algebraic-dumbass

[algebraic-dumbass]

Alright so them's polls are done so i thought i might share some thoughts

nobody is bald

i have no clue how these polls ended up on people who don't do math dashboards'

I know this is like an internet thing but I still have no clue why category theory and related things are overrepresented on the internet. there are definitely NOT 2x more category theorists than probability theorists or PDE people in real life. the easy explanation for this phenomenon is that someone who does category theory probably does not go outside much but it feels too easy of an explanation, I'd be interested if someone looks into this

same for Logic, which I have been told, is famously the subfield that makes it ultra hard to get a position

no one does rings and algebras? sad

dear quantum algebra people: what exactly is your subfield. i have no idea

I expected there to be much more algebraic geometers but I guess they're too busy living away from the world in the Pyrénées

(as I kinda expected) LOTS of budding mathematicians (and I mean i think I technically still fall under that umbrella for another year?) good luck on your math adventures yall

i wish i could say more things here but my current background is more in hole-counting rather than data analysis (insert TDA-related joke here), so if anyone has anything to add, that would be a welcome addition

has enough vanilla extract

Alright the last poll was bad, so, here's a better one (please only pick one option)

[algebraic-dumbass]

(thanks for participating. if you did. if you did not then you get no thanks. life is hard)

Alright the last poll was bad, so, here's a better one (please only pick one option)

[algebraic-dumbass]

(continued further)

Alright the last poll was bad, so, here's a better one (please only pick one option)

[algebraic-dumbass]

Alright the last poll was bad, so, here's a better one (please only pick one option)

(continued further)

[algebraic-dumbass]

I mean I get the idea but I don't think I can group people who study BDiff(M) with people who develop (infinity,n)-categories with people who answer questions such as "how many quadrics are in this threefold"

[algebraic-dumbass]

yeah this poll is terrible wish i had ways of making it multiple answers and have each option separately

[algebraic-dumbass]

Alive Internet: people on the Internet are humans

Dead Internet: people on the Internet are bots

Undead Internet: the bots have acquired consciousness

[algebraic-dumbass]

Analytic Bottomology by Axe

Out-of-character classes by Molnir and Stashgee

Outroduction to Epsilon-categories by Markus Sea

Lower Algebra and Lower Bottomoi Practice by Esau Lurie

Math textbooks in an alternate universe

Fake and simple analysis aka “small nicin”

Wonky algebra done wrong by Sheldon sledghammler

Opposite category theory out of context

The green book of uniformity and well meaning yet disorganized action by David dadstan

[algebraic-dumbass]

prev tags:

#One of my closest grad school friends turns out to have had one of their math posts go tumblr-viral#And I still feel an odd bit of pride about it? Like hell yeah one of my IRL friends is MATHBLR FAMOUS#And basically no one at our school outside our circle of friends even knows

some irl friends know I'm me, and once, one of my friends had one of their friends share one of my posts. i feel so powerful

me at the mathed conference

[algebraic-dumbass]

are you at maa fest? or a different thing?

different thing

[algebraic-dumbass]

me at the mathed conference

[algebraic-dumbass]

i absolutely love how people summarize their research. "we tried computing that. it's hard." "we tried adapting this very easy and well-known result to another setting. turns out it fails except when p = 2, then it's true".

[algebraic-dumbass]

i love how my plans for the future are currently "do math and try to get a position in a relatively shitty academic job market then get replaced by an AI and then fucking die"

[algebraic-dumbass]

400 posts yall

thanks to everyone for enabling my bad jokes <3

[algebraic-dumbass]

Actually I do wonder. I've heard of lattice people say they come up everywhere and it's a shame they're not more known. But to be frank I haven't seen any cool theorems involving them. You say they are as ubiquitous as groups, and I am enclined to believe that, but I know groups are convenient because they have enough structure to be quite practical to study (if I have a finite group acting on something, I immediately know about a lot of results. If I have a Lie group, I can apply Lie theory, etc etc). For lattices, my knowledge is lacking. What are some cool things the language of lattices gives you?

To be honest with you, I'm not really sure what the language of lattices affords us outside of some niche things like Stone duality. I just note that they show up a lot.

In any category we can consider automorphism groups of its objects, and group actions are just homomorphisms to some automorphism group. I think this is the *why* for the abundance of groups in mathematics.

Similarly, for any suitably nice category, we can construct a lattice of subobjects for any one of its objects. Basically, any category of mathematical structures produces a steady supply of lattices just as abundantly as it produces groups.

So why then are groups the premier thing in mathematics, but lattices are an afterthought? Is it that lattices simply are not rich enough to build an insightful general theory paralleling that of groups? Or is it just that we haven't yet found the motivation to do that as a community?

Part of me suspects that the growth of lattice theory may have been stunted by the phenomenon that lattices tend to arise in nature with a concrete representation already chosen. We could develop all of topology for lattices, but it's convenient to see topological spaces as set-theoretic objects so why change now? We could develop all of measure theory on top of complete Boolean algebras, but it's convenient to have \Sigma-algebras be sets of sets, so why change now? Etc.

[algebraic-dumbass]

Well, then I think that lattices are less studied than groups kind of like how monoids are less studied than groups. We also have an abundance of monoids in mathematics, by taking End(X) for X an object of a category, or even by just forgetting the additive structure of a ring - yet I rarely hear about monoids in pure mathematics, outside of when they get group-completed

Actually I do wonder. I've heard of lattice people say they come up everywhere and it's a shame they're not more known. But to be frank I haven't seen any cool theorems involving them. You say they are as ubiquitous as groups, and I am enclined to believe that, but I know groups are convenient because they have enough structure to be quite practical to study (if I have a finite group acting on something, I immediately know about a lot of results. If I have a Lie group, I can apply Lie theory, etc etc). For lattices, my knowledge is lacking. What are some cool things the language of lattices gives you?

To be honest with you, I'm not really sure what the language of lattices affords us outside of some niche things like Stone duality. I just note that they show up a lot.

In any category we can consider automorphism groups of its objects, and group actions are just homomorphisms to some automorphism group. I think this is the *why* for the abundance of groups in mathematics.

Similarly, for any suitably nice category, we can construct a lattice of subobjects for any one of its objects. Basically, any category of mathematical structures produces a steady supply of lattices just as abundantly as it produces groups.

So why then are groups the premier thing in mathematics, but lattices are an afterthought? Is it that lattices simply are not rich enough to build an insightful general theory paralleling that of groups? Or is it just that we haven't yet found the motivation to do that as a community?

Part of me suspects that the growth of lattice theory may have been stunted by the phenomenon that lattices tend to arise in nature with a concrete representation already chosen. We could develop all of topology for lattices, but it's convenient to see topological spaces as set-theoretic objects so why change now? We could develop all of measure theory on top of complete Boolean algebras, but it's convenient to have \Sigma-algebras be sets of sets, so why change now? Etc.