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...
Nov 07, 2017•40 min
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 been ...
Oct 11, 2017•44 min
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 as ...
Oct 05, 2017•1 hr
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 Breaking Math, al...
Sep 19, 2017•1 hr 12 min
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/breaking...
Sep 16, 2017•36 min
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
Aug 18, 2017•26 min
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 seem to...
Jul 30, 2017•1 hr
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
Jul 20, 2017•15 min
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 ...
Jul 11, 2017•1 hr 5 min
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 solitar...
Jun 27, 2017•49 min
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 fantastic...
Jun 13, 2017•53 min
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 Richard S...
May 31, 2017•1 hr 2 min
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 methodol...
May 16, 2017•1 hr 17 min
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 tran...
May 02, 2017•52 min
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
May 01, 2017•16 min
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
Apr 20, 2017•20 min
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 how c...
Apr 18, 2017•58 min
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
Apr 10, 2017•29 min
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 pro...
Apr 04, 2017•44 min
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...
Apr 01, 2017•25 min
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 as omnipresent as they are seemingly intangible. Language has thrived for almost, or as long as humans have possessed the ability to use it. But what can we say that language is? Is it a living breathing organism, a set of rigid ideals, somewhe...
Mar 21, 2017•50 min
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 always the case? There are cases where it seems as though mathematics itself has made predictions about the universe and vice versa. So how are these predictions made? And what can we learn about both physics and math by examining the way in whic...
Mar 07, 2017•48 min
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 recently been increasing exponentially. Or at least it seems like it’s recent; in fact, however, the digital revolution has been going on for hundreds of centuries. From numerals inscribed in“We live in an era of unprecedented change, and the tip of t...
Feb 21, 2017•53 min
“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 information in the context of mathematics? The answer is nothing short of miraculous; information theory has applications in telephony, human language, and even physics. So what is information theory, and what can we learn from it? --- Support this ...
Feb 07, 2017•49 min
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 inquiries have one thing in common: creation from “nothingness”. But is it really nothingness? The ancients used the term “chaos”, and, although to some “chaos” has become synonymous with “bedlam” or “randomness”, it has much more to do with the timel...
Feb 07, 2017•52 min
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 many people? Our answer is simple: math is, and always has been, in one way or another, guarded as an elite skill. We visit the worlds that were shaped by math, the secrets people died for, the false gods created through this noble science, and the...
Feb 07, 2017•59 min
