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Breaking Math Podcast

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Breaking Math is a podcast that aims to make math accessible to everyone, and make it enjoyable. Every other week, topics such as chaos theory, forbidden formulas, and more will be covered in detail. If you have 45 or so minutes to spare, you're almost guaranteed to learn something new!

*See our new math and science youtube show called "Turing Rabbit Holes" at youtube.com/turingrabbitholespodcast ! The Breaking Math Podcast team has teamed up with Particle Physicist and Science Fiction Author Dr. Alex Alaniz to deliver a show about science and society. Subscribe and never miss an episode! Support this podcast: https://anchor.fm/breakingmathpodcast/support
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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 the police? Distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. For more information, visit CreativeCommons.or [Featuring: Sofía Baca; Diane Baca] --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support
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 highway tolls? All of this and more on this episode of Breaking Math. Episode distributed under an Creative Commons Attribution-ShareAlike-NonCommercial 4.0 International License. For more information, visit CreativeCommons.org [Featuring: Sofía Baca, Meryl Flaherty] --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support
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.org Featuring 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 a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support
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 Math. This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org. The theme for this episode was written by Elliot Smith. [Featuring: Sofía Baca, Meryl Flaherty] --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support
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 exist in four dimensions. So what is a fiber? What can fiber bundles teach us about higher dimensional objects? All of this, and more, on this episode of Breaking Math. [Featuring: Sofía Baca, Meryl Flaherty] --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support
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 opposed to the more elementary classical geometry. One helpful metric in describing these objects is how they are curved around a certain point. So how is curvature defined mathematically? What is the difference between negative and positive curvature? And what can Gauss' Theorema Egregium teach us about eating pizza? This episode distributed under a Creative Commons Attribution ShareAlike 4.0 International License. For more information, go to creativecommons.org Visit our sponsor today at Brilliant.org/BreakingMath for 20% off their annual membership! Learn hands-on with Brilliant. [Featuring: Sofía Baca, Meryl Flaherty] --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support
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/2008.00922 This episode is distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. For more information, visit CreativeCommons.org! [Featuring: Sofía Baca, Gabriel Hesch] --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support
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 Premium! Patreon-Become a monthly supporter at patreon.com/breakingmath Merchandise Purchase a Math Poster on Tensor Calculus at our facebook store at facebook.com/breakingmathpodcast Ad contained music track "Buffering" from Quiet Music for Tiny Robots. Distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. For more information, visit creativecommons.org. --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support
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:   theGreatCoursesPlus.com/breakingmath Get a free month of the Great Courses Plus while supporting this show by clicking here and signing up!    brilliant.org/breakingmath Sign up at brilliant.org, where breaking math listeners get a 20% off of a year subscription of Brilliant Premium! Patreon-Become a monthly supporter at patreon.com/breakingmath Merchandise-Purchase a Math Poster on Tensor Calculus at our facebook store at facebook.com/breakingmathpodcast The theme for this episode was written by Elliot Smith. Episode used in the ad was Buffering by Quiet Music for Tiny Robots. [Featuring: Sofía Baca; Meryl Flaherty] --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support
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 brilliant.org, where breaking math listeners get a 20% off of a year subscription of Brilliant Premium! Patreon-Become a monthly supporter at patreon.com/breakingmath Merchandise Purchase a Math Poster on Tensor Calculus at our facebook store at facebook.com/breakingmathpodcast The theme for this episode was written by Elliot Smith. Music in the ad was Tiny Robot Armies by Quiet Music for Tiny Robots. [Featuring: Sofía Baca, Gabriel Hesch] --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support
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 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 Premium! Patreon-Become a monthly supporter at patreon.com/breakingmath Merchandise Purchase a Math Poster on Tensor Calculus at our facebook store at facebook.com/breakingmathpodcast (Correction: at 12:00, the paradox is actually due to Galileo Galilei) Distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. For more information, visit CreativeCommons.org Music used in the The Great Courses ad was Portal by Evan Shaeffer [Featuring: Sofía Baca, Gabriel Hesch] --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support
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 numbers? So what are ordinal numbers? What does "transfinite" mean? And what does it mean to have a number one larger than another infinite number? [Featuring: Sofía Baca; Diane Baca] 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 Premium! Patreon Become a monthly supporter at patreon.com/breakingmath Merchandise Purchase a Math Poster on Tensor Calculus at our facebook store at facebook.com/breakingmathpodcast This episode is released under a Creative Commons attribution sharealike 4.0 international license. For more information, go to CreativeCommoms.org This episode features the song "Buffering" by "Quiet Music for Tiny Robots" --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support
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 Baca] 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 Premium! Patreon Become a monthly supporter at patreon.com/breakingmath Merchandise Purchase a Math Poster on Tensor Calculus at our facebook store at facebook.com/breakingmathpodcast --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support
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 what does Bayes have to do with this? All of this and more on this episode of Breaking Math. [Featuring: Sofía Baca, Gabriel Hesch; Peter Zeidman] 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 Premium! Patreon Become a monthly supporter at patreon.com/breakingmath Merchandise Purchase a Math Poster on Tensor Calculus at our facebook store at facebook.com/breakingmathpodcast This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org. --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support
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 properties. To this point, a circle's circumference divided by its diameter is the mathematical constant pi, which has been a topic of fascination for mathematicians for as long as circles have been considered. [Featuring Sofía Baca; Meryl Flaherty] 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 Premium! Patreon Become a monthly supporter at patreon.com/breakingmath Merchandise Purchase a Math Poster on Tensor Calculus at our facebook store at facebook.com/breakingmathpodcast --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support
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/app Support this podcast: https://anchor.fm/breakingmathpodcast/support
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 as non-integer and complex bases. So how can the base systems we covered last time be extended to represent fractional numbers? How can fractional numbers be used as a base for integers? And what is pi plus e times i in base i + 1? This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org. [Featuring: Sofía Baca; Merryl Flaherty] 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 Premium! Patreon Become a monthly supporter at patreon.com/breakingmath Merchandise Purchase a Math Poster on Tensor Calculus at our facebook store at facebook.com/breakingmathpodcast --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support
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, Indians, Sumerians, and Mayans, had figured out how to chunk numbers indefinitely, and make numbers to count seemingly uncountable quantities using the mind, and write them down in a few easily mastered motions. These are known as place-value systems, and the study of bases has its root in them: talking about bases helps us talk about what is happening when we use these magical symbols. --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support
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2020-06-0308:45

#BLACKOUTDAY2020 George 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/support
Machines have been used to simplify labor since time immemorial, and simplify thought in the last few hundred years. We are at a point now where we have the electronic computer to aid us in our endeavor, which allows us to build hypothetical thinking machines by simply writing their blueprints — namely, the code that represents their function — in a general way that can be easily reproduced by others. This has given rise to an astonishing array of techniques used to process data, and in recent years, much focus has been given to methods that are used to answer questions where the question or answer is not always black and white. So what is machine learning? What problems can it be used to solve? And what strategies are used in developing novel approaches to machine learning problems? This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org. For more Breaking Math info, visit BreakingMathPodcast.app [Featuring: Sofía Baca, Gabriel Hesch] References: https://spectrum.ieee.org/tag/history+of+natural+language+processing 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 Premium! Patreon Become a monthly supporter at patreon.com/breakingmath Merchandise Purchase a Math Poster on Tensor Calculus at our facebook store at facebook.com/breakingmathpodcast --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support
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Comments (11)

Andrew Dias

I really wish there was another podcast that goes over the same topics but without Sophia hosting. She is not great at explaining concepts. There is the tendency to do the typical thing of trying to simplify ideas, but in the process end up making it too obscure to really understand. Case in point is the fact that her mom (who teaches math) can't understand what is being explained.

Feb 15th
Reply

Andrew Dias

Good episode content. A couple things: much of the discussion about the individual axioms become convoluted with the language and examples that are used. The point is to either clearly state the axiom or provide examples that simplify the understanding, not complicate it. Also, Gödel is roughly pronounced "GER-dle", not "go-DELL."

Nov 27th
Reply

Numoru WE3

Thank y'all for this episode... I've been down and depressed for a sec, this brought me back...thanks for the knowledge, laughs, and time taken for doing this during everything.love

Jun 16th
Reply

Christi Sewell

False assumptions, bad conclusions. What about the modern example of Jaime Escalante and his ability to challenge elitism to economically challenged young adults with no time to study? Still they overcame it. Why? They wanted something enough to MAKE time for it and they had a teacher that demanded discipline.

May 24th
Reply

Koenigsegg

Awesome

Jul 5th
Reply

Vincent Kong

keep up the good work, love from UK

Apr 23rd
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Paul Billington

wonderful

Apr 7th
Reply

Susa Rantanen

Just what i was looking for, although I can barely keep up sometimes, since my knowledge in math isn't great. Still super interesting!

Oct 12th
Reply

Elham Nazif

Lohnverstoß

Oct 10th
Reply

David Calano

Great podcast!

Apr 29th
Reply

Pratiksha Devshali

it's superb.. loved it.. the creators of this podcast are great :)

Oct 27th
Reply
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