Breaking Math Podcast

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,...

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...

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 informati...

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...

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....

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 f...

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 a...

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 Ackerma...

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...

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...

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]

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 (v...

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,...

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 oth...

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 ap...

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

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 th...

Learn more about radiative forcing, the environment, and how global temperature changes with atmospheric absorption with this Problem Episode about you walking your (perhaps fictional?) dog around a park.  This episode is distributed under a CC BY-SA license. For more information, visit CreativeCommons.org. [Featuring: Sofía Baca, Gabriel Hesch] ---  This episode is sponsored by  ·...

Since time immemorial, blacksmiths have known that the hotter metal gets, the more it glows: it starts out red, then gets yellower, and then eventually white. In 1900, Max Planck discovered the relationship between an ideal object's radiation of light and its temperature. A hundred and twenty years later, we're using the consequences of this discovery for many things, including (indirectly) LED TV...

Climate change is an issue that has become frighteningly more relevant in recent years, and because of special interests, the field has become muddied with climate change deniers who use dishonest tactics to try to get their message across. The website SkepticalScience.com is one line of defense against these messengers, and it was created and maintained by a research assistant professor at the Ce...

Mathematics, like any intellectual pursuit, is a constantly-evolving field; and, like any evolving field, there are both new beginnings and sudden unexpected twists, and things take on both new forms and new responsibilities. Today on the show, we're going to cover a few mathematical topics whose nature has changed over the centuries. So what does it mean for math to be extinct? How does this happ...

Learn more about calculus, derivatives, and the chain rule with this Problem Episode about you walking your (perhaps fictional?) dog around a park. This episode is distributed under a CC BY-SA 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://ancho...

Ben Orlin has been a guest on the show before. He got famous with a blog called 'Math With Bad Drawings", which is what it says on the tin: he teaches mathematics using his humble drawing skills. His last book was a smorgasbord of different mathematical topics, but he recently came out with a new book 'Change is the Only Constant: the Wisdom of Calculus in a Madcap World', which focuses more on ca...

On this problem episode, join Sofía and guest Diane Baca to learn about what an early attempt to formalize the natural numbers has to say about whether or not m+n equals n+m. This episode is distributed under a CC BY-SA 4.0 license ( https://creativecommons.org/licenses/by-sa/4.0/) --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podc...

Statistics is a field that is considered boring by a lot of people, including a huge amount of mathematicians. This may be because the history of statistics starts in a sort of humdrum way: collecting information on the population for use by the state. However, it has blossomed into a beautiful field with its fundamental roots in measure theory, and with some very interesting properties. So what i...