#math foundations

[then-ponder]

Truthfully, I am critical of most arguments that urge people to learn math. This is in particular because most public defenders of mathematics and math education argue with the implicit assumption that you should learn this if and only if it is useful. They will argue that because we can use all of our math to travel the stars and save our dying planet it is worth learning.

I do not blame them for this. After all this is a common practice under capitalism. The constant need to prove useful is a hellish practice in which all professions participate even if some have it easier than others. But it is harmful. It separates us from seeing math for what it is. Want it wants to be.

Many people would call math a science and there is a truth to that. Much of mathematics is a process of learning cold hard facts, even if the idea has been proven a million times over, but that ignores all the bits of it that we tend to not include. The parts about logic and reasoning, the parts about discovery, the parts that suggest a deeper explanation, the parts where intuition feels like magic and reality feels fake.

At the beginning of this post I said that “arguing math is useful is a harmful argument”. This is why. There is no discovery of facts. Logic, what should be the foundation of all mathematics, is not taught and proving that a statement is true goes ignored and is deathly fatal to students who seek the answers, yet are obscured. Worse, the facts we teach in math are plainly obvious to the student in a way that destroy any merit of the claim “ math is useful” because why would I use math when I could use logic. Why would I use the Pythagorean theorem when I know that two sides of a triangle are longer that the hypotenuse when I’m path finding and why the hell would I use a polynomial to describe anything. You use the language of usefulness you should be teaching useful things, but math can’t teach useful things. It’s math not a trade or a science.

And in truth mathematics isn’t useful. Nothing you point to that most people understand are useful things and the vast majority of research is on problems that most people either don’t care about or find utter nonsense. Truly I don’t mean this to be cruel, it’s just that the proof for 1+1 = 2 is a books worth of pages. And that’s the thing people can’t possibly be bothered to ask questions that a mathematician would lose years to. They just want a fucking answer and that’s fine, but this more explicit explanation is why Mathematicians don’t like ‘applied’ math. It’s because assholes take our prized possessions, our meow meows, and our blorbos and they throw them in a shredder and mangle them up till they have a thing that they like and then they give it to another person who fucking hates math because they got their degree in “I hate math but I love problem solving so I became a [insert stem field here]” so they can blow up that thing so that they can use it to solve something.

The truth is that math is a humanity because it is a reflection of our own reality. Quite like art. And the reason for studying art is the same reason you should study math which also happens to be the reason why math and art education sucks. You should learn about these things because you want to. No amount of money can justify it. You have to want it. And the thing is art is best taught as art. It’s not a just or simply a tool for people to make money. It’s an expression of the self - The very people who created it.

Many fear that if we allow people to stop studying the math people won’t. Fair, but high school math is not reflective of math. It doesn’t teach foundations, it doesn’t teach about the different sub-disciplines. It refuses to teach any math that can’t be directly applied to science and engineering. Of course people don’t want to learn that. You’ve ripped out the meat.

[brightshaw-shipper]

GUYS

GUYS

GUYS

THERE'S AN SCP TV SERIES THAT MIGHT BE COMING OUT IF IT GETS ENOUGH MONEY

I NEED YOU ALL TO REBLOG THIS POST, THEN WATCH THIS VIDEO IMMEDIATELY

NOW

[pv1isalsoimportant]

Mathematical platonists are so funny to me because they will say shit like "mathematics has this beautiful elegant design" meanwhile you get to the foundations and find out you have those "beautiful elegant statements" that are independent of ZF (or even ZFC), are not compatible with each other and each of them implies some insane monstrosity that shouldn't ever be true.

[daily-public-domain]

Day 393: Mandelbulb Fractal (this image is so big I had to downscale it, full resolution is 48.97MB)

link

–This image is part of the public domain, meaning you can do anything you want with it! (you could even sell it as a shirt, poster or whatever, no need to credit it!)–

Zoom anywhere and you've got a new wallpaper!

[alexiaa049]

I made this little doodle of the doctor in math class because I was bored

[confusedcanaries]

Set Theory Axioms

Extensionality: What a set is

Empty Set: Oh no we forgot to make a set that definitely exists

Pairing: Why do all our sets only contain one element

Union: But what if I want to ship these sets?

Powerset: But what if I only like a little bit of the set?

Comprehension: Russels Paradox was bad, but also really cool?

Infinity: It would be great if we could do some maths now. Guess we’ll just assume the natural numbers exist

Replacement: I mean infinity isn’t that big, we could give ourselves a little more room

Foundation: We should probably have made sure that all these sets made sense earlier, huh

Choice: This one simple trick might just break everything! A subset of mathematicians hate them!

[leprechaunbitch]

This is how I like to think Iceberg met Bright

Trascript for the Comic

Panel 1

Gears: Doctor Iceberg, this is my Senior, Doctor Jack Bright

Panel 4

Icebeg: wait

Panel 5

Iceberg: how old are you man?

Panel 6

Bright: About 110 years five or take

Panel 7

Iceberg is ranting angerly aboht how old Bright is.

Gears: Doctor Iceberg, please respect your elders.

[m---a---x]

Inspired by all the newly created communities i have also created one about the topic closest to my heart: Foundational Mathematics

It is inteded for all types of posts about and from people of all kinds of backgrounds interested in the topic.

Please share with anyone you think might be interested. If you want to be added comment on this post, so I can add you.

[king-of-moths-shoes]

Math doodles from yesterday

[foxgirltail]

*specifically gets into AI because of its ethical concerns*

[then-ponder]

Rate your favorite logic notation

[humormehorny]

Why don’t they teach mathematical logic earlier? It’s present in literally all the books you have to read anyway. Some algebra author is going to be like for vs real numbers a,b ≠ 0 there exists a ratio a/b that is also a real number. And most people can’t even read that. Like half of the book is completely inaccessible because logic is fucking wild and requires actual practice with.

I’m not saying that this stuff is incredibly hard; it’s not. However logic just isn’t taught even though it is clearly foundational.

Sets especially seem to trigger me. Like I think a lot of people struggle with trig specifically because this aspect of functions is just not taught well. Like of course the arcsin(x) isn’t defined for -pi/2 > x < pi/2. It would be so much better if we actually taught this stuff.

[pv1isalsoimportant]

Mathematics is the mirror image of humanity.

[daily-public-domain]

Day 389: Fractal Tree, 2005

link

–This image is part of the public domain, meaning you can do anything you want with it! (you could even sell it as a shirt, poster or whatever, no need to credit it!)–

[daincrediblegg]

[combeferret]

feeling kinda weird because i’ve hit the point where i realise i need to drop one of my uni classes because i just… i can’t do it. it was already a level too high for me when i started, but i figured as long as i worked hard and put the time in, i could keep up.

well, turns out trying to work hard and put the time into content you literally don’t understand is a futile, demoralising thing to do.

and my grades were going down after every assignment.

it’s also meaning that i’m not putting in enough time with my easier class because i’m using all my energy on this hard one, so. it’s not doing any favours at all.

i feel bad about dropping/deferring it, but… i just can’t understand the work right now.