The Foundation of Mathematics - Numberphile

Set theorist Asaf Karagila discusses the foundation of mathematics. More links & stuff in full description below ↓↓↓

NUMBERPHILE

Videos by Brady Haran
Animation and editing by Pete McPartlan

[OmateYayami]

You know that the video is really close to abstract base of maths when the paper isn't touched.

[zzzaphod]

After watching that video, we're all set

[kuretaxyz]

best definition ever: "mathematics is a social activity done by mathematicians"

[higgledypiggledycubledy]

This should be on the main channel. Top tier stuff 👍

[VarmDild]

Please make some more videos about the philosophy of mathematics! Formalism, intuitionism, logicism, Gödel's Incompleteness Theorem etc.!

[hamedajab]

Numberphile is one of the phew channels that has been churning quality quantity for over a decade now. Thanks a lot Brady and all the numberphile mathematicians!

[Galinaceo]

i have never thought i'd one day randomly come across a youtube video with Asaf Karagila in it. Big fan.

[Rubrickety]

I may have to start pronouncing it “kaTEEgary” just to level up my charm stat.

[msironen]

Whitehead and Russell didn't get to 1+1=2 until much later in the second volume. They got the preliminary proposition depicted in the video in the first few hundred pages, but they still lack the definition of arithmetic addition at that point.

[erin-rtvn]

your podcast episode with asaf karagila inspired me to take set theory as part of my undergrad degree - very glad i did!

[drhxa]

Simple, I see Asaf Karagila, I hit like

[Skybrg]

While “knowing everything works” is a good enough reason for foundations, I think a more important one is interdisciplinary connections.
For example, what is the connection between Point-Set topology and Locale theory (aka pointless topology)? What can you prove in one and not the other? Maybe there are interesting maps from objects in one field to objects in another. But to do so you have to think about each of these mathematical fields living in one “universe” to do math on.

[klnmn]

Love this guy. Insightful and personable, really concerned with getting ideas across in a human way.

[CorbinSimpson]

Important nuance: Type theory and category theory *extend* set theory. For types: a set is a type with a notion of equality. For categories: category theory is about sets and also functions between sets. Also, thank you for briefly including Metamath.

[katakana]

Finally someone who pronounces catiggory theory right

[riversplitter]

Really appreciate your videos! Math was always a favorite subject of mine, but I never formally studied higher mathematics. I really appreciate the windows you offer into the richness and diversity of the field!

[TranquilSeaOfMath]

This was a great video. It had a topic I'm interested in and a great guest speaker.

[titan]

I like Asaf Karagila. More of him, please!

[JohnDoe-tinp]

Inviting Asaf Karagila to discuss the foundations of mathematics is a great choice! Some minor corrections: 8:13 Voevodsky worked in homotopy theory, not differential geometry. 0:46 Cauchy did not eradicate infinitesimals from calculus; it was really Weierstrass, or arguably Bolzano, who did so.

[johelsen]

13:30
I already love this guy.

And probably everyone else who REALLY knows what they're talking about.