girl who is independent of ZFC :3

cute processing unit | she/her | @yoneda-emma but just the math posts, banner art by @omnisucker on twitter

[hustlerose]

if you ask a hypotheticalgirl if she exists she'll say "ummmm well maybe..."

[yoneda-emma]

Today in "math things that probably should have clicked for me sooner but I'm just happy they clicked": Gram-Schmidt is usually presented as "any finite-dimensional inner product space has an orthonormal basis", which is obviously very neat and useful to know. However, if you think about it, this also means that every single inner product (on a finite-dimensional vector space) is just the regular Euclidean dot product applied to a different basis! Which is, like, even cooler! "How do we formally explain why the Euclidean inner product is the 'correct' choice of a canonical inner product that matches our geometric intuition" is a question that's been stewing in my brain for a while, and now I have another good answer! :D

[yoneda-emma]

Do be careful that "all norms are equivalent" is a weaker statement than "all inner products can be translated into each other by a change of basis" - norms that aren't induced by inner products can still get up to pretty weird stuff and generally be "less similar" to each other, they just induce the same topology! "All inner products are equivalent up to a change of basis" means "the set of normalized vectors for any inner product forms an ellipse", while other norms can still draw rhombuses and rounded squares and other weirder shapes.

[yoneda-emma]

Today in "math things that probably should have clicked for me sooner but I'm just happy they clicked": Gram-Schmidt is usually presented as "any finite-dimensional inner product space has an orthonormal basis", which is obviously very neat and useful to know. However, if you think about it, this also means that every single inner product (on a finite-dimensional vector space) is just the regular Euclidean dot product applied to a different basis! Which is, like, even cooler! "How do we formally explain why the Euclidean inner product is the 'correct' choice of a canonical inner product that matches our geometric intuition" is a question that's been stewing in my brain for a while, and now I have another good answer! :D

[algebraic-dumbass]

Shit man, this algebra war is fucked. I just saw a guy clap his hands together and say "the six functors" or some similar shit, and every chain complex around him got put into a short exact sequence, had their long exact sequence taken out and then got their homology calculated. The camera didn't even go onto him, that's how common shit like this is. My ass is casting lagrange's theorem and degree 2 equations. I think I just heard "power word: operad" two groups over. I gotta get the fuck outta here.

[the-least-undefinable-ordinal]

I love when you read the early implementations of some algorithm and you're like "this makes sense, it seems like a reasonable way to extract truth from the universe". Then you keep reading and it goes "modern implementations represent a significant improvement over the Shit For Brains Method, whose usage is confined to computer scientists cooking eggs on their laptops. This one has the number 9801 as a load bearing part of the algorithm, the guy who came up with it claimed his god gave him the idea."

It really reinforces the theme that reality doesn't care all that much if it makes sense to us.

[garlend]

I like this quote that deals with the same kind of idea

[kfunc-vmlinux-utf8nlookup]

"Quantized angular momentum means a spin is a spin, you can't say it's only a half!" Well, T.J. "Henry" Yoshi,

[onrtrp]

the set of ships is nonempty and finite

(any reasonable notion of) size induces a total order on the set of equivalence classes of ships of the same size

every nonempty finite total order has a maximum

there exists a ship that is no smaller than any other ship

QED

[cohomoillogical]

Region I’m integrating the boundary of is the crust of a pizza. Function gives sauce plus cheese. Poles of function are toppings. Residues are how much I enjoy a given topping. So the residue theorem just says that how much I like the pizza (ie. The value of the integral) is equal to 2pi i times how much i like all the toppings.

Argument principle? Just saying that (for me at least cause I hate pineapple and love pepperoni ) the pizza from f’/f has one pineapple at each topping (pole) of f and one pepperoni at each zero of f.

[krasnoarmeyets-deactivated191907]

one of these days im gonna sit down in the middle of a field and do algebra

[noelements-setempty]

I'm going to get a group of people together to sit in a ring in the middle of a field and do algebra.

[abalidoth]

😈

[cohomoillogical]

[associativeglassdesert]

geometry is when topology gets hard. the harder it is, the more geometry it gets

[associativeglassdesert]

if it's a whole lot of hard, it's analysis

[algebraic-dumbass]

what should cohomosexual mean

heterosexual (right answer)

attracted to everything besides the same gender (wrong answer)

sexually attracted to cohomology theories (other right answer)

Voting ended onDec 6, 2025

[neatlymanifolded]

All wrong – is attractive to people of the same gender

[algebraic-dumbass]

welp poll over everyone we found the answer

[more-mathematics-mor-lam]

Sometimes a vision appears to you in class and you have to draw it

[acid-lich]

Updates

[more-mathematics-mor-lam]

Something is emerging

[velvxret]

there are infinitely many primes (topological proof due to Furstenberg)

[bagnificentmastard]

Profs love naming quantities "eta" or smth - at the bottom left margin of lecture 2's 17th slide and never clarifying it afterwards.

[mathematikerin-freyja]

Sometimes I wish there were a real element of physical skill in mathematics. Like I could be stuck at a proof, and having consulted unsuccessfully with my friends, determine that there is no path forward through mind. In such a state, I would journey out into the wilderness and punch a cave wall until my hand is shaking and broken so that it cracks open and I can peer through that crack for a just a moment, right before the protective cave secretions seal the crack shut, and glimpse the answer to my mathematical problem. It wouldn't be something to do every time I am stuck, as it would be very physically demanding. But it would be nice to have the option. The certain path to fall back upon, reassuring me, in my mathematical journey.

[mathematikerin-freyja]

Yesterday I was minding my own business at the park when a goose landed next to me, resting its head in my lap. I thought it just wanted to understand Hartshorne's book a little better, so I started to read to it. But whenever I said the word "scheme" it just honked at me, and when I said "derived functor" it pecked me and created a dent in my face. So, you know, that was that.