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! SFTM, our umbrella organization, also has another (explicit) podcast called "Nerd Forensics" all about nerd (and other) culture. Check it out wherever you get podcasts! Support this podcast: https://anchor.fm ...

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69: An Interview with Michael Brooks, Author of "The Art of More: How Mathematics Created Civilization"
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Michael Brooks is a science writer who specializes in making difficult concepts easier to grasp. In his latest book, Brooks goes through several mathematical concepts and discusses their motivation, history, and discovery. So how do stories make it easier to learn? What are some of the challenges associated with conveying difficult concepts to the …

There are times in mathematics when we are generalizing the behavior of many different, but similar, entities. One such time that this happens is the use cases of Big O notation, which include describing the long-term behavior of functions, and talking about how accurate numerical calculations are. On this problem episode, we are going to discuss B…

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68: LOL!!! SO RANDOM (Random Variables)
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The world is often uncertain, but it has only been in the last half millennium that we've found ways to interact mathematically with that concept. From its roots in death statistics, insurance, and gambling to modern Bayesian networks and machine learning, we've seen immense productivity in this field. Every way of looking at probability has someth…

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67: Wrath of Math (Mathematics Used Unwisely)
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Mathematics is a subject that has been used for great things over time: it has helped people grow food, design shelter, and in every part of life. It should be, then, no surprise that sometimes mathematics is used for evil; that is to say, there are times where mathematics is used to either implement or justify regressive things like greed, racism,…

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P11: Feeling Lucky? (Probability and Intuition)
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Join Sofía Baca with her guest Millicent Oriana from the newly launched Nerd Forensics podcast as they discuss some apparent paradoxes in probability and Russian roulette. Intro is "Breaking Math Theme" by Elliot Smith. Ads feature "Ding Dong" by Simon Panrucker [Featuring: Sofía Baca; Millicent Oriana] --- This episode is sponsored by · Anchor: Th…

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66: Hayhoe, Let's Go! (An Interview With Climate Scientist Katharine Hayhoe)
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Katharine Hayhoe was the lead author on the 2018 US Climate Assessment report, and has spent her time since then spreading the word about climate change. She was always faced with the difficult task of convincing people who had stakes in things that would be affected by acknowledging the information in her report. In her newest book, “Saving Us: A …

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P10: Chivalry is Dead (Knights and Knaves #1)
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One tells a lie, the other the truth! Have fun with Sofía and Meryl as they investigate knight, knave, and spy problems! Intro is "Breaking Math Theme" by Elliot Smith. Music in the ads were Plug Me In by Steve Combs and "Ding Dong" by Simon Panrucker. You can access their work at freemusicarchive.org. [Featuring: Sofia Baca; Meryl Flaherty] --- Th…

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65: An Interview with Author Ian Stewart (Book About Everyday Math)
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Distributed under a Creative Commons Attribution-ShareAlike-NonCommercial license. For more information, visit creativecommons.org. Ian is an author who has written many math and science books, and collaborated with Terry Pratchett. --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/appSupport this podca…

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64: What Projection Is This? (Map Projections)
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The world is a big place with a lot of wonderful things in it. The world also happens to be spherical, which can make getting to those things a challenge if you don't have many landmarks. This is the case when people are navigating by sea. For this reason, map projections, which take a sphere and attempt to flatten it onto a sheet, were born. So wh…

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RR36: The Most Boring Episode Ever (Rerun: Math Games)
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This is a rerun of one of our favorite episodes! We hope that you enjoy it if you haven't listened to it yet. We'll be back next week with new content! Thank you so much for listening to Breaking Math!Math is a gravely serious topic which has been traditionally been done by stodgy people behind closed doors, and it cannot ever be taken lightly. Tho…

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63: Broken Voting Systems (Voting Systems and Paradoxes)
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Voting systems are, in modern times, essential to the way that large-scale decisions are made. The concept of voicing an opinion to be, hopefully, considered fairly is as ancient and well-established as the human concept of society in general. But, as time goes on, the recent massive influx of voting systems in the last 150 years have shown us that…

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62: The Atom Bomb of Information Operations (An Interview with John Fuisz of Veriphix)
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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 ana…

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RR38: The Great Stratagem Heist (Game Theory: Iterated Elimination of Dominated Strategies)
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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…

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61: Look at this Graph! (Graph Theory)
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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, electric…

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P9: Give or Take (Back-of-the-Envelope Estimates / Fermi Problems)
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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 t…

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

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59: A Good Source of Fibers (Fiber Bundles)
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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 …

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58: Bringing Curvy Back (Gaussian Curvature)
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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 ab…

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

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P7: Root for Squares (Irrationality of the Square Root of Two)
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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.…

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

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P6: How Many Angles in a Circle? (Curvature; Euclidean Geometry)
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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…

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56: More Sheep than You Can Count (Transfinite Cardinal Numbers)
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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 me…

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55: Order in the Court (Transfinite Ordinal Numbers)
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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 infini…

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 'lar…