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! Support this podcast: https://anchor.fm/breakingmathpodcast/support

49: Thinking Machines II (Techniques in Artificial Intelligence)

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…

48: Thinking Machines (Philosophical Basis of Artificial Intelligence)

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…

P4: Go with the Flow (Conceptual Calculus: Related Rates of Change)

Join Gabriel and Sofía as they delve into some introductory calculus concepts. [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:…

47: Blast to the Past (Retrocausality)

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…

RR30: The Abyss (Part One; Black Holes; Rerun)

Sofia is still recovering from eye surgery, so this will be a rerun. We’ll probably be back next week. The idea of something that is inescapable, at first glance, seems to violate our sense of freedom. This sense of freedom, for many, seems so intrinsic…

P3: Radiativeforcenado (Radiative Forcing)

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…

46: Earth Irradiated (the Greenhouse Effect)

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…

45: Climate Denialism and Cranky Uncles (Interview with John Cook of Skeptical Science)

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…

44: Vestigial Math (Math That Is Not Used like It Used to Be)

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…

P2: Walk the Dog (Calculus: Chain Rule)

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.…

43: Interview II with Author Ben Orlin (Change is the Only Constant: the Wisdom of Calculus in a Madcap World)

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…

P1: Peano Addition

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…

42: Maybe? (Probability and Statistics)

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.…

SR1: Forty Intros (Catalogue)

We’ve been doing this show for a while, and we thought it’d be fun to put out our first forty intros, especially since we passed 500,000 listens very recently. License: CC BY-SA 4.0 (creativecommons.org for more info) —- Support this podcast:…

41: Reality Is More Than Complex (Group Theory and Physics)

Children who are being taught mathematics often balk at the idea of negative numbers, thinking them to be fictional entities, and often only learn later that they are useful for expressing opposite extremes of things, such as considering a debt an amount…

40: Save the Date (Calendrical Math)

A calendar is a system of dividing up time into manageable chunks so that we can reference how long ago something happened, agree on times to do things in the future, and generally just have a sense of reckoning time. This can be as simple as recognizing…

39: Syntax Matters: Syntax… Matters? (Formal Grammar)

We communicate every day through languages; not only human languages, but other things that could be classified as languages such as internet protocols, or even the structure of business transactions. The structure of words or sentences, or their…

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

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…

37: The One Where They Parody Saw [audio fixed again] (Game Theory)

Hello listeners. You don’t know me, but I know you. I want to play a game. In your ears are two earbuds. Connected to the earbuds are a podcast playing an episode about game theory. Hosting that podcast are two knuckleheads. And you’re locked into this…

Stay Tuned for Season 3

Breaking Math will return with a third season in early February with an episode series about game theory starting with “The One where they Parody ‘Saw’”. We also talk about some upcoming news and such. Until then, enjoy in-the-works podcast “The Soapbox:…

36: The Most Boring Episode Ever. (Math Games)

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…

35: Please Be Discrete (Discrete Math)

Centuries ago, there began something of a curiosity between mathematicians that didn’t really amount to much but some interesting thoughts and cool mathematical theorems. This form of math had to do with strictly integer quantities; theorems about whole…

34: An Interview with Mathbot.com’s JW Weatherman

In this episode, we interview JW Weatherman of mathbot.com, and ask him about his product, why he made it, and what he plans on doing with it. —- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this…

33: Interview with Math with Bad Drawings (Ben Orlin)

An interview with Ben Orlin, author of the book ‘Math with Bad Drawings,’ as well as the blog of the same name. The blog can be found at www.mathwithbaddrawings.com. —- This episode is sponsored by · Anchor: The easiest way to make a podcast.…

32X: Black Hole Heist (Comedy Sketch)

The hosts of Breaking Math had too much time on their hands. —- Support this podcast: https://anchor.fm/breakingmathpodcast/support

32: Gaze into the Abyss (Part Three; Black Holes)

A lot of the information in this episode of Breaking Math depends on episodes 30 and 31 entitled “The Abyss” and “Into the Abyss” respectively. If you have not listened to those episodes, then we’d highly recommend going back and listening to those. We’re…

31: Into the Abyss (Part Two; Black Holes)

Black holes are objects that seem exotic to us because they have properties that boggle our comparatively mild-mannered minds. These are objects that light cannot escape from, yet glow with the energy they have captured until they evaporate out all of…

30: The Abyss (Part One; Black Holes)

The idea of something that is inescapable, at first glance, seems to violate our sense of freedom. This sense of freedom, for many, seems so intrinsic to our way of seeing the universe that it seems as though such an idea would only beget horror in the…

29: War

In the United States, the fourth of July is celebrated as a national holiday, where the focus of that holiday is the war that had the end effect of ending England’s colonial influence over the American colonies. To that end, we are here to talk about war,…

28: Bell’s Infamous Theorem (Bell’s Theorem)

The history of physics as a natural science is filled with examples of when an experiment will demonstrate something or another, but what is often forgotten is the fact that the experiment had to be thought up in the first place by someone who was aware…

Back Next Tuesday!

Hello. This is Jonathan Baca from Breaking Math here with a quick message. We will be back Tuesday June 19th with an episode on Bell’s inequality, which is an important and meaningful problem in quantum physics that confirms some strange and unintuitive…

27: Peer Pressure (Cellular Automata)

The fabric of the natural world is an issue of no small contention: philosophers and truth-seekers universally debate about and study the nature of reality, and exist as long as there are observers in that reality. One topic that has grown from a…

26: Infinity Shades of Grey (Paradox)

A paradox is characterized either by a logical problem that does not have a single dominant expert solution, or by a set of logical steps that seem to lead somehow from sanity to insanity. This happens when a problem is either ill-defined, or challenges…

25: Pandemic Panic (Epidemiology)

The spectre of disease causes untold mayhem, anguish, and desolation. The extent to which this spectre has yielded its power, however, has been massively curtailed in the past century. To understand how this has been accomplished, we must understand the…

24: Language and Entropy (Information Theory in Language)

Information theory was founded in 1948 by Claude Shannon, and is a way of both qualitatively and quantitatively describing the limits and processes involved in communication. Roughly speaking, when two entities communicate, they have a message, a medium,…

Stay Tuned for Season 2!

Jonathan and Gabriel discuss what you have to expect with Breaking Math’s second season! —- 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

23: Don’t Touch My Circles! (Geometry)

In the study of mathematics, there are many abstractions that we deal with. For example, we deal with the notion of a real number with infinitesimal granularity and infinite range, even though we have no evidence for this existing in nature besides the…

22: Incomplet (Gödel, Escher, Bach: an Eternal Golden Braid: Chapter IV Discussion)

Gödel, Escher, Bach is a book about everything from formal logic to the intricacies underlying the mechanisms of reasoning. For that reason, we’ve decided to make a tribute episode; specifically, about episode IV. There is a Sanskrit word “maya” which…

21: Einstein’s Biggest Idea (General Relativity)

Some see the world of thought divided into two types of ideas: evolutionary and revolutionary ideas. However, the truth can be more nuanced than that; evolutionary ideas can spur revolutions, and revolutionary ideas may be necessary to create incremental…

20: Rational (Ratios)

From MC²’s statement of mass energy equivalence and Newton’s theory of gravitation to the sex ratio of bees and the golden ratio, our world is characterized by the ratios which can be found within it. In nature as well as in mathematics, there are some…

19: Tune of the Hickory Stick (Beginning to Intermediate Math Education)

The art of mathematics has proven, over the millennia, to be a practical as well as beautiful pursuit. This has required us to use results from math in our daily lives, and there’s one thing that has always been true of humanity: we like to do things as…

18: Frequency (Fourier and Related Analyses)

Duration and proximity are, as demonstrated by Fourier and later Einstein and Heisenberg, very closely related properties. These properties are related by a fundamental concept: frequency. A high frequency describes something which changes many times in a…

17: Navier Stoked (Vector Calculus and Navier-Stokes Equations)

From our first breath of the day to brushing our teeth to washing our faces to our first sip of coffee, and even in the waters of the rivers we have built cities upon since antiquity, we find ourselves surrounded by fluids. Fluids, in this context, mean…

BFNB2: Thought for Food (Discussion about Learning)

Sponsored by www.brilliant.org/breakingmath, where you can take courses in calculus, computer science, chemistry, and other STEM subjects. All online; all at your own pace; and accessible anywhere with an internet connection, including your smartphone or…

BFNB1: Food for Thought (Discussion about Learning)

This is the first group podcast for the podcasting network ___forNon___ (pronounced “Blank for Non-Blank”), a podcasting network which strives to present expert-level subject matter to non-experts in a way which is simultaneously engaging, interesting,…

A Special Message

Hello. This is Jonathan from Breaking Math to bring you a special message. Gabriel, my co-host, has recently had a child. The child is healthy, but both children and Breaking Math take time, and we’re still figuring out how to make use of said time most…

Minisode 0.6: Four Problems

Jonathan and Gabriel discuss four challenging problems. —- 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

15: Consciousness

What does it mean to be a good person? What does it mean to make a mistake? These are questions which we are not going to attempt to answer, but they are essential to the topic of study of today’s episode: consciousness. Conscious is the nebulous thing…

Minisode 0.5: ___forNon___

Jonathan and Gabriel discuss ___forNon___ (blank for non-blank); a podcasting collective they’ve recently joined. Check out more at blankfornonblank.com. —- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app…

14: Artificial Thought (Neural Networks)

Go to www.brilliant.org/breakingmathpodcast to learn neural networks, everyday physics, computer science fundamentals, the joy of problem solving, and many related topics in science, technology, engineering, and math. Mathematics takes inspiration from…

13: Math and Prison Riots (Interview with Frank Salas)

Frank Salas is an statistical exception, but far from an irreplicable result. Busted on the streets of Albuquerque for selling crack cocaine at 17, an age where many of us are busy honing the skills that we’ve chosen to master, and promply incarcerated in…

12: Math Factory (Algorithms)

In a universe where everything is representable by information, what does it mean to interact with that world? When you follow a series of steps to accomplish a goal, what you’re doing is taking part in a mathematical tradition as old as math itself:…

11: A Culture of Hacking (Hacker Culture)

The culture of mathematics is a strange topic. It is almost as important to the history of mathematics as the theorems that have come from it, yet it is rarely commented upon, and it is almost never taught in schools. One form of mathematical inquiry that…

10: Cryptomath (Cryptography)

Language and communication is a huge part of what it means to be a person, and a large part of this importance is the ability to direct the flow of that information; this is a practice known as cryptography. There are as many ways to encrypt data as there…

9: Humanity 2.0 (Transhumanism)

Humanity, since its inception, has been nebulously defined. Every technological advancement has changed what it means to be a person, and every person has changed what it means to advance. In this same vein, there is a concept called “transhumanism”,…

Minisode 0.4: Comin’ Up Next

Jonathan and Gabriel talk about the next four episodes coming down the pike, including Humanity 2.0, which debuts Tuesday, April 2nd 2017. —- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this…

Minisode 0.3: Lights, Camera, Action!

Jonathan and Gabriel discuss their recent news debut! You can find what they’re talking about at news.unm.edu —- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast:…

8: Evolution and Engineering (Genetic Algorithms)

Computation is a nascent science, and as such, looks towards the other sciences for inspiration. Whether it be physics, as in simulated annealing, or, as now is popular, biology, as in neural networks, computer science has shown repeatedly that it can…

Minisode 0.2: What’s Up, Bangalore?

Jonathan and Gabriel discuss everything Bangalore, evolutionary algorithmic, and more! —- 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

7: QED? Prove it. (Proofs)

Proofs are sometimes seen as an exercise in tedium, other times as a pure form of beauty, and often as both. But from time immemorial, people have been using mathematics to demonstrate new theorems, and advance the state of the art of mathematics.…

Minisode 0.1: Hypercubes and Other Stranger Things

We are proud to announce that we have recorded our very first minisode! In addition, we are introducing a new blog which can be found at www.breakingmathpodcast.com/blog.html —- This episode is sponsored by · Anchor: The easiest way to make a podcast.…

6: Word (Linguistics)

Mathematics has a lot in common with language. Both have been used since the dawn of time to shape and define our world, both have sets of rules which one must master before bending, both are natural consequences of the way humans are raised, and both are…

5: Language of the Universe (Relationship Between Physics and Math)

1948. A flash, followed by an explosion. Made possible by months of mathematical computation, the splitting of the atom was hailed as a triumph of both science and mathematics. Mathematics is seen by many as a way of quantifying experiments. But is that…

4: Digital Evolution (Digital Computing)

We live in an era of unprecedented change, and the tip of the spear of this era of change is currently the digital revolution. In fact, in the last decade we’ve gone from an analog to a digitally dominated society, and the amount of information has…

3: TMI (Information Theory)

“ABABABABABABABAB”. How much information was that? You may say “sixteen letters worth”, but is that the true answer? You could describe what you just read as “AB 8 times”, and save a bunch of characters, and yet have the same information. But what is…

2: Wreaking Chaos (Chaos Theory)

The void has always intrigued mankind; the concept of no concept defies the laws of human reasoning to such a degree that we have no choice but to pursue it. But ancient Assyrian, Norse, Judeo-Christian creation stories, and even our own scientific…

1: Forbidden Formulas (Elitism in Math)

From Pythagoras to Einstein, from the banks of the Nile to the streamlined curves of the Large Hadron Collider, math has shown itself again and again to be fundamental to the way that humans interact with the world. Then why is math such a pain for so…