Breaking Math Podcast

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 Climate Scientist’s Case for Hope and Healing in a Divided World”, she discusses the challenges associated with these conversations, at both the micro and macro level. So who is Katherine Heyhoe? How has she learned to get people to acknowledge the reality of climate science? And is she the best, or worst, person to strike up a discussion about how the weather’s been? All of this, and more, on this episode of Breaking Math. Papers Cited: -“99.94 percent of papers agree with the scientific consensus.”More info: https://journals.sagepub.com/doi/10.1177/0270467617707079This episode is distributed under a CC BY-NC 4.0 International License. For more information, visit c

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]

Welcome to another engaging episode of the Breaking Math Podcast! Today's episode, titled "What is the Use?," features a fascinating conversation with the renowned mathematician and author, Professor Ian Stewart. As Professor Stewart discusses his latest book "What's the Use? How Mathematics Shapes Everyday Life," we dive deep into the real-world applications of mathematics that often go unnoticed in our daily technologies, like smartphones, and their unpredictable implications in various fields.We'll explore the history of quaternions, invented by William Rowan Hamilton, which now play a critical role in computer graphics, gaming, and particle physics. Professor Stewart will also shed light on the non-commutative nature of quaternions, mirroring the complexities of spatial rotations, and how these mathematical principles find their correspondence in the natural world.Furthermore, our discussion will encompass the interconnectivity within mathematics, touching upon how algebra, geometry, and trigonometry conv

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 what is a map projection? Why are there so many? And why is Gall-Peters the worst? All of this, and more, on this episode of Breaking Math.Theme was written by Elliot Smith.This episode is distributed under a Creative Commons 4.0 Attribution-ShareAlike-NonCommercial International License. For more information, visit CreativeCommons.org.--- This episode is sponsored by · Anchor: The easiest way to make a podcast.  https://anchor.fm/appSupport this podcast: https://anchor.fm/breakingmathpodcast/support

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. Those who have fun with mathematics mock science, medicine, and the foundation of engineering. That is why on today's podcast, we're going to have absolutely no fun with mathematics. There will not be a single point at which you consider yourself charmed, there will not be a single thing you will want to tell anyone for the sake of enjoyment, and there will be no tolerance for your specific brand of foolishness, and that means you too, Kevin.Theme by Elliot Smith.Distributed under a CC BY-SA-NC 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/appSupport this podca

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 there are as many ways to vote as there are flaws in the way that the vote is tallied. So what problems exist with voting? Are there any intrinsic weaknesses in group decision-making systems? And what can we learn by examining these systems? All of this, and more, on this episode of Breaking Math.Licensed under Creative Commons Attribution-ShareAlike-NonCommercial 4.0 International License. For more information, visit CreativeCommons.org.

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 episode of Breaking Math.The theme for this episode was written by Elliot Smith.[Featuring: Sofía Baca, Gabriel Hesch; John Fuisz]

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/appSupport 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.orgFeaturing theme song and outro by Elliot Smith of Albuquerque.[Featuring: Sofía Baca, Meryl Flaherty]

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]

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]

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.orgVisit our sponsor today at Brilliant.org/BreakingMath

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 CreativeCommons.org![Featuring: Sofía Baca, Gabriel Hesch]

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]Patreon-Become a monthly supporter at patreon.com/breakingmathMerchandiseAd 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.

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:Patreon-Become a monthly supporter at patreon.com/breakingmathThe 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]

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:Patreon-Become a monthly supporter at patreon.com/breakingmathThe 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]

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:Patreon-Become a monthly supporter at patreon.com/breakingmath(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.orgMusic used in the The Great Courses ad was Portal by Evan Shaeffer[Featuring: Sofía Baca, Gabriel Hesch]

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:PatreonBecome a monthly supporter at patreon.com/breakingmathThis episode is released under a Creative Commons attribution sharealike 4.0 international license. For more information, go to CreativeCommoms.orgThis episode features the song "Buffering" by "Quiet Music for Tiny Robots"

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:PatreonBecome a monthly supporter at patreon.com/breakingmathMerchandisePurchase a Math Poster on Tensor Calculus at our facebook store at facebook.com/breakingmathpodcast

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]PatreonBecome a monthly supporter at patreon.com/breakingmathThis episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org.