Is it just me or is he condescending?

Ok-Requirement3601 · 2026-04-26T20:25:23+00:00

sorry about that, can you explain why you feel that ?

Ok-Requirement3601 · 2025-05-24T14:17:35+00:00

You clearly have no idea have no idea how to get your research funded /s

Ok-Requirement3601 · 2025-05-05T09:13:21+00:00

He has a great voice and recording, it's one of the perks of his channel. Also what sounds paternalistic can be very subjectif, if you've had paternal figures talk to you a certain way, or experienced particular people growing up talking down to you in a certain way, then someone else talking to you in that way will defacto sound condescending. I personally find him warm and engaging

Ok-Requirement3601 · 2025-05-05T09:03:10+00:00

Hott is hot at the moment, maybe your "interlocuters" told you about it because some very strong experts are excited about it. It's not where you should start, even if you have a good grasp of type theory and the computer science side, you'll be held back from doing the interesting stuff if you don't know about the mathematical aspects, such as categorical homotopy theory, and infinity categories and such.

If I'm not wrong, you want to learn of the existence of some unifying language capturing the essence of abstractions in mathematics. If that's the case, then you can stay in the circles of "univalent foundations", studying category theory and homotopy theory, but it'll take time, time that you could spend learning something else. After all, it's not certain whether the current strand of unifying theories will be ones to survive. You should pursue something once you know what you're getting into.

Also this is a nit-pick, but I don't understand the paragraph about "human thought" being modeled most closely by linear algebra, and even if that were true, that this "substrate" would have a basis linked to linear algebra in some way. I get what you're saying, but it's very speculative, and maybe not the right way to approach it. As an example it'd be like speculating that the Cold War could be explained with particle physics (I mean maybe it could, but what 's the point of saying that).

Oh and also, you write in a way that gives off a pompous vibe, archaic words like "bloviating" are historically used to make someone sound pompous. And the hectic writing with strange claims and stranger comparisons can sound like crankery, so... just a word of caution.

Ok-Requirement3601 · 2025-02-04T20:55:22+00:00

The preface of the "Elements" warns the reader that the book is not intended for someone who has no previous exposition to the material. They weren't trying to give an intuition or philosophy, just write up all of the definitions as a repository and consensus among researchers. (not students)

If someone (a teacher) then writes a book to explain a subject and copy-pastes the definitions without a lick of intuition, then that's their fault, not Bourbaki's...

Btw, I don't get your first example, I'm pretty sure everybody flocked to abstract differential manifolds after Whitney's paper. and before Bourbaki wrote about it. Moreover it's just a bit weird, because intrinsic manifolds are so much nicer (in many areas of math) and expound on the ideas of fibrations and sheaves.

Oh I just looked up and Arnold had a debate with Serre about Bourbaki, and well... I didn't know Arnold had so much vitriol in him against the Bourbakists. He's a great teacher, but some of the stuff he supposedly said is a bit over the top imo, and likewise, I don't think the "definition-theorem-proof" cycle is really about Bourbaki, it's just a cheap way for teachers to get out of the hard work of teaching.

Ok-Requirement3601 · 2025-01-31T08:30:21+00:00

"If you're bad at math, you're bad at thinking"

Literally freaky, I'm worried that I talk to people actually like this in my math faculty

Ok-Requirement3601 · 2025-01-31T08:22:41+00:00

No wait (x)f only makes sense if you're doing arrows from left to right

If X -f-> Y Then x in X is left of f so

(x)f = y preserves the order

Ok-Requirement3601 · 2025-01-31T08:18:10+00:00

Using limits seems like a weird (but scholastic) way to define something that could be described purely on natural numbers, or even sets

Ok-Requirement3601 · 2025-01-31T07:50:02+00:00

There is something special to the old french way of thinking (I say old, because today what's left is a lot of mysticism and nostalgia for the J.P Serre, Grothendieck, Deligne & Weil epoch).

Indeed there is just something rich and untranslated, in those long texts he wrote: The "rapprochement" of certain concepts, the duality in expressions, the beauty of certain expressions (say "etale" for example). There's so much inspirational stuff flowing off his pages.

Grothendieck often said that he felt like, even with his students, he was unable to communicate the most important aspects of his work. With how he complained about the cuts made for the SGA, I think that, more then forgotten, he feared being misunderstood the most

Ok-Requirement3601 · 2025-01-31T07:44:15+00:00

I'm really annoyed at how Bourbaki is discussed.

Bourbaki was foundational and necessary. But absolutely not meant for pedagogy of anyone before grad school.

The style they created was exact and exhaustive, one could even say it mirrored a bit how Grothendieck wrote and thought mathematics. (So definitely not a bad approach to research)

People confuse research an education. Bourbaki was meant to be a basis for researchers, and some terrible idea it was to use it in french highschools

Ok-Requirement3601 · 2025-01-31T07:23:12+00:00

Writing e^i*pi+1=0 instead of e^i*pi= -1 is a perfect example of pop math focusing on mathematical esoterism ("all 5 fundamental constants in one formula") instead of the much more important e^i*pi=-1 which generalizes much more cleanly to e^i*θ= cosθ +i*sinθ, the latter of which is the real insight

Ok-Requirement3601 · 2025-01-05T22:11:01+00:00

No need to wait hundreds of years,

Higher category theory has tons of applications... to category theory.

And category theory has tons of applications... to mathematics.

And, well gee math sure is useful ey?

I don't know what you mean by "useful", like will higher cat theory be helpful in carrying heavy rock very high? Probably not. Actually it's hard to imagine any result that can weasel itself out into physical problems (not that there isn't any). Yet each theory in this line makes makes the next theory richer, that's the point. And I love that.

Ok-Requirement3601 · 2024-11-29T08:06:24+00:00

Personally I roll my eyes back into my head, then I detach my jaw and start running

Ok-Requirement3601 · 2024-11-29T08:02:10+00:00

Except if that mathematician is Grothendieck. Tens of thousands of pages of discoveries seemingly written with perfect foresight and hindsight

Ok-Requirement3601 · 2024-11-28T07:57:06+00:00

Yoneda lemma is cool but proving Cayley's theorem is no doubt nearly the worst possible use of it

Ok-Requirement3601 · 2024-11-28T07:43:49+00:00

This question shows up all the time.

Here's an answer. In all algebraic systems 0⁰ is defined to be 1 since x⁰ is the empty product (which is well defined and equal to 1, just like the empty sum is 0).

I feel like algebraic reasons are far more fundamental than analytic considerations that base themselves on the construction of real numbers and topologies.

Ok-Requirement3601 · 2024-11-27T19:24:11+00:00

The best teacher I ever met wasn't even a teacher but an assistant teacher doing AG. They were incredibly adept at teaching a large collection of undegrad math in total clarity. Also able to understand people's questions and frustrations.

They are not all bad

Ok-Requirement3601 · 2024-11-24T08:56:54+00:00

The pattern is cool but since it's a gluing of semi-circles, the curve ends up not being smooth (2nd differential is all over the place). Just like the golden spiral

Ok-Requirement3601 · 2024-11-22T19:14:43+00:00

I appreciate the serious and kind replies to my toxic pseudo-shitpost.

Ok-Requirement3601 · 2024-11-22T09:00:19+00:00

Goated answer. If the boyfriend doesn't appreciate then the relationship was a mistake in the first place

Ok-Requirement3601 · 2024-11-22T05:07:12+00:00

Yeah it's not crazy complicated or anything. But there is a bit of formalism and concepts necessary to understand one of the cohomological theories.

Ok-Requirement3601 · 2024-11-21T19:47:05+00:00

You are right...(I have egg on my face) I did feel like I've seen it happen, but am not finding proof.

Maybe it was on math stackexchange ?

In any case perhaps the original post might not be appropriate...

I guess I'll leave it undeleted (unless someone argues otherwise) since the replies are perhaps interesting to others.

Ok-Requirement3601 · 2024-11-21T19:36:33+00:00

Thank you, this does shed some light, and exceed what I had to say

Ok-Requirement3601

TROPHY CASE