Best Computational Logic Podcasts (2025)

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Measure Functions and Termination of STLC 21:42

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1h ago21:42

21:42

In this episode, I talk about what we should consider to be a measure function. Such functions can be used to show termination of some process or program, by assigning a measure to each program, and showing that as the program computes, the measure decreases in some well-founded ordering. But what should count as a measure function? The context for…

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Who is Francis Crick? 50:26

2h ago50:26

50:26

This conversation delves into the life and legacy of Francis Crick, co-discoverer of the DNA structure. Dr. Matthew Cobb, the guest, explores Crick's multifaceted personality, his poetic inspirations, collaborative nature, and his later pursuits in consciousness. The discussion also touches on the controversies surrounding his work, particularly re…

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Filters, unfiltered 1:13:44

1h ago1:13:44

1:13:44

I chat with Phil Z about a good number of things, including, occasionally, about the notion of filter which comes up quite a bit in logic, and other areas of mathematics. But as usual, we cover a bunch of other subjects, like "what even are we doing here?" and "why do we define things at all?"

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Lynn Rothschild: Nature’s Hardware Store 1:16:23

20h ago1:16:23

1:16:23

What if the solutions to humanity’s greatest challenges — on Earth and beyond — have already been invented by nature? In this forward-looking talk, evolutionary biologist and astrobiologist Dr. Lynn Rothschild explores how life’s patterns, materials, and mechanisms, refined over billions of years, can serve as a blueprint for building better future…

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Mathematics and Humanity: The Untold Stories of the Great Math War 43:33

10d ago43:33

43:33

This conversation explores the intersection of mathematics and human experience, focusing on historical figures, philosophical debates, and the ethical implications of scientific progress. Jason Socrates Bardi discusses his book 'The Great Math War', which delves into the personal stories of mathematicians, the challenges of teaching math, and the …

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The Future of Physics: Portals to a New Reality 48:44

9d ago48:44

48:44

In this conversation, Dr.Vlatko Vedral discusses the complexities of quantum mechanics and its implications for our understanding of reality. He explores the stagnation in physics, the importance of thought experiments, and the potential for new discoveries through technological advancements. Vlatko emphasizes the need for adventurous research and …

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AI vs Human Intelligence: The Emergent Mind 50:25

12d ago50:25

50:25

In this conversation, Drs. Gaurav Suri and Jay Mcclelland delves into the intricate relationship between artificial intelligence and human cognition, exploring similarities and differences, the evolution of AI from rule-based systems to learning models, and the concept of emergence in both fields. The discussion also touches on the efficiency of hu…

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The Giant Leap 56:57

16d ago56:57

56:57

In this conversation, Dr. Caleb Scharf discusses the evolution of space exploration, drawing parallels to historical figures like Darwin. He explores the implications of humanity's expansion into space, the challenges of microgravity, and the allure of Mars as a potential habitat. Scharf emphasizes the interconnectedness of space exploration with o…

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Dinosaurs with Rachel Ignotofsky 30:30

23d ago30:30

30:30

In this engaging conversation, Rachel Ignotofski discusses her new book Dinosaurs, exploring the fascination with these ancient creatures, the impact of mass extinctions, and the evolution of life on Earth. She highlights the importance of paleontology, the legacy of Mary Anning, and the artistic choices made in illustrating the book. The discussio…

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Blaise Agüera y Arcas: What is Intelligence? 1:14:40

1M ago1:14:40

1:14:40

Blaise Agüera y Arcas’s talk took us on a journey through What is Intelligence?, his groundbreaking new work connecting the evolutionary dots between life, computation, and symbiogenesis. He explores how, in our symbiotic world, things combine to make larger things all the time. We might think of humanity in terms of the individual — but we're alre…

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Charlatans with Quico Toro 39:52

1M ago39:52

39:52

By Breaking Math

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Economica with Victoria Bateman 1:04:48

1M ago1:04:48

1:04:48

In this conversation, economist Dr. Victoria Bateman discusses the critical role of women in shaping economic prosperity throughout history. She argues that women's choices, independence, and labor have been overlooked in traditional economic narratives. The discussion covers various themes, including the impact of women's marriage decisions on pop…

1
TREE(3) and the Kruskal theorem, Part II 22:43

2M ago22:43

22:43

We give the proof the Tree Theorem. It's cute!

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Blueprints with Marcus du Sautoy 59:39

2M ago59:39

59:39

In this conversation, Marcus Du Sautoy explores the intricate relationship between mathematics and various forms of art, including music, literature, and visual arts. He discusses how mathematical concepts such as prime numbers, symmetry, and randomness influence creative processes and artistic expressions. Through examples from renowned artists li…

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Unequal with Eugenia Cheng 46:49

2M ago46:49

46:49

In this conversation, Eugenia Cheng discusses the importance of making math accessible and engaging for everyone, particularly those who have been discouraged by traditional education methods. She emphasizes the intersection of math and art, the dangers of oversimplifying complex issues with numbers, and the need for a more nuanced understanding of…

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TREE(3) and the Kruskal theorem 13:19

3M ago13:19

13:19

Let's talk about that most legendary of large numbers: TREE(3). Or rather, let's talk about the theorem that is used to show that such a number exists. We're going to try to go in more depth than the Numberphile video (though I do recommend it!). We're going back to basics a bit, with some short and sweet episodes without animations.…

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Breaking Math: When Math Meets a Technology Glitch 4:14

2M ago4:14

4:14

This week’s episode isn’t our usual deep dive—it’s a behind-the-scenes update. On Monday, Breaking Math vanished from Spotify, Apple, YouTube, and more without warning. After digging in, we discovered a strange RSS glitch that merged our feed with another podcast. In this quick update, Autumn shares: What happened behind the scenes when the show di…

1
Schematic Affine Recursion, Oh My! 18:49

3M ago18:49

18:49

To solve the problem raised in the last episode, I propose schematic affine recursion. We saw that affine lambda calculus (where lambda-bound variables are used at most once) plus structural recursion does not enforce termination, even if you restrict the recursor so that the function to be iterated is closed when you reduce ("closed at reduction")…

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The Stunner: Linear System T is Diverging! 21:03

3M ago21:03

21:03

In this episode, I shoot down last episode's proposal -- at least in the version I discussed -- based on an amazing observation from an astonishing paper, "Gödel’s system T revisited", by Alves, Fernández, Florido, and Mackie. Linear System T is diverging, as they reveal through a short but clever example. It is even diverging if one requires that …

1
Hate the Game 34:25

3M ago34:25

34:25

In this conversation, Dr. Daryl Fairweather, chief economist at Redfin, discusses her book “Hate the Game,” that frames life and career decisions as strategic games. She emphasizes the importance of understanding economic principles to navigate personal and professional challenges, negotiate effectively, and reclaim agency in various aspects of lif…

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Eigenvalues and Eigenvectors: The Secret Sauce of Modern Tech (From Graphics to Google) 18:06

3M ago18:06

18:06

This episode outlines Eigenvalues and Eigenvectors in Linear Algebra. We highlight the practical uses of these abstract topics.By AmCan Tech

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Decoding Language: The Power of Context-Free Grammars in Computing 17:07

3M ago17:07

17:07

This bonus episode explores what context-free grammars are in automata theorem.By AmCan Tech

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Demystifying Automata Theory: From Finite Machines to Regular Languages 1:03:36

3M ago1:03:36

1:03:36

This deep dive offers comprehensive overview of automata theory and formal languages. They begin by introducing finite automata (FA), including Deterministic Finite Automata (DFA) and Non-deterministic Finite Automata (NFA), alongside fundamental concepts like alphabets, strings, and languages, and their associated operations.…

1
Dots and Lines: Hidden Networks 37:17

3M ago37:17

37:17

In this conversation, Autumn and Dr. Anthony Bonato explore the fascinating world of networks, discussing their significance in various fields, including mathematics, social interactions, and even the spread of diseases like COVID-19 in his new book Dots and Lines. Anthony shares his journey into network science, the importance of understanding net…

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A proof of God (maybe) 1:44:36

3M ago1:44:36

1:44:36

Another long one, to make up for the lack of episodes! I'm joined by the self-described "friend of the pod", Siva Somayyajula, whose lack of a proper webpage only increases the mystique, to talk about the famous (and infamous) Ontological Proof of God by the logician Kurt Gödel, who never ceases to surprise. I've heard of this argument many times, …

1
Robin Hood Math 32:35

3M ago32:35

32:35

In this episode of Breaking Math, Dr. Noah Giansiracusa discusses his book 'Robin Hood Math', emphasizing the importance of mathematical literacy in navigating an algorithm-driven world. He explores how math can empower everyday people, the writing process behind his book, and practical applications of math in daily life, including social media alg…

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Terminating Computation First? 11:27

4M ago11:27

11:27

In this episode, I discuss an intriguing idea proposed by Victor Taelin, to base a logically sound type theory on an untyped but terminating language, upon which one may then erect as exotic a type system as one wishes. By enforcing termination already for the untyped language, we no longer have to make the type system do the heavy work of enforcin…

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What are Swim Training Patterns? 45:54

3M ago45:54

45:54

In this conversation, Dr. Christoph Bartneck discusses the intersection of swimming and computer science, exploring how mathematical patterns can enhance swim training. He introduces the concept of a formal swim markup language to improve data exchange and training efficiency. The discussion also delves into the visualization of swimming techniques…

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AI Ethics: Algorithms Go To College 11:35

4M ago11:35

11:35

In this episode of Breaking Math, Autumn explores the complex world of AI ethics, focusing on its implications in education, the accuracy of AI systems, the biases inherent in algorithms, and the challenges of data privacy. The discussion emphasizes the importance of ethical considerations in mathematics and computer science, advocating for transpa…

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Random Shuffle Isn't Random At All 8:20

4M ago8:20

8:20

In this episode, we explore the intricate mathematics behind Sp0tify's (ok... and other's) shuffle feature, revealing how it is designed to feel random while actually being carefully curated. We discuss the psychological implications of randomness, the Fisher-Yates shuffle algorithm, and how engineers have created a system that respects human perce…

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Algorithms & AI Simplified - The Not So Mathy Version 9:19

4M ago9:19

9:19

This conversation explores the intricate relationship between mathematics and artificial intelligence (AI) for people who don't want to get too math heavy and want things simplified as much as possible. It delves into how algorithms, machine learning, and various mathematical tools like linear algebra, calculus, and statistics form the backbone of …

1
What is Cryptography? 40:56

5M ago40:56

40:56

This conversation delves into the intersection of quantum computing and cryptography, focusing on the implications of quantum computers for current encryption methods and the necessity for post-quantum cryptography. Dr. Dustin Moody from NIST discusses the threats posed by quantum computing, particularly through Shor's algorithm, and the ongoing ef…

1
We Live in a Radioactive World: What is Dosimetry? 32:10

5M ago32:10

32:10

In this episode, Autumn interviews Dr. Ileana Pazos, an expert in dosimetry, discussing the critical role of radiation measurement in various industries, including healthcare and food safety. They explore the science behind dosimetry, the applications of radiation, the challenges faced in accurate measurements, and the misconceptions surrounding fo…

1
Kim Carson: Inspired by Intelligence 48:03

5M ago48:03

48:03

What if AI is not here actually to replace us, but to remind us who we actually are?That was the question at the heart of Kim Carson’s Long Now Talk. In _Inspired by Intelligence: Purpose and Creativity in the AI Era_, Carson challenged us to avoid the easy narratives of tech-driven utopia and dystopia, charting a course through those two extremes …

1
What is Life? 41:32

5M ago41:32

41:32

In this conversation, Dr. Elizabeth Strychalski discusses the fascinating field of synthetic biology, particularly focusing on synthetic cells. She shares her journey into this research area, the challenges of defining life, and the ethical considerations surrounding synthetic biology. The conversation also explores the potential applications of sy…

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Fire Science: What are Photoacoustic Measurements? 49:49

5M ago49:49

49:49

In this episode of Breaking Math, hosts Autumn and Gabriel explore the innovative intersections of fire science and technology with experts Amy Mensch and Ryan Falkenstein-Smith who work at NIST. They discuss the groundbreaking photoacoustic technique for measuring soot deposition, its applications in fire safety and forensic investigations, and th…

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Sara Imari Walker: An Informational Theory of Life 1:10:54

6M ago1:10:54

1:10:54

“What is life?”In her Long Now Talk, astrobiologist and theoretical physicist Sara Imari Walker explores the many dimensions of that seemingly simple question. Starting from the simplest precursors, Walker assembled a grand cathedral of meaning, tracing an arc across existence that linked the fundamentals of organic chemistry, the possibility space…

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Collatz, Conway and Computation 21:18

6M ago21:18

21:18

I return, alone, to talk about the notorious Collatz conjecture, and a pretty cool observation made by mathematician and all-around interesting person John Conway in 1972. An interesting little intersection of logic, computer science and number theory.

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Secrets Hidden in PDF Pages 17:50

6M ago17:50

17:50

In this episode, we explore a novel method for distributed steganography using PDF files. The technique involves splitting a secret message using secret sharing algorithms and embedding the parts into PDFs by manipulating their internal structure—specifically through hidden pages. We discuss how this approach makes the embedded data virtually invis…

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Ezra Klein & Derek Thompson: Abundance 59:28

6M ago59:28

59:28

As they look upon the United States of America in 02025, Ezra Klein and Derek Thompson see a country wrought by a half-century of failed governance. They see states and cities theoretically committed to progressive futures instead bogged down in labyrinthine mires of process — a society stuck in low gear. Yet they also see opportunity to turn those…

1
Correction: the Correct Author of the Proof from Last Episode, and an AI flop 7:10

6M ago7:10

7:10

I correct what I said in the last episode about the author of the proof of FD from last episode based on intersection types. I also describe AI flopping when I ask it a question about this.By Aaron Stump

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Krivine's Proof of FD, Using Intersection Types 21:35

7M ago21:35

21:35

Krivine's book (Section 4.2) has a proof of the Finite Developments Theorem, based on intersection types. I discuss this proof in this episode.By Aaron Stump

1
Kim Stanley Robinson & Stephen Heintz: A Logic For The Future 57:10

7M ago57:10

57:10

Stephen Heintz and Kim Stanley Robinson say we live in an “Age of Turbulence.”Looking around our geopolitical situation, it’s easy to see what they mean. Faced with the ever-growing threat of climate change, the looming potential breakdown of the post-01945 international order, and the ambiguous prospects of rapid technological changes in fields li…

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Joel David Hamkins 1:57:11

7M ago1:57:11

1:57:11

This time we are enchanted by the presence of Notre Dame Professor of Philosophy and Mathematics ⁠Joel David Hamkins⁠! His work sparks so much interesting breadth that it was quite hard to limit ourselves to the subjects we did. But that still includes talking about crazy Turing Machines that can do anything, about the multiverse of mathematical in…