German Mathematics and scientists

Try rediscovering what Gauss did on your own and see how that works.

He didn't even know set theory so pretty much he didn't know math.

I mean, the way I've been though mathematics in university feels like set theory was the first thing that came. It feels like set theory is so perfect, it is so fitting as the foundation for everything else. If you just make functions, numbers, spaces and objects sets it all works. If you make algebraic structures objects that come from sets and relations defined on sets it all makes sense.

A mathematician without set theory is not a mathematician. Gauss was simply a guy that did cool things. If he was truly smart he would have invented set theory.

Any pre-set theory "mathematician" would have invented Set Theory if they were actually good at math. It is a sad thing that we were dumb monkeys who had to jump to the applications of set theory before we developed the god-given theory itself.

mathematics is much more than the formalism used to study it
mathematic is an organic, living thing, and formalism is trying to approximate it

Do you even know who was Euler? Just the greatest of all time. And he was swiss.

Give me any pre-modern mathematician and their achievements and I would trade all of their achievements for them inventing set theory just that much sooner instead.

Math without sets was useless because in the end 19th century people had to pretty much re-prove everything so basically every proof that came before the 19th century is garbage we do not use today.

I know that because even the elementary euclidean geometry proofs I've done and seen in class were made using set theory, which implies that there were non-set theoretical proofs that were garbage and that we modern mathematicians had to remake because of how shit they were.

>Swiss
German defectors.

If greek mathematicians had forgotten about their shit arithmethic and geometry and instead made Set Theory right now there would be no millenium problems because mathematics would have been solved long ago and we would be colonizing Andromeda.

We would be teaching Interuniversl Teichmuller Theory to elementary school children and even they would say that it is trivial.

>non of them remarkable

math was not created to fit set theory
set theory was created to fit our ideas of math

set theory is a capstone of mathematical achievement, which could have only been conceived after we already have a big body of mathematics

a proof, like math, is much more than a correct succession of formal steps. a proof is a succession of good ideas.

Newton is pretty based, though I agree he is not greater than Gauss.

I understand when, how and why Set Theory came to be. I am just saying that it would have been better if someone came up with it sooner.

I emphasize my point of pre-set theory proofs being useless because mathematicians had to pretty much reinvent the proofs inside of set theory because everything before set theory was shit.

I am glad for the mathematicians that came before and did good stuff but in the long game everything that they did was useless.

If Physicists ever discover a 'theory of everything' that describes everything then the same could be said of the physicists that invented classical mechanics and the other physics systems that can only explain a "part" of the universe.

All that our physicists do will have been relatively useless if we ever find a theory of everything that has no limits with what it can explain.

The only relevant shit Newton did (Calculus), he has cribbed from Leibniz who was, surprise surprise: a German.

> thinks "being smart" means "establishing the current paradigm"

> If Archemedes had just invented nukes, then he wouldn't have gotten stabbed by some random roman soldier. What an idiot.

you couldn't have "come up with it" sooner. it came naturally forward, as a complement for the body of math that was already formed

writing down a correct proof formally is not "reinventing" a proof. the huge body of correct theories and proofs we had were not "shit". everything they did was clearly not "useless".

math is not like you see it in books, it's not an already polished, complete body of knowledge on a topic. it's a breathing, living thing and working with it entails much more than formalism.

>> If Archemedes had just invented nukes, then he wouldn't have gotten stabbed by some random roman soldier. What an idiot.

False equivalence.

You do not need any kind of modern technology to invent set theory. What was needed to invent set theory was always there and in a sense you know that mathematicians always had a mental image of mathematics that resembled set theory but was not quite it.

I am really sad that it took us so much to invent set theory. It shows that we are not as smart as we thought as a species.

>I am glad for the mathematicians that came before and did good stuff but in the long game everything that they did was useless.

What? If they hadn't done all that stuff, how would we know that we should reproduce it? :\

>You do not need any kind of modern technology to invent set theory
Yes, you do. You need both the barebone tools to formalize it and a good idea of what it's exactly supposed to do.

If you consider their achievements in the normal context of history then they are pretty good.

If you consider their achievements with the mindset of 'but if they had done set theory though' then you know that all they did was relatively useless because inventing set theory would have always been better than anything they did.

We'd be in spaceships right now man. Fucking spaceships.

Richard Dawkins isn't German.

>inventing set theory means spaceships
>It shows that we are not as smart as we thought as a species.

you really need to stop. you don't know what you're talking about. you sound like you're stuck in the initial "formalism" phase of someone's mathematical development.

>you sound like you're stuck in the initial "formalism" phase of someone's mathematical development.

Maybe I am but I just can't help but thinking that if we just had known set theory from the beginning we would already have genetically modified cat girls.

I mean, set theory implies better mathematicians and bette mathematicians implies better science which implies spaceships and nekogirls.

I dream in set theory, man.

It's always easier in retrospect. These were once novel ideas, and they happened the way they did because they had to.

See
>If Archemedes had just invented nukes, then he wouldn't have gotten stabbed by some random roman soldier. What an idiot
it's not a false equivalence, it's exactly what you're saying.

Better mathematics doesn't imply better practical applications of engineering. Math is way, way more advanced than what's used.

>beethoven
>goethe
>kant
>gauss
>einstein
>oliver kahn
Hitler was right.

A mathematician invented modern physics.

If that mathematician had been a better mathematician then we would have had better physics.

A mathematician with set theory is a better mathematician.

I am just saying that a faster development of mathematics would have lead to a faster development of science in general.

What we needed was the bible to be a god-send book of set theory with the ten commandments being the 9 axioms of ZF and the axiom of choice.

Let a man dream. Right now I would be fucking neko pussy fucking hell.

>The world would have been better if Euclid had just invented Riemannian geometry instead of dumb ol' Euclidean.

>Let a man dream.
No, your dream is idiotic.

But it is idiotic because it is so unrealistically good that you cannot even imagine how better our world would be if Set Theory was invented from the beginning.

I am telling you. We need to invent time travel and then go back in time and re-write the bible with the commandments being the axioms of ZFC and then when we go back to the present we will all be at our floating sky homes and we will all have like 10 neko girl maids waiting to please our for us to create an injective function from our cocks to their pussies.

>to create an injective function from our cocks to their pussies.

>10 minutes into Set Theory and chill and he gives you this look

Set theory is gross

Cauchy was french and has his work all over Math. When you study math in university you hear his name every week

No it is fucking beautiful.

What else do you use to make sense of your math then?

Set Theory has it fucking all.

Functions and generalizations of thereof

>Fucking spaceships.

>changing your language puts you in God-mode

You're acting like Set Theory is debug-mode for mathematics, and that everything is just a trivial corollary. It's not. It was invented as a potential rigorous framework in which to fit the VAST bulk of mathematics which already existed.

For example, how might we prove the Gauss-Bonnet theorem in the framework of Set Theory? Well, one thing you could do is to first formulate the language they were using in terms of sets, and then you REPEAT THEIR PROOF. Set theory isn't making the proof any more trivial. While there are more modern methods of proof for this result, none of them are "by Set Theory."

inb4 HoTT

>Set Theory and chill
I'm using this.

That is all bullshit.

Set Theory is like that shy girl from school who you know is reserved and won't give into sex. You know that if you pick any other girl she will put out in like the second date and that is why all the other mathematicians are fucking her and her axioms but you just give Set Theory a try and it takes you up until your 5th date but when she opens her legs wide you see that she has a mechanically enhanced pussy with vibration mode and automatic jerking motion and then you realize that your theorems will never be the same they were before.

...in your first semester

I want to fuck set theory.

>goes back in time
>extols the virtues of Set Theory
>everyone completely ignores it
>Russel says "hey we need a rigorous framework for mathematics" and a random loon from the back of the room says "Hey, there's this 'Set Theory' thing.."

Use our modern technology to establish an authoritarian government that forces primary education to be simply set theory and also makes it illegal to publish anything in math that is not using set theory.

Though I bet if you carefully explained Set Theory to various famous mathematicians in history they would immediately get the value of it and would study it rigorously without needing to be forced.

So now you're just speculating about going back in time and arbitrarily changing everything to suit your own idealist agenda? I thought we were talking about good mathematicians who weren't German.

i suppose someone took complex analysis their first year

Wow.
complex analysis is like a 4th semester course at a regular university in Germany. Still though, mostly you hear about Cauchy in your first semester covering Analysis I, where the stuff is about limits and so on Cauchy sequences etc.

In my Analysis 1 course (first semester) we defined the real line as equivalence classes of Cauchy sequences of rational numbers.

Cauchy did a LOT more than his integral formula from complex analysis. In particular he spear-headed the initiative to make analysis actually rigorous

>he still thinks set theory is good
how's sophomore year treating you

>formalizing the real numbers is more important or even comparable to the fundamental holormophic -> analytic
jesus, no.

Where did I say "more important"?

talking about cauchy sequences in the same post as

>Cauchy did a LOT more than his integral formula from complex analysis

is just ridiculous. the integral formula is much, much more important.
It's like saying

>Cauchy did a LOT more than work in analysis. He could also count from 1 to 10.

it's silly

the post was in response to someone saying "the only way you'd hear about Cauchy in first semester is if you took Complex Analysis" so I pointed out that he'd done more elementary stuff that one would be likely to hear about. You're just being a pedantic prick.

so you replied to someone talking about Cauchy sequences to inform them Cauchy sequences exist

>assuming "more" meant with respect to quality as opposed to quantity

someone's english is really good

>pedantic prick

oh wait I forgot, this is sci
>"the only way you'd hear about Cauchy in first semester is if you took Complex Analysis"

Cauchy did not invent Set Theory so pretty much he sucks. All he did is trivial.

>mfw Mengele