Is mathematics analytic or synthetic?

If they're so far ahead, where is their fusion? Where are their space programs? Where are their advancements in high technology? The japs haven't done anything notable except invent anime.

calculus 1 is easy enough to be taught to 12 year olds. honestly you should have learned enough math by the end of high school that you're read to study analysis and modern algebra in freshman year of college

>If they're so far ahead, where is their fusion? Where are their space programs? Where are their advancements in high technology?
They are only good at math, they can't seem to think physics/engineering/chemistry wise, they are Veeky Forums's wet dream society.

quite differnt to how it is in straya
where its basically calc 1,2 and 3 and ode's all within senior year of hs.

>senior year and still no real math class
some people actually learn math in school, not pretend math.

>PDE's
>Not real math

Lmao keep jerking off to your category theory bullshit while other people do useful things with math.

Synthetic.

It's both because any human activity uses both.

>muh quine sed so
Quine offered an argument, but there have been many counter-arguments made against him. There are never conclusive answers in philosophy.

good luck getting anywhere in pdes without analysis

But what do YOU think, user?

Where in my post did I trash on analysis?

You don't need analysis to do PDEs. All you need is calc and ODEs

Did you just took baby's first PDE for engineers?

I said DO PDEs, not understand them autistically. If I wanted to learn more about PDEs, I could learn analysis. I'm not the one saying that PDEs aren't real math.

Again, where in my post did I trash on analysis?

If it were fully synthetic you wouldn't be able to analyse anything with it. That being said, there is a lot of pure math that isn't used to analyse anything.

>OP posts titty monster
>arguing about the nature of mathematics
Yup I'm in Veeky Forums alright.

japantimes.co.jp/news/2015/08/06/national/science-health/21st-century-nobel-rankings-japan-third-just-behind-u-k-way-back-u-s/

Someone explain this dichotomy in the context of math.

and even that was a mistake

linear algebra*

analysis is a waste of time for understanding PDEs. Newton never learned real analysis and did great with his PDEs.

maybe you should go back to your containment board

newton more or less invented analysis. he didn't have fucking linear algebra though lol

lol

dare i say it, we don't give a fuck? if its useful it is, if its not who the fuck cares

>if its useful it is
*flushes pure math down the toilet*

Underrated

It's synthetic a priori.

I didn't understand either, I only know of the concept in linguistics though I think that's outdated anyway.

I found this, seems to be what we're looking for.
plato.stanford.edu/entries/analytic-synthetic/

I've heard the term synthetic used in some areas of mathematical research. The gist I get is that it is used when one approaches a field of study by abstracting everything away and looking only at it as an axiomatic system with many possible models of that system.

I do not know if this is the correct way to use it but it is how I've been using it.

I understand what that page is getting at but I'm not sure how it applies to mathematics (there is certainly more than one way I can think of).

synthetic

How does it feeel knowing anime girls can do algebraic geometry AND eat cupcakes while being dainty???

lmao they don't actually do this

t. jap american with family in japan

Analytic. Anyone who says otherwise is a filthy physicist.

DON'T DRAW THE INTEGRAL AS AN "S" YOU FUCKING BITCH

I had integrals when I was 17, including integration by parts

t. European

Analytic. Fight me m8.

Right here

axioms are synthetic.
their consequences are analytic

>He has never read a book in category theory.

The entire shit is:

Proof: consider the diagram.

QED

I graduated early and started uni at 16, taking most Maths courses
t.America

What's the difference between "analytic" and "synthetic"?

>it's an undergrad cannot do math outside undergrad maths episode

is analytical philosophy analytic or synthetic?

It's neither.

>it's another Raphi thread

The question is wrong. Analytic ultimately implies that all of math can be deduced from first principles, like set theory or whatnot. Bertrand russell tried this and failed. gödel proved this is impossible.

Math ad synthetic means its an arbitrary himan construct culturally contingiwnt. This had also been prooved false. There is only a single system of math with many fields homomorphic to each other.

The best "theory" is platonic mathematical realism, followed by pythagorus, gödel and mac tegmark.

>There is only a single system of math with many fields homomorphic to each other.
>homomorphic
Under which category? Or are you simply trying to sound smart by misusing category theory terminology?

>There is only a single system of math
I really doubt this statement. Mind expanding on it?

>say junior year
>as in, 16-17
>eurofag comes in saying 17 condescendingly as if he did it earlier

Most PDE's are solved numerically these days anyway. The most important things to know are linear algebra and some functional analysis.

Here in the Chicago suburbs I learned this when I was 14, faggot.

>where are their non-math contributions

>its here here, look at this pure math this jap made with to practical what so ever in the next 150 years.