Then ponder

A blog about pure mathematics and my learnings of it. Side blog of @humormehorny

[then-ponder]

This post is a link to all the different notations I have for different subjects, I might compose a complete list in time, but for right now this format allows me flexibility and prevents my pinned post from bing so long.

Everything will be in alphabetical order and Type set to the specified field.

Definitions: https://www.tumblr.com/then-ponder/726502395950088192/definitions-used-in-proofs

Logic: https://www.tumblr.com/then-ponder/724689032193425408/logic

Set Notation: https://www.tumblr.com/then-ponder/724021901968752640/set-notation

Common tags

Gender theory - I tag posts with this when they talk about gender in a math-y way.

The Arcane Arts - this is sort of a pet project of mine. More to come later.

Proofs - sort of self explanatory. All of my proofs are tagged with this.

Math Notation - I tag all of the notation notes with this.

Learning to fly - post about me learning maths at the University level

Tex Recs - posts about texts recommendations.

Binary Drift - I am working to find a set of solutions for a star system

Textbook recommendations

[adamtotscomix]

[asidewalksymphony]

[error-code-864g]

I feel like every "math person" has a textbook/textbook author that they absolutely adore. Should any fellow "math people" see this post, tell me what your favorite textbooks are. Bonus points if you include which textbooks you hate and it starts a disagreement with someone else who loves that textbook.

[then-ponder]

I hate Ron’s calculus. I barely like his Precalc/trig stuff. Always a fan of Stewart

I’m a huge fan of book of proofs by Richard Hammond. Especially because of its relatively light use of grade school maths.

Also shout out to linear and geometric algebra by Alan Macdonald and its sequel that introduces geometric calculus. Always a big fan of anything that makes electricity easier

[sludgebitch]

1 horsepower = lifting 550lb 1 foot in 1 second

1 dogpower = making 1 items yucky in 1 second

[then-ponder]

1 dogpower = 1 itemyuckhertz

[then-ponder]

The worst part about finance aside from how destructive it is, is that you have to take so many classes just to get to the math. Like you really would think that finance bros would learn calc super early. But no. They don’t. It fucking mystifies me that you can study supply and demand without calculus.

[derinthescarletpescatarian]

Been sealing wood with linseed oil today and I am enjoying working with a relatively mild, natural chemical that still carries a good chance of spontaneous combustion if mishandled. Much safer for my lungs and skin, all the spice of a fire risk.

[derinthescarletpescatarian]

#ok my partner failed to informed me about THAT little quirk of linseed oil what the fuck do you MEAN it spontaneously combusts

Linseed oil produces heat as it solidifies. So if you coat something flammable in it (like cotton fabric, or small pieces of dry wood), or use it in an area where there are flammables around (like wood chips or hay), then your project can heat up and start a fire. You can greatly reduce this risk by using boiled linseed oil, but you can't stop the exothermic reaction entirely, it's just part of how the oil works.

It's a relatively easy problem to deal with; you just have to make sure that your project has adequate ventilation so it can cool down and be careful not to put it anywhere extra flammable until the oil has fully solidified. Hang your fabrics on an outdoor clothes line to dry, don't bunch them up in the corner; lay your wood spread out on a nonflammable table in a large room or outdoors, don't pile it in the corner in a tiny messy shed next to a bottle of turpentine. Once the project has completely dried, there's no further danger (except of course for normal fire danger).

Also don't forget to ventilate your tools. If you're slathering linseed oil on wood and drying off the excess with an old towel, you need to spread out that towel to dry, too.

[derinthescarletpescatarian]

#reminds me of when i was in art school and the paint dep regularly set on fire.#none of the departments that actually use fire in their processes had this issue#i think about that a lot

That's hilarious. "They're not flammable if they're being used in paint or canvas sealers! That doesn't count!"

[then-ponder]

I worked with oil paints for a semester or two in college and let me tell you fuck that distilled distillate or whatever, I refuse to work with the stuff purely out of hatred, only reason I haven’t thrown it out is because you can’t poor it down the drain - especially with bullshit paint in it is because going to the fire department is bullshit. Can confirm that it would be nice to use something I didn’t need a p95 and proper ventilation for.

Similar reason I fear flour so much. It’s proper explosive if mishandled, but it’s such a common item that if I went to the hospital because of a flour explosion I would probably lie because no the fuck I didn’t die to flour.

[labelleizzy]

[eriyu]

[abbaswift]

not to be a number nerd on main but 2025 (45^2) will be the only square year most of us ever experience. the last one was 1936 and the next one will be 2116

[ace-misplaced]

i very much will be a number nerd on main and the 27th of September will be extra special...

[micknikblanket]

i'm a math major at a liberal arts school, so when I say that I hate my math class everyone assumes I just hate math. I have to be like "nooo sorry I just wish I was in my favorite class, another math class"

People here cant comprehend 1) that there are different types of math and 2) that some people actually like math

[stillhereandstillqueer]

PLEASE remember to include trans men and mascs and intersex men in your fight for reproductive rights. And breast health education. And free period products. We are so easily erased from these conversations. Insurance deny claims and clinics refuse to see us because of an M marker. Don't forget about us!

[raginggaypossums]

*Trying to seem like a tough butch*

“Hey girl,,, Wanna see me curl~?”

*Frantically pulls out a whiteboard and starts to calculate the curl of three dimensional scalar-valued function whilst excitedly explaining what I’m doing*

[eepy-abby]

Curls are of vector valued functions though?

(also, fun fact, the kernel of the curl operator is precisely the image of the gradient operator. This silly little fact is fundamental in de Rham cohomology.)

[raginggaypossums]

I was being too gay and mistaken curl for gradient

[dat-physics-gal]

You will be Laplace transformed for your sins. Get ready.

[yaldabaothadeez]

Definitionally, you can't "not be into" MILFs (or DILFs etc). At best, you consider the set of milves to be empty, and thus vacuously find them all attractive.

[yaldabaothadeez]

Prev:

#pretty sure MILFs are actually a proper class#prf. exercise (hint: ur mum)

First, definitions: a MILF is anything that (i) is female, (ii) has children, (iii) the subject would L to F.

(This proof will go through without (i). Some have claimed that a MILF must additionally be human - for a disproof, spend any length of time on tumblr.com )

Lemma 1: there is at least one MILF

Proof: ur mum, whom everyone would L to F, and indeed did last night.

Lemma 2: any nonempty set of milves is itself a MILF

Proof: Let M be such a set. A set of gendered entities is considered to have a gender if all its elements share that gender; this is the case for M, so (i) holds.

Similarly, a set "has" something, if at least one of its members has that thing. Assuming the axiom of choice, we pick one m in M, and pick one of m's children c. M has c, and so (ii) holds.

Finally, one would L to F a set of entities if one would L to F any finite subset of its members (sequentially. not necessarily simultaneously), this is true of M, thus (iii) holds.

Theorem: No set contains all milves

Proof: Let M be a purported set of all milves. By lemma 1 M is nonempty, By lemma 2, M is a MILF, but by regularity M cannot contain itself. Contradiction.

Hence milves are a proper class.

[phen00b]

10/10 excellent work OP

One remark: Choice isn't needed to pick a single element from a nonempty set,¹ so the Milf Theorem should be constructively valid as well!

¹(unless I'm tripping, it's been a while)

[mssbambi-deactivated20250803]

i'm kinda enjoying doing math exercises rn ????? what the actual fuck happened to me

[mathematics-official]

We're frens now :3

[positively-knotted]

Topology Intuition Request

Let M be a closed orientable 3-manifold, S a compact surface, and f : S -> M a generic immersion. Then f(S) has self-intersections which are circles or arcs.

Let C be a circle of self-intersection in f(S), and suppose that the preimage of C is two circles. Let T be a small nbh of C in M, so that T is a solid torus. Let B1, B2 be nbhs of the preimage circles, which are either annuli or Möbius bands, such that f(B1), f(B2) are properly embedded in T. We should be able to choose T small enough that f(B1) and f(B2) are disjoint away from C. So in particular, the boundaries of f(B1) and f(B2) in the torus boundary of T are disjoint! So either both B1 and B2 are annuli or both are Möbius bands.

This seems wrong to me? Why can't a generic immersion make a non-orientable circle and an orientable circle have the same image? I think I'm convinced by the argument above, so I guess the result it true but. I have no intuition for why, from the surface's perspective.

Any clean intuition or visualisations would be appreciated!

[m---a---x]

We should be able to choose T small enough that f(B1) and f(B2) are disjoint away from C.

I dont think this is true? Is there a theorem about this?In particular B1 being an annulus and B2 being a Möbius strip is a counter example.

In particular, suppose our surface is the disjoint union of a Möbius strip and a disk. Then sqish the disk and the Möbius strip together through each other in Euklidean 3d space. If we want their intersection to contain a circle then at some point they are parallel to each other. So the minimal intersection is a circle glued to an arc at one point.

[positively-knotted]

If I'm picturing your map right, that isn't a generic immersion — if you perturb the interior of the disc a little (say "downwards") it just intersects the Möbius band in an arc. The arc is properly embedded in the Möbius strip, and is entirely in the interior of the disc.

I'm pretty sure this is a theorem, though I can't find a reference right now. The self-intersections of a generic immersion of a surface into a 3-manifold consists of circles and arcs of double points, which intersect at isolated triple points. In particular, since your example had no triple points, any circles/arcs of double points must be disjoint else it's not generic.

[m---a---x]

If I'm picturing your map right, that isn't a generic immersion — if you perturb the interior of the disc a little (say "downwards") it just intersects the Möbius band in an arc.

Ok, maybe i am mistemembering the def of generic immersion, i don't have it on hand. But i think that if you "perturb the disk a little downward" such that it no longer intersects the Möbius strip in a circle, then you must have perturbed it over the whole width of the additional intersecting arc. Otherwise the intersection just shifts.

So i guess it is very dependent on the exact definition of generic in this case.

[tinysweetvoid]

[elvis-official]

Woah mama if you are transphobic you get the Elvis Special (a bullet)

[garbagechocolate]

What is the center and radius of the circle indicated by the equation?

(x−2)2+y2=36

-Cousin Throkmorton Anon

[hilberts-hotellensatz]

the saddest thing about finally learning algebraic geometry is the realisation that everything there is infected by the axiom of choice. in undergrad it felt confined to fringe counterintuitive results about duplicating spheres but now i find myself using facts like "every non-unit of a ring is contained in some maximal ideal" all the time to prove very general things about schemes :(

[qhd4]

If you only work over some nice fields/rings then I guess you can get away with less, but also embrace the axiom of choice and be free

[algebraic-dualist]

yes yes embrace choice and be free

[hilberts-hotellensatz]

i know ill probably have to for my own comfort but it feels so gross for an axiom of set theory to assert the existence of sets whose elements cant be described

[algebraic-dualist]

I know.... *offers a reassuring look and pauses for a moment, considering her words carefully, before proceeding* soon the type theorists will save us all from this.... *looks up wistfully at the sky* we just have to keep faith until then.

[m---a---x]

✨️ *(Seeing the algebraists hoping for alternatives to the axiom of choice fills you with determination.)

[then-ponder]

I have read about the axiom of choice paradox several times and every time I see someone talking about it I feel like I actually don’t know what it is at all. Because like, It doesn’t bother me? Like, maybe I just need to encounter it In the wild or just plainly understand it, but it doesn’t feel bad to me.