Breaking Math Podcast

P1: Peano Addition

September 29, 2019 03:54 - 37 minutes - 51.3 MB

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 podcast: https://anchor.fm/breakingmathpodcast/support

42: Maybe? (Probability and Statistics)

August 15, 2019 04:24 - 32 minutes - 45.1 MB

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 is statistics? What is Bayes' theorem? And what are the differences between the frequentist and B...

SR1: Forty Intros (Catalogue)

August 04, 2019 20:40 - 33 minutes - 45.6 MB

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: https://anchor.fm/breakingmathpodcast/support

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

July 29, 2019 20:47 - 54 minutes - 75.3 MB

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 of money with a negative sum. Similarly, students of mathematics often are puzzled by the idea of complex numbers, saying that it makes no sense to be able to take the square root of something negative, and only realizing later that these ca...

40: Save the Date (Calendrical Math)

July 07, 2019 22:37 - 31 minutes - 42.7 MB

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 the seasons of the year, as arcane as the Roman Republican calendar, or as accurate as atomic clocks. So what are the origins of calendars? What is intercalation? And when is Easter? --- This episode is sponsored by · Anchor: The easiest ...

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

May 29, 2019 00:30 - 33 minutes - 45.5 MB

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 metaphorical equivalents, in that language is known as their syntax. There is a way to describe certain syntaxes mathematically through what are known as formal grammars. So how is a grammar defined mathematically? What model of language is often us...

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

April 23, 2019 02:32 - 32 minutes - 44.8 MB

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 problem-solving that is used in game theory. So what is strict dominance? How can it help us solve some games? And why are The Obnoxious Seven wanted by the police? Patreon Become a monthly supporter at patreon.com/breakingmath

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

February 25, 2019 19:48 - 39 minutes - 54.1 MB

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 episode. The key is at the end of the episode. What is game theory? Why did we parody the Saw franchise? And what twisted lessons will you learn? -See our New Youtube Show "Turing Rabbit Holes Podcast" at youtube.com/TuringRabbitHolesPodcast....

Stay Tuned for Season 3

January 26, 2019 18:26 - 18 minutes - 24.8 MB

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: a Podcast about Speech and Debate" by Santa Fe Trail Media (our parent organization), which is featured here on Breaking Math. --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support ...

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

November 23, 2018 05:44 - 46 minutes - 64 MB

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 t...

35: Please Be Discrete (Discrete Math)

November 05, 2018 06:00 - 34 minutes - 47.5 MB

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 numbers. Things started to change in the 19th century with some breakthroughs in decrypting intelligence through examining the frequency of letters. In the fervor that followed to increase the security of existing avenues of communication, an...

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

October 20, 2018 20:50 - 39 minutes - 53.9 MB

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 podcast: https://anchor.fm/breakingmathpodcast/support

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

October 03, 2018 20:22 - 40 minutes - 55.8 MB

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

32X: Black Hole Heist (Comedy Sketch)

September 23, 2018 19:27 - 12 minutes - 16.6 MB

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)

September 23, 2018 19:16 - 1 hour - 107 MB

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 choosing to present this information this way because otherwise we'd waste most of your time re-explaining concepts we've already covered. Black holes are so bizarre when we measured against the yardstick of the mundanity of our day to day...

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

August 23, 2018 00:15 - 56 minutes - 78 MB

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 their mass. They thus have temperature, but Einstein's general theory of relativity predicts a paradoxically smooth form. And perhaps most mind-boggling of all, it seems at first glance that they have the ability to erase information. So what i...

30: The Abyss (Part One; Black Holes)

August 02, 2018 22:13 - 51 minutes - 70.3 MB

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 human mind. And black holes, being objects from which not even light can escape, for many do beget that same existential horror. But these objects are not exotic: they form regularly in our universe, and their role in the intricate web of exis...

29: War

July 14, 2018 01:34 - 34 minutes - 46.9 MB

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, and how it has been influenced by mathematics and mathematicians. The brutality of war and the ingenuity of war seem to stand at stark odds to one another, as one begets temporary chaos and the other represents lasting accomplishment in the...

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

June 19, 2018 22:46 - 34 minutes - 47.1 MB

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 of more than one plausible value for a property of the universe, and realized that there was a way to word a question in such a way that the universe could understand. Such a property was debated during the quantum revolution, and involved Ei...

Back Next Tuesday!

June 12, 2018 02:57 - 2 minutes - 3 MB

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 properties of entanglement. So how do particles speak to each other from far away? What do we mean when we say we observe something? And how is a pair of gloves like and unlike a pair of walkie talkies? Stay tuned! --- This episode is spons...

27: Peer Pressure (Cellular Automata)

May 14, 2018 18:10 - 51 minutes - 71.2 MB

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 curiosity to a branch of mathematics within the last century is the topic of cellular automata. Cellular automata are named as such for the simple reason that they involve discrete cells (which hold a (usually finite and countable) range of values) ...

26: Infinity Shades of Grey (Paradox)

April 26, 2018 20:19 - 48 minutes - 66.5 MB

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 the status quo. The thing that all paradoxes, however, have in common is that they increase our understanding of the phenomena which bore them. So what are some examples of paradox? How does one go about resolving it? And what have we learned...

25: Pandemic Panic (Epidemiology)

April 13, 2018 17:06 - 44 minutes - 61.2 MB

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 science and mathematics of epidemiology. Epidemiology is the field of study related to how disease unfolds in a population. So how has epidemiology improved our lives? What have we learned from it? And what can we do to learn more from it?

24: Language and Entropy (Information Theory in Language)

March 07, 2018 06:27 - 44 minutes - 61.2 MB

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, confusion, encoding, and decoding; and when two entities communicate, they transfer information between them. The amount of information that is possible to be transmitted can be increased or decreased by manipulating any of the aforementione...

Stay Tuned for Season 2!

February 25, 2018 20:31 - 2 minutes - 3.19 MB

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)

January 15, 2018 17:55 - 52 minutes - 72.3 MB

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 generally noted demi-rules 'smaller things keep getting discovered' and 'larger things keep getting discovered'. In a similar fashion, we define things like circles, squares, lines, planes, and so on. Many of the concepts that were just mentio...

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

December 23, 2017 23:43 - 56 minutes - 77.6 MB

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 describes the difference between a symbol and that which it symbolizes. This episode is going to be all about the math of maya. So what is a string? How are formal systems useful? And why do we study them with such vigor? --- This episode is...

21: Einstein's Biggest Idea (General Relativity)

December 04, 2017 22:53 - 40 minutes - 55.4 MB

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 advancements. General relativity is an idea that was evolutionary mathematically, revolutionary physically, and necessary for our modern understanding of the cosmos. Devised in its full form first by Einstein, and later proven correct by exp...

20: Rational (Ratios)

November 18, 2017 04:52 - 40 minutes - 55.4 MB

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 quantities which equal one another: every action has its equal and opposite reaction, buoyancy is characterized by the displaced water being equal to the weight of that which has displaced it, and so on. These are characterized by a qualitativ...

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

November 07, 2017 03:39 - 39 minutes - 54.7 MB

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 easily as possible. Therefore, some very peculiar and interesting mental connections have been developed for the proliferation of this sort of paramathematical skill. What we're talking about when we say "mental connections" is the cerebral ...

18: Frequency (Fourier and Related Analyses)

October 11, 2017 19:58 - 44 minutes - 60.5 MB

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 short amount of space or time, and a lower frequency describes something which changes few times in the same time. It is even true that, in a sense, you can ‘rotate’ space into time. So what have we learned from frequencies? How have they b...

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

October 05, 2017 02:02 - 1 hour - 83 MB

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 anything that can take the shape of its container. Physically, that means anything that has molecules that can move past one another, but mathematics has, as always, a slightly different view. This view is seen by some as more nuanced, others ...

BFNB2: Thought for Food (Discussion about Learning)

September 19, 2017 03:57 - 1 hour - 98.7 MB

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 tablet! Start learning today! Check out: https://blankfornonblank.podiant.co/e/357f09da787bac/ What you're about to hear is part two of an episode recorded by the podcasting network ___forNon___ (Blank for Non-Blank), of which Breakin...

BFNB1: Food for Thought (Discussion about Learning)

September 16, 2017 02:31 - 35 minutes - 49.2 MB

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, and simple. The episode today delves into the problem of learning. We hope you enjoy this episode. --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm...

A Special Message

September 02, 2017 23:47 - 2 minutes - 3.87 MB

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 efficiently. So I'm here to tell you what you can expect in the mean time. In the mean time, you can expect some minisodes from us. These will be covering a variety of topics, hopefully including the millennium problems. You can also expect ...

Minisode 0.6: Four Problems

August 18, 2017 20:00 - 26 minutes - 35.7 MB

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

July 30, 2017 03:50 - 1 hour - 82.9 MB

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 that lends a certain air of importance to experience, but as we’ve seen from 500 centuries of fascination with this topic, it is difficult to describe in languages which we’re used to. But with the advent of neuroscience and psychology, we see...

Minisode 0.5: _forNon_

July 20, 2017 04:25 - 14 minutes - 20.1 MB

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

14: Artificial Thought (Neural Networks)

July 11, 2017 00:05 - 1 hour - 89.7 MB

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 all forms with which life interacts. Perhaps that is why, recently, mathematics has taken inspiration from that which itself perceives the world around it; the brain itself. What we’re talking about are neural networks. Neural networks have ...

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

June 27, 2017 01:45 - 49 minutes - 67.3 MB

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 one of the myriad concrete boxes that comprise the United States penal system. There, he struggled, as most would in his position, to better himself spiritually or ethically, once even participating in a prison riot. After two stints in sol...

12: Math Factory (Algorithms)

June 13, 2017 00:28 - 53 minutes - 73 MB

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: algorithms. From time immemorial, we've accelerated the growth of this means of transformation, and whether we're modeling neurons, recognizing faces, designing trusses on a bridge, or coloring a map, we're involving ourselves heavily in a fantas...

11: A Culture of Hacking (Hacker Culture)

May 31, 2017 02:17 - 1 hour - 85.7 MB

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 has cropped up in the last two centuries has been the algorithm. While not exclusive to this time period, it has achieved a renaissance, and with the algorithm has come what has come to be known as "hacker culture". From Lord Byron to Richar...

10: Cryptomath (Cryptography)

May 16, 2017 05:02 - 1 hour - 105 MB

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 are ways to use them, ranging from cryptoquips solvable by children in an afternoon to four kilobit RSA taking eons of time. So why are there so many forms of encryption? What can they be used for? And what are the differences in their metho...

9: Humanity 2.0 (Transhumanism)

May 02, 2017 06:02 - 52 minutes - 71.6 MB

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”, which refers to what it will mean to be a person. This can range from everything from genetic engineering, to artificial intelligence, to technology which is beyond our current physical understanding. So what does it mean to be a person? And is ...

Minisode 0.4: Comin' Up Next

May 01, 2017 02:51 - 16 minutes - 22.4 MB

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 podcast: https://anchor.fm/breakingmathpodcast/support

Minisode 0.3: Lights, Camera, Action!

April 20, 2017 20:31 - 20 minutes - 27.8 MB

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: https://anchor.fm/breakingmathpodcast/support

8: Evolution and Engineering (Genetic Algorithms)

April 18, 2017 06:00 - 57 minutes - 79.2 MB

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 learn great things from other sciences. Genetic algorithms are one such method that is inspired, of course, by biological evolution. So what are genetic algorithms used for? What have they taught us about the natural process of evolution? And h...

Minisode 0.2: What's Up, Bangalore?

April 10, 2017 23:04 - 29 minutes - 39.9 MB

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)

April 04, 2017 07:18 - 44 minutes - 60.5 MB

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. However, it is only relatively recently, within the last 3,000 years, that the art of mathematical proof has been considered essential to the study of mathematics. Mathematicians constantly fight over what constitutes a proof, and even what makes a...

Minisode 0.1: Hypercubes and Other Stranger Things

April 01, 2017 22:53 - 24 minutes - 33.7 MB

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

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