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PODCAST

Breaking Math Podcast

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 Gabriel Hesch, an electrical engineer (host from 2016-2024) with a passion for mathematical clarity, the show is dedicated to uncovering the mathematical structures behind science, engineering, technology, and the

science mathematics

All Episodes

45:32

62: The Atom Bomb of Information Operations (An...

Breaking Math Podcast ·

2021/08/22

Forecasting is a constantly evolving science, and has been applied to complex systems; everything from the weather, to determining what customers might like to buy, and even what governments might rise and fall. John Fuisz is someone who works with this science, and has experience improving the accuracy of forecasting. So how can forecasting be analyzed? What type of events are predictable? And why might Russia think a Missouri senator's race hinges upon North Korea? All of this and more on this

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32:49

RR38: The Great Stratagem Heist (Game Theory:...

Breaking Math Podcast ·

2021/05/23

This is a rerun of one of our favorite episodes while we change our studio around.Game theory is all about decision-making and how it is impacted by choice of strategy, and a strategy is a decision that is influenced not only by the choice of the decision-maker, but one or more similar decision makers. This episode will give an idea of the type of problem-solving that is used in game theory. So what is strict dominance? How can it help us solve some games? And why are The Obnoxious Seven wanted by

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30:09

61: Look at this Graph! (Graph Theory)

Breaking Math Podcast ·

2021/04/25

In mathematics, nature is a constant driving inspiration; mathematicians are part of nature, so this is natural. A huge part of nature is the idea of things like networks. These are represented by mathematical objects called 'graphs'. Graphs allow us to describe a huge variety of things, such as: the food chain, lineage, plumbing networks, electrical grids, and even friendships. So where did this concept come from? What tools can we use to analyze graphs? And how can you use graph theory to minimize

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31:38

P9: Give or Take (Back-of-the-Envelope Estimates /...

Breaking Math Podcast ·

2021/04/19

How many piano tuners are there in New York City? How much cheese is there in Delaware? And how can you find out? All of this and more on this problem-episode of Breaking Math.This episode distributed under a Creative Commons Attribution-ShareAlike-Noncommercial 4.0 International License. For more information, visit creativecommons.orgFeaturing theme song and outro by Elliot Smith of Albuquerque.[Featuring: Sofía Baca, Meryl Flaherty]--- This episode is sponsored by · Anchor: The easiest way to make

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29:24

60: HAMILTON! [But Not the Musical] (Quaternions)

Breaking Math Podcast ·

2021/04/03

i^2 = j^2 = k^2 = ijk = -1. This deceptively simple formula, discovered by Irish mathematician William Rowan Hamilton in 1843, led to a revolution in the way 19th century mathematicians and scientists thought about vectors and rotation. This formula, which extends the complex numbers, allows us to talk about certain three-dimensional problems with more ease. So what are quaternions? Where are they still used? And what is inscribed on Broom Bridge? All of this and more on this episode of Breaking

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47:28

59: A Good Source of Fibers (Fiber Bundles)

Breaking Math Podcast ·

2021/03/21

Mathematics is full of all sorts of objects that can be difficult to comprehend. For example, if we take a slip of paper and glue it to itself, we can get a ring. If we turn it a half turn before gluing it to itself, we get what's called a Möbius strip, which has only one side twice the length of the paper. If we glue the edges of the Möbius strip to each other, and make a tube, you'll run into trouble in three dimensions, because the object that this would make is called a Klein flask, and can only

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44:49

58: Bringing Curvy Back (Gaussian Curvature)

Breaking Math Podcast ·

2021/03/03

In introductory geometry classes, many of the objects dealt with can be considered 'elementary' in nature; things like tetrahedrons, spheres, cylinders, planes, triangles, lines, and other such concepts are common in these classes. However, we often have the need to describe more complex objects. These objects can often be quite organic, or even abstract in shape, and include things like spirals, flowery shapes, and other curved surfaces. These are often described better by differential geometry as

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22:57

P8: Tangent Tango (Morikawa's Recently Solved Problem)

Breaking Math Podcast ·

2021/02/25

Join Sofía and Gabriel as they talk about Morikawa's recently solved problem, first proposed in 1821 and not solved until last year!Also, if you haven't yet, check out our sponsor The Great Courses at thegreatcoursesplus.com/breakingmath for a free month! Learn basically anything there.The paper featured in this episode can be found at https://arxiv.org/abs/2008.00922This episode is distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. For more information, visit

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17:04

P7: Root for Squares (Irrationality of the Square...

Breaking Math Podcast ·

2021/02/07

Join Sofía and Gabriel as they discuss an old but great proof of the irrationality of the square root of two.[Featuring: Sofía Baca, Gabriel Hesch]Ways to support the show:-Visit our Sponsors: theGreatCoursesPlus.com/breakingmath Get a free month of the Great Courses Plus while supporting this show by clicking the link and signing up! brilliant.org/breakingmath Sign up at brilliant.org, where breaking math listeners get a 20% off of a year's subscription of Brilliant

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33:07

57: You Said How Much?! (Measure Theory)

Breaking Math Podcast ·

2021/02/01

If you are there, and I am here, we can measure the distance between us. If we are standing in a room, we can calculate the area of where we're standing; and, if we want, the volume. These are all examples of measures; which, essentially, tell us how much 'stuff' we have. So what is a measure? How are distance, area, and volume related? And how big is the Sierpinski triangle? All of this and more on this episode of Breaking Math.Ways to support the show:-Visit our Sponsors:

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31:38

P6: How Many Angles in a Circle? (Curvature;...

Breaking Math Podcast ·

2021/01/28

Sofía and Gabriel discuss the question of "how many angles are there in a circle", and visit theorems from Euclid, as well as differential calculus.This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org.Ways to support the show:-Visit our Sponsors: theGreatCoursesPlus.com/breakingmath Get a free month of the Great Courses Plus while supporting this show by clicking the link and signing up! brilliant.org/breakingmath Sign up at

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37:21

56: More Sheep than You Can Count (Transfinite...

Breaking Math Podcast ·

2021/01/24

Look at all you phonies out there.You poseurs.All of you sheep. Counting 'til infinity. Counting sheep.*pff*What if I told you there were more there? Like, ... more than you can count?But what would a sheeple like you know about more than infinity that you can count?heh. *pff*So, like, what does it mean to count til infinity? What does it mean to count more? And, like, where do dimensions fall in all of this?Ways to support the show:-Visit our Sponsors: theGreatCoursesPlus.com/breakingmath Get a

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34:36

55: Order in the Court (Transfinite Ordinal Numbers)

Breaking Math Podcast ·

2021/01/14

As a child, did you ever have a conversation that went as follows:"When I grow up, I want to have a million cats""Well I'm gonna have a billion billion cats""Oh yeah? I'm gonna have infinity cats""Then I'm gonna have infinity plus one cats""That's nothing. I'm gonna have infinity infinity cats""I'm gonna have infinity infinity infinity infinity *gasp* infinity so many infinities that there are infinity infinities plus one cats"What if I told you that you were dabbling in the transfinite ordinal

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28:13

54: Oodles (Large Numbers)

Breaking Math Podcast ·

2020/12/21

There are a lot of things in the universe, but no matter how you break them down, you will still have far fewer particles than even some of the smaller of what we're calling the 'very large numbers'. Many people have a fascination with these numbers, and perhaps it is because their sheer scale can boggle the mind. So what numbers can be called 'large'? When are they useful? And what is the Ackermann function? All of this and more on this episode of Breaking Math[Featuring: Sofía Baca; Diane

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45:12

53: Big Brain Time (An Interview with Peter Zeidman...

Breaking Math Podcast ·

2020/12/11

Neuroscience is a topic that, in many ways, is in its infancy. The tools that are being used in this field are constantly being honed and reevaluated as our understanding of the brain and mind increase. And it's no surprise: the brain is responsible for the way we interact with the world, and the idea that ideas hone one another is not new to anyone who possesses a mind. But how can the tools that we use to study the brain and the mind be linked? How do the mind and the brain encode one another? And

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31:57

52: Round (Circles and Spheres)

Breaking Math Podcast ·

2020/12/05

Spheres and circles are simple objects. They are objects that are uniformly curved throughout in some way or another. They can also be defined as objects which have a boundary that is uniformly distant from some point, using some definition of distance. Circles and spheres were integral to the study of mathematics at least from the days of Euclid, being the objects generated by tracing the ends of idealized compasses. However, these objects have many wonderful and often surprising mathematical

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14:01

P5: All Your Base Are Belong to Us (Fractional Base...

Breaking Math Podcast ·

2020/11/26

Join Sofia and Gabriel on this problem episode where we explore "base 3-to-2" — a base system we explored on the last podcast — and how it relates to "base 3/2" from last episode.[Featuring: Sofía Baca; Gabriel Hesch]--- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/appSupport this podcast: https://anchor.fm/breakingmathpodcast/supportBecome a supporter of this podcast: https://www.spreaker.com/podcast/breaking-math-podcast--5545277/support.

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35:20

51: Episode "-2,0,1" (Bases; Exotic Bases)

Breaking Math Podcast ·

2020/11/15

A numerical base is a system of representing numbers using a sequence of symbols. However, like any mathematical concept, it can be extended and re-imagined in many different forms. A term used occasionally in mathematics is the term 'exotic', which just means 'different than usual in an odd or quirky way'. In this episode we are covering exotic bases. We will start with something very familiar (viz., decimal points) as a continuation of our previous episode, and then progress to the more odd, such

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44:56

50: Episode "101" (Bases)

Breaking Math Podcast ·

2020/08/31

Numbering was originally done with tally marks: the number of tally marks indicated the number of items being counted, and they were grouped together by fives. A little later, people wrote numbers down by chunking the number in a similar way into larger numbers: there were symbols for ten, ten times that, and so forth, for example, in ancient Egypt; and we are all familiar with the Is, Vs, Xs, Ls, Cs, and Ds, at least, of Roman numerals. However, over time, several peoples, including the Inuit,

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8:46

#BLACKOUTDAY2020

Breaking Math Podcast ·

2020/06/03

#BLACKOUTDAY2020George Perry Floyd was murdered by police on May 25, 2020.Learn more on twitter or your favorite search engine by searching #BLACKOUTDAY2020--- Support this podcast: https://anchor.fm/breakingmathpodcast/supportBecome a supporter of this podcast: https://www.spreaker.com/podcast/breaking-math-podcast--5545277/support.

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