/sci/ - Science & Math

>>9839003
What's your background?
Do you know formal logic, set theory, lambda calculus, Curry-Howard?

Here's an excellent text

https://www.cs.kent.ac.uk/people/staff/sjt/TTFP/ttfp.pdf

The guy who bought the HoTT book out of the blue should certainly also start here.

>>9526010
I guess you can frame it like that.

On that note,

>anno 20's
>It was at this point that Wigner, Hund, Heitler, and Weyl entered the picture with their "Gruppenpest": the pest [that is] group theory... The authors of the "Gruppenpest" wrote papers which were incomprehensible to those like me who had not studied group theory, in which they applied these theoretical results to the study of the many electron problem. The practicle consequences appeared to be negligible, but everyone felt that to be in the mainstream one had to learn about it. Yet there were no good texts from which one could learn group theory. It was a frustrating experience, worthy of the name of a pest. I had what I can only describe as a feeling of outrage at the turn which the subject had taken... As soon as this [Slater's] paper became known, it was obvious that a great many other physicists were as disgusted as I had been with the group-theoretical approach to the problem. As I heard later, there were remarks made such as "Slater has slain the 'Gruppenpest'". I believe that no other piece of work I have done was so universally popular.

https://hsm.stackexchange.com/questions/170/how-did-group-theory-enter-quantum-mechanics/173#173

>>9399233
stories of the in-fights for acknowledgement in french academia, with Delinge and the bunch.

Here's a short public bio and discussion, but I'm not sure that's the source where I picked this idea up
http://xahlee.info/math/i/Alexander_Grothendieck_cartier.pdf
There's also a book, but I didn't read it.

>>9399312
I've been using Emma Stone pics on /sci/ since 2009, would be dishonest to discontinue it

>>9323417
It's from the 40's. People tried to capture the notion of natural transformation and for that they had to define functors and for that they had to define categories.
People then discovered adjunctions as a similarly abundant notion (together with the related Kan extension), and then there are some gimmicks like the Yoneda lemma. That's about it, unless you define more structure on the object or the hom-classes themselves.
The n-category theory people today use the web in an extensive fashion, so there you have an abstract subfield.

What you seem to speak about is the battles of the Frenchies in the 60's and 70's. Yes, mathematicans (and also physicists) work in fields and produce content that ultimately, in the very very most cases, don't matter to anyone but themselves, and the hierachy and those games are very ugly. I agree with that.
Especially now, you have a bunch of angry topos theorist in their 60's and 70's who are a bit mad that they never really got recognition for their work and downplay anything that is new but uses their stuff. A few years ago, this happend - you'll like it

http://www.oliviacaramello.com/Unification/InitiativeOfClarificationResults.html

>What's worse is that people actually distinguish between things that are category theory and things that aren't.
not sure what that means