Breaking Math Podcast

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...

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...

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 Obnox...

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? -...

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...

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 letter...

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

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

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

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...

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-bogg...

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...

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 o...

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 unive...

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...

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...

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 epidemiolog...

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 p...

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 th...

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?...

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 understa...

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...

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 par...

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 se...

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 mathemat...