Breaking Math Podcast

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! *See our new math and science youtube show called "Turing Rabbit Holes" at ! The Breaking Math Podcast team has teamed up with Particle Physicist and Science Fiction Author Dr. Alex Alaniz to deliver a show about science and society. Subscribe and never miss an episode! Support this podcast:

Eine durchschnittliche Folge dieses Podcasts dauert 41m. Bisher sind 83 Folge(n) erschienen. Dieser Podcast erscheint jede zweite Woche.

Gesamtlänge aller Episoden: 2 days 8 hours 13 minutes


60: HAMILTON! [But Not the Musical] (Quaternions)

i^2 = j^2 = k^2 = ijk = -1. This deceptively simple formula, discovered by Irish mathematician William Rowan Hamilton in 1843, led to a revolution in the way 19th century mathematicians and scientists thought about vectors and rotation. This formula, which extends the complex numbers, allows us to talk about certain three-dimensional problems with more ease...



59: A Good Source of Fibers (Fiber Bundles)

Mathematics is full of all sorts of objects that can be difficult to comprehend. For example, if we take a slip of paper and glue it to itself, we can get a ring. If we turn it a half turn before gluing it to itself, we get what's called a Möbius strip, which has only one side twice the length of the paper...



58: Bringing Curvy Back (Gaussian Curvature)

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, flowery shapes, and other curved surfaces...


 2021-03-04  45m

P8: Tangent Tango (Morikawa's Recently Solved Problem)

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 for a free month! Learn basically anything there.

The paper featured in this episode can be found at


 2021-02-25  23m

P7: Root for Squares (Irrationality of the Square Root of Two)

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]

Ways to support the show:

-Visit our Sponsors:   theGreatCoursesPlus...


 2021-02-07  17m

57: You Said How Much?! (Measure Theory)

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 on this episode of Breaking Math...


 2021-02-01  33m

P6: How Many Angles in a Circle? (Curvature; Euclidean Geometry)

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

Ways to support the show:

-Visit our Sponsors:   theGreatCoursesPlus...


 2021-01-28  31m

56: More Sheep than You Can Count (Transfinite Cardinal Numbers)

Look at all you phonies out there.
You poseurs.
All of you sheep. Counting 'til infinity. Counting sheep.
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?


 2021-01-24  37m

55: Order in the Court (Transfinite Ordinal Numbers)

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...


 2021-01-14  34m

54: Oodles (Large Numbers)

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...


 2020-12-21  28m