n into non-integral powers. We’ll walk through the OEIS entry’s precise definition, notice the offset (A3 = 3, A4 = 14, …
00:11:37 |
Mon 30 Jun 2025
OEIS A000262: Partitions of sets into ordered lists
A000262 counts the number of ways to partition an n-element set into any number of nonempty ordered lists (an unordered collection of ordered blocks). We’ll trace the definition through small n (1, 1…
00:13:34 |
Fri 27 Jun 2025
Superdiffusion: The Fast Lane of Diffusion and Turbulent Transport
What happens when spreading isn’t linear? We explore superdiffusion, where the mean-squared displacement grows with time faster than normal diffusion (an alpha between 1 and 2). From atmospheric turb…
00:18:56 |
Thu 26 Jun 2025
OEIS A00261: Beads, Necklaces, and Permanents
We dive into OEIS A00261, a rapidly growing sequence defined by a two-term recurrence with initial terms a1=0 and a2=1. It shows up in surprising combinatorial ways: (i) as the permanent of a special…
00:12:14 |
Thu 26 Jun 2025
Three-Dimensional Time: The New Six-Dimensional Frontier of Physics
In this Deep Dive from Science Corner, we explore Gunther Kletečka’s 2025 framework of three time dimensions (T1, T2, T3) that together form a six-dimensional space-time. We unpack what each time dim…
00:17:55 |
Thu 26 Jun 2025
Context Engineering: Orchestrating Smarter AI Agents
An essential guide for product teams, engineers, and leaders aiming to cut through AI noise. We demystify context engineering—the art of building dynamic contexts that let LLMs and agentic systems ac…
00:18:30 |
Wed 25 Jun 2025
OEIS A800260: Lambda calculus, rooted 3-polytopes, and hidden connections in combinatorics
Today we unpack lambda calculus, a foundational formal language for defining and applying functions, and then trace how its ideas echo through the world of A800260. What is lambda calculus? It’s a mi…
00:20:58 |
Wed 25 Jun 2025
RASP: Peering into the Transformer Mind
In this Science Corner deep dive, we peel back the mystery of how transformer models think by introducing RASP, the Restricted Access Sequence Processing Language. Learn the two core operation famili…
00:21:01 |
Wed 25 Jun 2025
OEIS A00259: Number of rooted planar maps
A concise, intuition-first tour of OEIS A00259. We’ll connect the abstract world of rooted planar maps to an accessible lattice-path picture: count NE paths from (0,0) to (2n,n) that begin with a nor…
00:11:04 |
Tue 24 Jun 2025
Blockdiff Rapid VM Disk Snapshots and Diffs
Learn about Blockdiff Rapid VM Disk Snapshots and Diffs
Note: These podcasts are AI-generated, and sometimes AI can make mistakes. Please double-check any critical information.
Sponsored by Embersilk …
00:25:33 |
Tue 24 Jun 2025
Beyond the Solar Bubble: Voyager, the Heliopause, and the Wall of Fire
Join The Deep Dive as we journey to the edge of our solar system—the heliopause—the dynamic boundary where solar wind meets interstellar space. We’ll unpack the heliosphere’s layered structure (termi…
00:17:50 |
Mon 23 Jun 2025
Masking Time: MIT’s AI-Driven, Reversible Art Restoration
An inside look at MIT’s AI polymer masks—the reversible, color-accurate two-layer films that let conservators repair damaged paintings in hours rather than months. We trace how targeted computer visi…
00:12:13 |
Mon 23 Jun 2025
Rush Talks: Sororities as the Next Wave of Brand Influencers
A deep dive into how sorority recruitment content has become a major marketing lever for big brands. We unpack why brands invest in sororities, how authentic, peer-driven partnerships work (from Popp…
00:11:16 |
Mon 23 Jun 2025
OEIS A00258: Two-Level Partitions and Three-Level Labeled Rooted Trees
In this episode we dive into OEIS A00258. We unpack its two-stage counting: partitions of a set into blocks, then partitions of those blocks, equivalently three-level labeled rooted trees with N leav…
00:11:32 |
Mon 23 Jun 2025
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