#proofs

[catscomputerscreativewriting]

It's so funny to me that people think of Math/Mathematicians as being hyper-logical and rational. Like, have you seen some of the wild things hiding in the Math?

Did you know there are non-computable numbers?? (https://en.wikipedia.org/wiki/Chaitin%27s_constant)

Did you know that there are things that are true, but we can't prove them??? (https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems)

Did you know that we can prove that something exists, and yet never actually figure out what that thing is?? (https://mathworld.wolfram.com/NonconstructiveProof.html)

Math is crazy. Math is wild. Math hardly makes sense, and when you think you understand the weirdest parts of it, everyone who hears you explain it to thinks you're a gibbering lunatic.

"In mathematics you don’t understand things. You just get used to them." - von Neumann

(please share more unhinged math with me, i want to see more scary math)

[tea-for-patchouli]

For your enjoyment, a lovely mathematical paper which can fit in a single image.

[mentalknot]

As a math major trying not to get bogged down in the hellscape of severe social anxiety once again, proofs are shockingly comforting.

How wonderful to behold a carefully chosen sequence of arguments and accompanying symbols that remains absolutely logical…

…while navigating a mind that does nothing but lie at every juncture of my life.

[umaymen]

Listen

[djudy-just-found]

Page 3 of my comic book on "My Hero Academia & True Education"

And here is the promised page from the comic book.

I will be very glad if you support me with a subscription and a like. I will also be glad to read your comments about what you think about this work.

I'll see what interest you have in him and decide if I should continue to draw him. Subscribe if you are waiting for the continuation!

Carefully read the text to my posts. In one of the previous posts it is written how to get free art from me. If I see a response from you, I will continue to do so. Read past posts and don't miss this opportunity!

[humormehorny]

Yo math people, what was your first proof?

[greetings-inferiors]

If proof by contradiction was a person I’d give them a big fat kiss on the lips

[kelyghtbooks]

Had to order three proofs from amazon before they got the cover right. It was so dark you couldn't see a thing the first time, but I'm glad I had the opportunity to fix it before release.

[mohelconvention]

Just know, when I write, “Now, observe that…” in a proof, it could mean any of the following:

— watch me cook nerds

— Observe… (with the condescending tone of a 1980s supervillain)

— look at it bitch (with warmth and love)

— look at it bitch (derisive)

— look at it bitch (hesitantly like I’m trying to be dominate in the bedroom, and I think you might be into it, but I’m really not sure. Like you’ve said you might be into that kinda thing but were you dropping hints? I don’t know but the actual follow-thru feels unnatural and weird :/)

— look at it bitch (confidently, cause now I know you like it)

— I don’t want to fuck with latex right now, so I’m writing this by hand and I’m really tired, so everyone just nod in agreement

[catscomputerscreativewriting]

Listen, textbook, I admire the dedication to grifting my students into learning most of Constructive Logic before they've realized it. They are computer scientists after all. It's good for them. But... really? No explanation of formal proofs by contradiction in the undergraduate, Logic for CS textbook? You do include double negation elimination, which is an equivalent Classical axiom, but not, like, (A -> Bottom) -> ~A?

You mean I'm gonna have to derive that myself from the completely random and arbitrary Classical axioms you've decided to adopt and then neglected to prove the completeness of? Otherwise, all of these proofs will become extremely cumbersome and all of my students will swear off CS theory for the rest of their lives?

... ok fine, it'll be in the slides. T-T

[a-dux]

One of the fun things about being a math major is learning new notation options and then getting to watch everyone almost immediately decide what they're gonna use forever. I have visuals for non-math people because math shorthand stuff is very fun to me! :D

For completing a proof:

Q.E.D. is considered kind of old fashioned but classic, the open box is quite common and the default for LaTeX (a program often used to help type up math), and I don't know what the general view on those last two are. I use the crossed box because I like the emphasis it adds and it's fun to write.

For stating a contradiction:

I will use that wondrous lightning-bolt symbol at any possible opportunity because it's delightful to have an opportunity to draw a small arrow-headed bolt of lightning in the middle of a math problem.

[mentalknot]

Sharing of Proof Between Friends

After spending over nearly eight hours of each day in a mathematics department for two years straight, I’m shocked that many high schoolers believe math is a solitary pursuit.

In reality, this community seems to be one of most welcoming and collaborative academic communities I’ve found. Let me share some moments:

“Hey! How’s it going?”

“Alright, been stuck on this interesting question my friend emailed me the other day… he said the first part of the proof is pretty easy, but I’ve been at it for 10 hours…”

“Never trust a mathematician who throws around the word ‘easy,’ c’mon let’s try it together at the board.”

Thirty minutes later, they had completed the proof, and sat back with wide smiles to admire their work. In truth, there was rarely a conversation that didn’t eventually turn to math in that department…

“Yeah, and I heard that the guy cheated with his best friend’s sister… wild right?”

“Yeah… not to interject, but I have this representation theory question… would you all be willing to take a look?”

The conversation took an immediate turn with collective enthusiasm. I have been lucky to have my own “collaborative math” moments since returning to my undergraduate studies, and do my best to share this part of “math culture” with younger students curious about the major.

“So that’s the proof that motivates our paper! It’s quite short, but there’s something about it I love.”

“Wait… but you’ve only done half, and this is a biconditional statement, let’s try it together.”

There was a reason my mentor never encouraged me to look at the other side of the proof… it was far more “ugly,” but tons of fun to piece together with a fiend. We looked back at our work after forty minutes with satisfaction before returning to our neglected problem sets…

And finally, I tried to assist a student with a calculus question using the “process of questioning” the research world had taught me:

“I need to find a closed-form equation for this geometric series… but I can’t seem to get the alteration sign?”

“Try writing out the first six terms, do you see anything that you could simplify? Look at the denominator specifically…”

“Well, they’re all multiples of three…”

“Try pulling that three out, any more similarities?”

“The numbers multiplying the threes are powers of two! But I still need that alternating sign…”

“Remind me, what happens when you raise a negative number to an odd/even power? Try it with (-1)^n”

“If it’s odd, the number stays negative, and positive if even… so if I add this to the denominator, the sign is alternating depending on the index n!”

“YES! This little (-1)^n trick comes up everywhere, it’s a nice ‘tool’ to hold on to if you decide to take more math.”

The exchange was wonderful… and motivated me to review the calculus I’d excitedly ran past when I was younger. I wish this type of discourse was taught more expansively.

[my-alter-egos]

Kids these days are writing geometric proofs as fill-in-the blanks, multiple choice drop-downs online. Back in my day, we had to hand write those suckers with no guidance whatsoever. Truly so much easier the "modern" way

[djudy-just-found]

Alastor (fragments of how the drawing was created)

That's what I got. It is a pity that I did not use the recording of the process of creating this drawing step by step.