Why does this balloon have -1 holes?

If you are need of urgent mental health support please check for crisis help lines available in your country.

Do check out Jordan Ellenberg's book Shape. This video was inspired by Chapter 2.

Trouser animations thanks to:

CORRECTIONS:
- When talking about the Euler Characteristic of the torus at 16:29 I say the value of zero is "only on our friend the torus" which is technically wrong. In the moment I was just talking about the sphere and the torus but loads of other shapes have an Euler Characteristic of zero. Like the cylinder.
- I'm undecided if the string method of thinking about holes at 17:04 was helpful. I could have talked about the dimension of the boundary manifold, but that felt like I was repeating the previous bit too much and wanted a different way to think about it. Not sure if this counts as a 'correction' per se, but I just needed to talk to someone about it. Thanks for listening.
- Let me know if you spot any other mistakes!

Filming and trouser sewing by Alex Genn-Bash
Editing by Michelle Martin
Graphics by Sam Hartburn
Doughnuts later eaten by Matt Parker
Music by Howard Carter
Design by Simon Wright and Adam Robinson

MATT PARKER: Stand-up Mathematician

[ezgarrth]

"Topology is a very big area of mathematics"
Yeah, but it's continuously deformable into a small area

[johnbeauvais]

“The jam inside this donut is not mathematically relevant” this might be my favorite line ever

[BlankPicketSign]

Captain: "HOW MANY HOLES DO WE HAVE IN OUR AIRSHIP?!"
Me: "Well first let us explore the Euler Characteristics of the..."
Also Me: *Gets thrown off to my death

[Xalies]

I think he's ability to break a bagel perfectly on the line is underrated

[kitludd]

dont apologise for confusing trousers and pants, after all topologically they're the same

[TBA_]

The jokes, the maths, the visual aids - I just love this video as a whole.

[DrTrefor]

This is such a fun intro to the Euler Characteristic! I think it's kinda sad that so often we don't expose students to these accessible ideas from topology until late in an undergrad program, but there is no reason it can't be explored way way earlier.

[firestormdb]

"I have bought the world's supply of toroidal balloons" sounds like the world's daftest supervillain plot

[GiatrasKon]

Man, Swiss cheese must be the bane of topologists' existence

[pyglik]

The worst thing about topology is drawing with markers on doughnuts.

[ahorribleperson]

"Things are gonna get a lot worse"
*Ominously brings out a second balloon*

[mattomanx]

He knew EXACTLY what he was doing bringing in a torus balloon and saying "Things are gonna get a lot worse"
Things always get worse when you start bringing those in

[mr.johnson]

I can't believe he established a temporary monopoly on the distribution of *torus* balloons in order to make being his Patreon supporter more desirable. This is peak economics.

[subnatural]

Topologist jokes before: "Topologists can't tell a doughnut and a mug apart."

Topologist jokes now: "Topologists can't tell jeans and g-strings apart."

[themightymcb]

Whenever the "holes" type questions came up, my first critical thought on the question was immediately to consider that straws and clothing are 3D objects, which immediately complicates things for me in such a way that I'm honestly just out of my depth. This video helped me work out some of the more abstract ideas around topology. Good stuff!

[mokopa]

11:51 Matt apologises to blue balloon for being mean to it about calling its homology class horrible
13:18 Matt continues insulting balloon's homology class right in its face

[DeathlyTired]

If the barrier to entry to a subject is that you've got to be as smart as Poincaré, Riemann, Betti & Noether, I think, at that point, it's acceptable to simplify things a bit.

[frankhooper]

It took me a while to realise that you were using the balloon as a model of a sphere - my first thought was that the balloon was in essence a disc as I was considering that it could be flattened topologically once you untied the place where you blew it up.

[MmKayUltra]

You keep asking about the pair of trousers but never told us the number of belt loops which I feel are important.

[leorussellmoore]

"Now, from personal experience, it's pretty hard to draw on a doughnut. It's a lot easier to draw on a bagel. Although technically, still a doughnut." - think this has to be my absolute favourite Matt quote now. Had to pause the video cause I was laughing too much.