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, classism, and even genocide. So when has math been used for destructive purposes? What makes us mis-apply mathematics? And why can oversimplification...
Dec 09, 2021•24 min
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: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support...
Nov 30, 2021•30 min
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...
Nov 21, 2021•1 hr 12 min
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]
Nov 14, 2021•19 min
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...
Oct 24, 2021•44 min
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 wr...
Sep 29, 2021•47 min
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 absol...
Sep 19, 2021•49 min
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 we...
Sep 05, 2021•34 min
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...
Aug 22, 2021•45 min
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 mini...
Apr 25, 2021•30 min
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]
Apr 19, 2021•31 min
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...
Apr 03, 2021•29 min
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 ...
Mar 21, 2021•42 min
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...
Mar 03, 2021•43 min
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, vi...
Feb 25, 2021•20 min
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/breakingmath Merchandise 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.
Feb 07, 2021•14 min
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 pa...
Feb 01, 2021•30 min
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/breakingmath 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, Gabri...
Jan 28, 2021•29 min
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/brea...
Jan 24, 2021•35 min
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 o...
Jan 14, 2021•31 min
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 Bac...
Dec 21, 2020•27 min
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?...
Dec 11, 2020•43 min
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 p...
Dec 05, 2020•31 min
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]
Nov 26, 2020•13 min
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, s...
Nov 15, 2020•34 min
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, ...
Aug 31, 2020•55 min
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 y...
May 26, 2020•58 min
Machines, during the lifetime of anyone who is listening to this, have advanced and revolutionized the way that we live our lives. Many listening to this, for example, have lived through the rise of smart phones, 3d printing, massive advancements in lithium ion batteries, the Internet, robotics, and some have even lived through the introduction of cable TV, color television, and computers as an appliance. All advances in machinery, however, since the beginning of time have one thing in common: t...
May 18, 2020•55 min
Join Gabriel and Sofía as they delve into some introductory calculus concepts. [Featuring: Sofía Baca, Gabriel Hesch] Ways to support the show: Patreon Become a monthly supporter at patreon.com/breakingmath
Mar 10, 2020•36 min
Time is something that everyone has an idea of, but is hard to describe. Roughly, the arrow of time is the same as the arrow of causality. However, what happens when that is not the case? It is so often the case in our experience that this possibility brings not only scientific and mathematic, but ontological difficulties. So what is retrocausality? What are closed timelike curves? And how does this all relate to entanglement? This episode is distributed under a CC BY-SA 4.0 license. For more in...
Feb 29, 2020•29 min
