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my list of recommendations

in each section they are loosely ordered by how much i like them, with my favourite first, but they are all incredibly good!

format:

name with link (release year); description; total runtime/playtime; authors

↓↓↓↓↓↓

#rec list #recs #recommendations #tv series #films #audiodramas #podcasts #books #musicals #concept albums #videogames #tabletop #board games #games #board game geek

groupoids

so-called "free thinkers" when they're left adjoint to a forgetful thinker (me)

mossquitoman

Yeah girth... shortest cycle... less than g(n-2)/g-2 edges... hah... ill edge you... trees... forests... leaves... n^n-s-1 forests... the trees have n-1 edges..... n^n-2 trees... so many trees... one connected component?? Dont know... dont know anything... euler... I love u euler... n-e+f=2... euler...

abalidoth

Workers of the world, unite!

Co-workers of the world, intersect!

markovchaingang

my lord. the two statues you commissioned are finally complete. yeah, the double-order with the vast and trunkless legs of stone and the shattered visage. i like to think we captured the sneer of cold command pretty well. it's a really thought-provoking piece my lord. very deconstructionist. i'm sure that even a traveller a thousand years from now could take one look at it and instantly recognise it must have come from an artistically enlightened culture

el-hollow-gamer

Quick one today! Tell me something niche or oddly specific about your field of work / study; or a fact that you really like :)

>>You find an old, ragged book, worn by time. Read it? Y/N

Shipmaster's log

Day 1: I have been tasked with a most gruelling job: choosing one (just one!) interesting, or rather fun fact about my field of study. Is it even possible to do such a thing? My first thought was the old classic, "functions are actually just sets", but I had already posted about it a long time ago. I must keep looking.

Day 2: For a moment, I thought I had it. Lebesgue's measure! How could I not think of it sooner! It's interesting, expands on commonly known concepts, and is intuitive enough to be grasped by anyone, as long as the right explanation is given. But wait, how was I going to be able to explain it in such a small space? It needs room to breathe, it needs formulas to be understood. It's no use. I must look further.

Day 3: I have been betrayed. After desperately looking for answers I finally gave in and asked someone else, someone I trusted, someone I cared about: "Excuse me, good friend, what would you say is a niche or oddly specific fact about our field of study?" Only disappointment followed. "idk bro just talk about the axiom of choice". I must not fall into their trap. There has to be something else I can explain. There has to be something else. I must look deeper.

Day 4: I have found it. The topologist's sine curve. It was so easy! "Hey, did you know that the connection of a topological space is not the same as its path connection? You see, if you take the image of the open set (0,1) through the function sin(1/x) and then..." Wait. Wait, no, wait. I failed to consider a key element. What is connection? What is a topological space? What is an open set? I have been such a fool. This is not oddly specific, this is just specific. This is not a fun fact. Is it even a fact? How can the readers be sure if no proof is given? There has to be something else. I need to find something else. I must find it. Deeper.

Day 5: It's tempting me again. It whispers to me in my sleep. That damn axiom. I must not fall. I must resist. It's not even that interesting! It's just useful. Conveniently useful. It can help you a lot when in dire need... No. I must not. I will not talk about the axiom of choice.

Day 6: The Gulliver distribution. Fundamental group of dick and balls. Did you know Euler did a theorem? The monster group. Entire function plus bounded implies constant. Did you know Euler did a formula? Every maximal ideal is also prime. Transfinite induction. Did you know you can apply Cauchy's formula to prove Cauchy's theorem? Deeper. Further. More.

Day 7: I give up. I can't do this. There has to be another way. I'll find something else. This is my oath. I will not write anything else until I find a better idea. This is my last stand. I will not fall.

>>The rest of the pages are blank.

nos acabamos de quedar sin César

#julio cesar #julius caesar #idus de marzo #ides of march #idesposting #nos acabamos de quedar sin cena

art-who-is-dead

i made a shitty comic for pi day >:3

mathematicians naming stuff: more like comedians

Maybe you are familiar with the hairy ball theorem, the law of the unconscious statistician (LOTUS) or the sandwich theorem (not to be confused with the ham sandwich theorem). Perhaps you are even familiar with the symplectic camel. If you were not, now you are. Welcome to mathematicians' humour.

There are many kind of numbers: abundant, amicable, cake, deficient, evil, fortunate, happy, lucky, narcissistic, odious, powerful, practical, sociable, undulating, untouchable, vampire, weird and more. Also prime numbers can be sexy.

In algebra there are rings, which are not jewelry, but structures. And a ring without identity (i) is a rng. Politically, there are also radical ideals. Of course, algebra also studies algebras. And yes, there are Tits groups, Cox rings and even a Cox–Zucker machine.

And guess what? Topology studies topologies of spaces, not to be confused with toposes or topoi (plural of topos). These spaces might be sober if "every point we see is really there and we never see double". If you are kinky, there are knots, braids and even suspensions! And if you are hungry you can curry a function.

Unfortunately, there are also many disasters. There is the sausage catastrophe, the blue sky catastrophe and the curse of dimensionality. There is even a monster with a baby monster and their whole happy family. This is also related to the monstrous moonshine and the no-ghost theorem.

But the funniest area by far is Category Theory, where a coconut is just a nut. Moreover, a 2-category is just a monoidal monoidoidoid and monads are just monoids in the category of endofunctors. There is also a peculiar agricultural terminology with fiber bundles, sheaves, stalks and germs. But beware! Sheaves can be perverse and skeletons are evil!

There are plenty of diagrams named after their shape. There are forks and horns, and in a Kan complex “all horns have fillers”. There is also whiskering, in case you want your diagram to look like whiskers. Structures can even be walking! There are walking morphisms and walking adjunctions, the same way someone may be a "walking pair of eyebrows".

In graph theory there are trees with leaves and sometimes a root. Several trees form a forest, a rooted tree is also an arborescence and a small tree is a bonsai. But not everything is botany, there are also animals such as octopuses and vertebrates. And if the tail of a vertebrate coincides with its head, then it is called degenerate.

And if you think you don't like mathematics yet, maybe you'll like fuzzy mathematics!

Of course, there are more abstract nonsense names in maths, but those are left as an exercise for the reader. Feel free to add your own contributions! :)

#mathblr #mathematics #maths posting #pi day

ethubbie

so abstract algebra pilled rn that i searched "image of rings" and was shocked when i got this

b0morphism

i keep a list of times this has happened to me:

- spectrum of a ring

- localisation map

- annihilator

- residue

- plane bush (ultra specific type of graph for some reason)

- Kahn complex (okay this one is a typo, i meant Kan)

please add your own :)

#mathblr #almost pi day

the-axiom-of-hope-deactivated20

Mathematics: What do grad students in math do all day? - gist:4158578

“A lot of math grad school is reading books and papers and trying to understand what’s going on. The difficulty is that reading math is not like reading a mystery thriller, and it’s not even like reading a history book or a New York Times article.

The main issue is that, by the time you get to the frontiers of math, the words to describe the concepts don’t really exist yet. Communicating these ideas is a bit like trying to explain a vacuum cleaner to someone who has never seen one, except you’re only allowed to use words that are four letters long or shorter.

What can you say?

“It is a tool that does suck up dust to make what you walk on in a home tidy.”

That’s certainly better than nothing, but it doesn’t tell you everything you might want to know about a vacuum cleaner. Can you use a vacuum cleaner to clean bookshelves? Can you use a vacuum cleaner to clean a cat? Can you use a vacuum cleaner to clean the outdoors?

The authors of the papers and books are trying to communicate what they’ve understood as best they can under these restrictions, and it’s certainly better than nothing, but if you’re going to have to work with vacuum cleaners, you need to know much more.

Fortunately, math has an incredibly powerful tool that helps bridge the gap. Namely, when we come up with concepts, we also come up with very explicit symbols and notation, along with logical rules for manipulating them. It’s a bit like being handed the technical specifications and diagrams for building a vacuum cleaner out of parts.

The upside is that now you (in theory) can know 100% unambiguously what a vacuum cleaner can or cannot do. The downside is that you still have no clue what the pieces are for or why they are arranged the way they are, except for the cryptic sentence, “It is a tool that does suck up dust to make what you walk on in a home tidy.”

OK, so now you’re a grad student, and your advisor gives you an important paper in the field to read: “A Tool that does Suck Dust.” The introduction tells you that “It is a tool that does suck up dust to make what you walk on in a home tidy,” and a bunch of other reasonable but vague things. The bulk of the paper is technical diagrams and descriptions of a vacuum cleaner. Then there are some references: “How to use air flow to suck up dust.” “How to use many a coil of wire to make a fan spin very fast.” “What you get from the hole in the wall that has wire in it.”

So, what do you do? Technically, you sit at your desk and think. But it’s not that simple. First, you’re like, lol, that title almost sounds like it could be sexual innuendo. Then you read the introduction, which pleasantly tells you what things are generally about, but is completely vague about the important details.

Then you get to the technical diagrams and are totally confused, but you work through them piece by piece. You redo many of the calculations on your own just to double check that you’ve really understood what’s going on. Sometimes, the calculations that you redo come up with something stupid, and then you have to figure out what you’ve understood incorrectly, and then reread that part of the technical manual to figure things out. Except sometimes there was a typo in the paper, so that’s what screwed things up for you.

After a while, things finally click, and you finally understand what a vacuum cleaner is. In fact, you actually know much more: You’ve now become one of the experts on vacuum cleaners, or at least on this particular kind of vacuum cleaner, and you know a good fraction of the details on how it works. You’re feeling pretty proud of yourself, even though you’re still a far shot from your advisor: They understand all sorts of other kinds of vacuum cleaners, even Roombas, and, in addition to their work on vacuum cleaners, they’re also working on a related but completely different project about air conditioning systems.

You are filled with joy that you can finally talk on par with your advisor, at least on this topic, but there is a looming dark cloud on the horizon: You still need to write a thesis.

So, you think about new things that you can do with vacuum cleaners. So, first, you’re like: I can use a vacuum cleaner to clean bookshelves! That’d be super-useful! But then you do a Google Scholar search and it turns out that someone else did that like ten years ago.

OK, your next idea: I can use a vacuum cleaner to clean cats! That’d also be super-useful. But, alas, a bit more searching in the literature reveals that someone tried that, too, but they didn’t get good results. You’re a confident young grad student, so you decide that, armed with some additional techniques that you happen to know, you might fix the problems that the other researcher had and get vacuuming cats to work. You spend several months on it, but, alas, it doesn’t get you any further.

OK, so then, after more thinking and doing some research on extension cords, you think it would be feasible to use a vacuum cleaner to clean the outdoors. You look in the literature, and it turns out that nobody’s ever thought of doing that! You proudly tell this idea to your advisor, but they do some back of the envelope calculations that you don’t really understand and tell you that vacuuming the outdoors is unlikely to be very useful. Something about how a vacuum cleaner is too small to handle the outdoors and that we already know about other tools that are much better equipped for cleaning streets and such.

This goes on for several years, and finally you write a thesis about how if you turn a vacuum cleaner upside-down and submerge the top end in water, you can make bubbles!

Your thesis committee is unsure of how this could ever be useful, but it seems pretty cool and bubbles are pretty, so they think that maybe something useful could come out of it eventually. Maybe.

And, indeed, you are lucky! After a hundred years or so, your idea (along with a bunch of other ideas) leads to the development of aquarium air pumps, an essential tool in the rapidly growing field of research on artificial goldfish habitats. Yay!”

more-mathematics-mor-lam

A combinatorialist: there are bijections all around for those with eyes to see

#mathblr #combinatorics #this is literally what my paper is about #tfg

marigold-22

Analysts will be like “I am trying to make progress on the navier stokes equations because it would have a serious impact on applied math and physics”

And algebraists will be like “hoo hoo hoo, my name is Goblin Wizardman do you like my cubes? I call them the little k-cubes operad, also I hate capitalism and the monarchy.”

more-mathematics-mor-lam

I’m sorry but I still can’t get over the fact that the analyst Jean Leray was captured by Nazis in 1940 and knew it was time to become Goblin Wizardman & this is why the world contains sheaves

unconventiononthelawofthesea

it's generally a good idea to only say things if you know what they mean. this way you can avoid the embarrassment of saying things like "33 deaths per capita" which would mean that everyone died 33 times.

king-of-men

"Average person dies 33 times" factoid actualy just statistical error. Average person dies once. Cowardly Georg, who lives in fear and dies a thousand deaths, is an outlier adn should not have been counted.

b0morphism

#doctor who #twelfth doctor #peter capaldi #heaven sent

today i learned that the voice actor for Skarrsinger Karmelita in Hollow Knight Silksong, Siobhán Owen, is from Llanfairpwllgwyngyllgogerychwyrndrobwllllantysiliogogogoch

#silksong #karmelita #skarrsinger karmelita #silksong karmelita #Siobhán Owen #Llanfairpwllgwyngyllgogerychwyrndrobwllllantysiliogogogoch

idontwanttoboldlygo

Eve, who is only limited by laws of Nature, is quickly becoming one of my favourite characters in, uhh... *checks notes* mathematics?

idontwanttoboldlygo

Put her in a situation

huiopl064

too good to leave in the tags

algebraic-dumbass

Short exact sequence: 0 -> A -> B -> C -> 0 Very Short exact sequence: 0 -> A -> B -> 0 Way Too Short exact sequence: 0 -> A -> 0 Tiny exact sequence: 0 -> 0 Long exact sequence: ... -> A_{n} -> B_{n} -> C_{n} -> A_{n-1} -> ... Too Long exact sequence: ... -> A_{n} -> B_{n} -> C_{n} -> D_{n} -> E_{n} -> F_{n} -> G_{n} -> H_{n} -> I_{n} -> J_{n} -> K_{n} -> L_{n} -> M_{n} -> N_{n} -> O_{n} -> P_{n} -> Q_{n} -> R_{n} -> S_{n} -> T_{n} -> U_{n} -> V_{n} -> W_{n} -> X_{n} -> Y_{n} -> Z_{n} -> A_{n-1} -> ... Mysterious exact sequence: ... -> ... -> ... -> ... Ominous exact sequence: ... -> ... -> ... -> ... -> ... -> ... -> ... -> ... -> ... -> ... -> ... -> Z -> ... -> ... -> ... -> ... Inexact exact sequence: 0 -> Z -> 0 Exponential exact sequence: 0 -> Z -> C -> C* -> 0 Logarithmic exact sequence: 0 -> 0 -> R^{+*} -> R -> 0 Linear exact sequence: 0 -> A -> A -> 0 -> 0 Uncontroversial exact sequence: 0 -> 0 -> 0 -> 0 -> 0 -> 0 Historically plausible string of events exact sequence: 0 -> Samurai -> Fax Machine -> Abraham Lincoln -> 0

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