Breaking Math Podcast

By Autumn Phaneuf & Noah GiansiracusaScience Natural Sciences Mathematics

Breaking Math Podcast episodes

November 07, 2017 19: Tune of the Hickory Stick (Beginning to Intermediate Math Education)
The art of mathematics has proven, over the millennia, to be a practical as well as beautiful pursuit. This has required us to use results from math in our daily lives, and there's one thing that has always been true of humanity: we like to do things as easily as possible. Therefore, some very peculiar and interesting mental connections have been developed for the proliferation of this sort of paramathematical skill. What we're talking about when we say "mental connections" is the cerebral process of doing arithmetic and algebra. So who invented arithmetic? How are algebra and arithmetic related? And how have they changed over the years?

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40 min
October 11, 2017 18: Frequency (Fourier and Related Analyses)
Duration and proximity are, as demonstrated by Fourier and later Einstein and Heisenberg, very closely related properties. These properties are related by a fundamental concept: frequency. A high frequency describes something which changes many times in a short amount of space or time, and a lower frequency describes something which changes few times in the same time. It is even true that, in a sense, you can ‘rotate’ space into time. So what have we learned from frequencies? How have they been studied? And how do they relate to the rest of mathematics?

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45 min
October 05, 2017 17: Navier Stoked (Vector Calculus and Navier-Stokes Equations)
From our first breath of the day to brushing our teeth to washing our faces to our first sip of coffee, and even in the waters of the rivers we have built cities upon since antiquity, we find ourselves surrounded by fluids. Fluids, in this context, mean anything that can take the shape of its container. Physically, that means anything that has molecules that can move past one another, but mathematics has, as always, a slightly different view. This view is seen by some as more nuanced, others as more statistical, but by all as a challenge. This definition cannot fit into an introduction, and I’ll be picking away at it for the remainder of this episode. So what is a fluid? What can we learn from it? And how could learning from it be worth a million dollars?

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1 hr 1 min
September 19, 2017 BFNB2: Thought for Food (Discussion about Learning)
Sponsored by www.brilliant.org/breakingmath, where you can take courses in calculus, computer science, chemistry, and other STEM subjects. All online; all at your own pace; and accessible anywhere with an internet connection, including your smartphone or tablet! Start learning today!

Check out: https://blankfornonblank.podiant.co/e/357f09da787bac/
What you're about to hear is part two of an episode recorded by the podcasting network ___forNon___ (Blank for Non-Blank), of which Breaking Math, along with several other podcasts, is a part. To check out more ___forNon___ content, you can click on the link in this description. And of course, for more info and interactive widgets you can go to breakingmathpodcast.com, you can support us at patreon.com/breakingmathpodcast, and you can contact us directly at [email protected]. We hope you enjoy the second part of the first ___forNon___ group episode. You can also support ___forNon___ by donating at patreon.com/blankfornonblank.

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1 hr 12 min
September 16, 2017 BFNB1: Food for Thought (Discussion about Learning)
This is the first group podcast for the podcasting network ___forNon___ (pronounced "Blank for Non-Blank"), a podcasting network which strives to present expert-level subject matter to non-experts in a way which is simultaneously engaging, interesting, and simple. The episode today delves into the problem of learning. We hope you enjoy this episode.

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Support this podcast: https://anchor.fm/breakingmathpodcast/support
36 min
September 02, 2017 A Special Message
Hello. This is Jonathan from Breaking Math to bring you a special
message. Gabriel, my co-host, has recently had a child. The child
is healthy, but both children and Breaking Math take time,
and we're still figuring out how to make use of said time most
efficiently. So I'm here to tell you what you can expect in the
mean time.
In the mean time, you can expect some minisodes from us. These will
be covering a variety of topics, hopefully including the millennium
problems.
You can also expect us to release new episodes again in a very short
amount of time. The hosts and their families have discussed how time
is going to be spent, and all that remains to be seen is if this plan
is realistic, and to tweak it to make sure that you all get the same
content you've grown to know and love.
So thank you all for your patience, and if you have anything to say
to us in the mean time, you can write to us at [email protected]
or write to us on our facebook page, which is at facebook.com/breakingmathpodcast.
Thank you, and until we see you again, don't forget to check
periodically for updates of Breaking Math. Bye!
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Support this podcast: https://anchor.fm/breakingmathpodcast/support
3 min
August 18, 2017 Minisode 0.6: Four Problems
Jonathan and Gabriel discuss four challenging problems.

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26 min
July 30, 2017 15: Consciousness
What does it mean to be a good person? What does it mean to make a mistake? These are questions which we are not going to attempt to answer, but they are essential to the topic of study of today’s episode: consciousness. Conscious is the nebulous thing that lends a certain air of importance to experience, but as we’ve seen from 500 centuries of fascination with this topic, it is difficult to describe in languages which we’re used to. But with the advent of neuroscience and psychology, we seem to be closer than ever to revealing aspects of consciousness that we’ve never beheld. So what does it mean to feel? What are qualia? And how do we know that we ourselves are conscious?

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Support this podcast: https://anchor.fm/breakingmathpodcast/support
1 hr 1 min
July 20, 2017 Minisode 0.5: ___forNon___
Jonathan and Gabriel discuss ___forNon___ (blank for non-blank); a podcasting collective they've recently joined. Check out more at blankfornonblank.com.

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This episode is sponsored by
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Support this podcast: https://anchor.fm/breakingmathpodcast/support
15 min
July 11, 2017 14: Artificial Thought (Neural Networks)
Go to www.brilliant.org/breakingmathpodcast to learn neural networks, everyday physics, computer science fundamentals, the joy of problem solving, and many related topics in science, technology, engineering, and math.

Mathematics takes inspiration from all forms with which life interacts. Perhaps that is why, recently, mathematics has taken inspiration from that which itself perceives the world around it; the brain itself. What we’re talking about are neural networks. Neural networks have their origins around the time of automated computing, and with advances in hardware, have advanced in turn. So what is a neuron? How do multitudes of them contribute to structured thought? And what is in their future?

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Support this podcast: https://anchor.fm/breakingmathpodcast/support
1 hr 6 min

About Breaking Math Podcast

From the publisher's feed

Breaking Math is a deep-dive science, technology, engineering, AI, and mathematics podcast that explores the world through the lens of logic, patterns, and critical thinking.…

Hosted by Autumn Phaneuf, an expert in industrial engineering, operations research, and applied mathematics, and Noah Giansiracusa, a mathematician and leading voice in algorithmic literacy and technology ethics, the show is dedicated to uncovering the mathematical structures behind science, technology, and the systems shaping our future.

What began as a conversation about math as a pure and elegant discipline has evolved into a platform for bold, interdisciplinary dialogue. Each episode of Breaking Math takes listeners on an intellectual journey—into the strange beauty of chaos theory, the ethical dilemmas of AI and algorithms, the hidden math of biology and evolution, or the physics governing black holes and the cosmos. Along the way, Autumn and Noah speak with working scientists, researchers, and thinkers across fields: computer scientists, physicists, chemists, engineers, economists, philosophers, and more.

But this isn’t just a podcast about equations. It’s a show about how mathematics shapes the way we think, decide, build, and understand the world. Breaking Math pushes back against the idea that STEM belongs behind a paywall or an academic podium. It’s for the curious, the critical, and the creative—for anyone who believes that ideas should be rigorous, accessible, and infused with wonder.

If you’ve ever wondered:

What’s the math behind machine learning and modern algorithms?
How do we quantify uncertainty in climate and economic models?
Can intelligence or consciousness be meaningfully described in AI?
Why does beauty matter in an equation?

You’re in the right place.

At its heart, Breaking Math is about building bridges—between disciplines, between experts and the public, and between abstract mathematics and the messy, magnificent reality we live in. With humor, clarity, and deep respect for complexity, Autumn and Noah invite you to rethink what math can be—and how it can help us shape a better future.

Listen wherever you get your podcasts.

Website: https://breakingmath.io

Linktree: https://linktr.ee/breakingmathmedia

Email: [email protected]