/sci/ - Science & Math » Thread #14374684

183KiB, 742x932, egaenjoyer.jpg

View Same Google iqdb SauceNAO

What does /sci/ think about logic, algebraic geometry?

Anonymous Fri 08 Apr 07:35:57 2022 No.14374684 View Reply Original Report

Quoted By: >>14374689 >>14374807 >>14374817 >>14374820 >>14375633 >>14378133 >>14378177 >>14378337 >>14379043

What does /sci/ think about mathematical logic, set theory, proof theory, model theory, computability theory?

I love mathematics and want to do it on a research level. I am curious to study the most fundamental things and I find mathematics interesting for that reason. But are there any fundamental areas in mathematics?

A mathematician friend of mine told me that general topology can be interesting because it studies space, connectivity, dimensionality, openness, closedness. It seems to me myself that algebra might be one of the most fundamental areas. But I have little experience with group theory.

It frustrates me that people at /sci/ take a negative view of mathematical logic and consider it primitive, autistic.

Apparently algebraic geometry, algebraic/topological k-theory, algebraic topology have the most authority and prestige. I don't know what these fields are about, why they are so popular and prestigious among /sci/?

Anonymous

Anonymous Fri 08 Apr 2022 07:37:00 No.14374689 Report

Quoted By: >>14374694

>>14374684
you sure do seem to like talking about yourself

Anonymous

Anonymous Fri 08 Apr 2022 07:39:41 No.14374694 Report

Quoted By:

>>14374689
Sorry about that

May I ask what you think about mathematical logic and the other areas I mentioned?

I don't know much myself, but I would be happy to get a little explanation

Anonymous

Anonymous Fri 08 Apr 2022 09:11:59 No.14374807 Report

Quoted By:

>>14374684
>What does /sci/ think about mathematical logic, set theory, proof theory, model theory, computability theory?
Don't like them.

>But are there any fundamental areas in mathematics?
Yes.

>to me myself that algebra might be one of the most fundamental areas
Obviously "foundations" is the most fundamental field, algebra can get very "high level".

>why they are so popular and prestigious among /sci/?
It's the most autistic area of active research.

Anonymous

Anonymous Fri 08 Apr 2022 09:21:03 No.14374817 Report

Quoted By:

>>14374684
>mathematical logic, set theory, proof theory, model theory, computability theory?
All pretty based. However, be warned that much of the really natural/easy to understand topics have been studied in depth for 100 years and it is hard to do new things without it being autistic weird shit that you cant explain to normies without sounding autistic or like a con artist
> algebraic geometry, algebraic/topological k-theory, algebraic topology
Case in point. These fields originate in relatively down to earth questions which were mostly resolved 100 years ago and now even mainstream type work, be it B-lister or fields medal work, is impossible to sell to an outsider unless you are a con artist

Anonymous

Anonymous Fri 08 Apr 2022 09:22:17 No.14374820 Report

Quoted By: >>14375633

>>14374684
Logic is basically its own discipline, set theory is the most fundamental math there is.
I don't know if you're interested in the actual setting up of mathematical foundations itself (as in constructing the naturals, defining addition, etc) but all of this is pretty novice set theory.
The actual research level stuff has not much to do with foundations.
Research level logic deals with different models of set theory which probably affects foundations but as a whole, modern research isn't too concerned. Also logic is primitive, it's really, really boring imo and all of the things you prove are pretty trivial (at least up till the part I've taken for set theory).
If you're in it for the money you'd be far better equipped in some applied field like apllied probability or CS.

Anonymous

Anonymous Fri 08 Apr 2022 14:29:27 No.14375633 Report

Quoted By:

>>14374820
Largely correct. There also a %ood bit of work in applied model theory relating to number theory and geometry. Sadly though, logic in general gets very little attention or funding today, and it would be hard to study or do research in these fields unless you already have an amazing resume. Combinatorics and optimization are probably the closest area to logic that are highly active at the moment.

>>14374684
Algebraic geometry and algebraic topology and differential geometry are considered very prestigious I guess because (1) theyre very esoteric and take like half a decade of university math study to even begin to understand, (2) most fields medals are awarded in these topics, (3) theyre closely related to very abstract and philosphical topics like the Langlands programs and very complicated topics in mathematical physics like super symmetry and the standard model and string theory and the study of Lie Groups and representations of Lie Groups.

Anonymous

Anonymous Sat 09 Apr 2022 07:08:30 No.14378133 Report

Quoted By: >>14378150

>>14374684
I mean, I find it pretty ironic that mathematical logic, which is supposed to be the most fundamental branch of math that there is, turns out to be largely disconnected from the rest of math. Most mathematicians believe that actual set theory (not the kind of stuff that you learn in grade school, but large cardinals, proofs of independence, forcing, etc.) is irrelevant to their work and the same goes for theorems in logic like Gödel's incompleteness theorem (overhyped).
General topology is for the most part considered irrelevant as far as I am aware. You can cover the important stuff in less than a quarter. The rest seems to be concerned with pathological shit that happens when your topological spaces aren't nice enough, but in practice, people just say "Let X be a Hausdorff space" or "Let X be a topological space that is locally euclidean" and that gets rid of most of the pathologies that you study in general topology. See this: https://math.stackexchange.com/questions/2380944/where-does-a-topology-student-go-after-munkres?rq=1
https://math.stackexchange.com/questions/4040158/relation-between-the-topology-definition-and-the-real-example
https://math.stackexchange.com/questions/3874778/regarding-various-types-of-topology?noredirect=1&lq=1
I do find it a shame that things are that way though. Set theory looks very interesting to me. Model theory actually has several applications to other fields of math, so it is not as disconnected from math like the other branches of logic.

Anonymous

Anonymous Sat 09 Apr 2022 07:24:50 No.14378150 Report

Quoted By:

>>14378133
When it comes to algebraic geometry, I recommend reading at least the first answer, even if you don't understand most of it: https://math.stackexchange.com/questions/255063/why-study-algebraic-geometry
I am quoting a particular part:
"So, mathematicians study algebraic geometry because it is at the core of many subjects, serving as a bridge between seemingly different disciplines: from geometry and topology to complex analysis and number theory"
There is also this quote at the end
"Algebraic geometry seems to have acquired the reputation of being esoteric, exclusive, and very abstract, with adherents who are secretly plotting to take over all the rest of mathematics. In one respect this last point is accurate..." - David Mumford.

I believe that you should try to work on stuff that you find interesting, and I do believe that mathematical logic can be really interesting and I would love to know more about it, I just find it a shame that it seems so disconnected from everything else (though you might not care about that, depending on what you mean by "fundamental"). However, one thing that you should take into account is that logicians are kind of discriminated against, there is little funding and few job posts, so working in academia is harder and you might end up in the CS department doing complexity theory and computability.

Anonymous

Anonymous Sat 09 Apr 2022 07:36:03 No.14378155 Report

Quoted By: >>14379781

>mathematical logic
dead
>set theory
dead
>proof theory
incredibly niche field, it will be difficult to get into it
>model theory
almost dead
>computability theory
in it's most theoretical form, it's incredibly niche, but if you're willing to get a bit more applied, there's a lot of activity with regards to quantum computing
>Apparently algebraic geometry, algebraic/topological k-theory, algebraic topology have the most authority and prestige. I don't know what these fields are about, why they are so popular and prestigious among /sci/?
these are the best fields for larping as a researcher. it's incredibly easy to publish meaningless papers in this field. there's a reason why most "academic" mathematicians at third-rate universities do most of their research in these areas

Anonymous

View Same Google iqdb SauceNAO 1647727692045.jpg, 98KiB, 1073x1003

Anonymous Sat 09 Apr 2022 08:07:25 No.14378177 Report

Quoted By:

>>14374684
Energy can be stored, you have a cell phone after all.

The issue is the capacity and cost involved. When you have big industrial processes or running an office building, at those scales batteries are a hard sell.

The two main energy storage mechanisms are batteries and pumped hydro (pump water up a hill when you have excess electricity and run it though turbines when you need that energy back). Flywheels are a very distant third.

Right now batteries and pumped hydro are no where near viable for storing up a days worth of power to use all night for large industrial use. They are however quite viable for replacing Peaker plants and evening out little blips in supply and demand.

We have viable technology to turn off all carbon fuels for electrical generation if only the environmentalists would stop cock blocking nuclear. Nuclear, Wind, Solar, Hydro with batteries and pumped storage to even things out is completely within our grasp if only we would do it.

Transportation will get there eventually. Electric trains have been around forever, they work well. Cars and Semi trucks will take 20 years or so before we can electrify most new production.

Ocean ships could do it but but the capital costs would be high. Reginal air travel is also doable but long distance flight is still not feasible with electric.

Other industries like steel and cement production would be hard to make carbon neutral.

I still don't think it's an issue. Humans live in fucking Arizona, if your temps go up a degree or two who gives a fuck. Nature seems to like the heat almost everywhere. We have an entire nation that lives under sea level, they have been doing it for 2000 years, regardless I don't care that much about the faggots that live on the coast anyhow.

Anonymous

View Same Google iqdb SauceNAO _r1_640.png, 152KiB, 626x554

Anonymous Sat 09 Apr 2022 08:08:26 No.14378179 Report

Quoted By:

Sorry, wrong thread, too lazy to erase.

Anonymous

Anonymous Sat 09 Apr 2022 09:58:35 No.14378337 Report

Quoted By:

>>14374684
>It frustrates me that people at /sci/ take a negative view of mathematical logic and consider it primitive, autistic.
I found learning mathematical logic to be very useful. The skills generalize to writing.

Anonymous

Anonymous Sat 09 Apr 2022 14:54:49 No.14379043 Report

Quoted By: >>14382011

>>14374684
>set theory
cringe
>proof theory
cringe
>model theory
based
>computability theory
cringe

Anonymous

Anonymous Sat 09 Apr 2022 19:02:44 No.14379781 Report

Quoted By:

>>14378155
t.faggot who never understood schemes.

Anonymous

Anonymous Sun 10 Apr 2022 12:21:06 No.14382011 Report

Quoted By:

>>14379043
model theory is a branch of set theory you retard

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches