Is mathematics analytic or synthetic?

Is this, dare I say it, philosophy of mathematics?

Both

>analytic/synthetic dichotomy
Shiggy

>>8947469
I didn't start doing integrals until my junior year. These girls are supposed to be in their freshman year. Just how far ahead are the japs of us?

>>8947639
What's wrong, anon?

>>8947469
both, but analytic is more popular nowadays.

For example, a drawing is not an acceptable proof for a theorem in today's world.

>>8947643
cal 1 in 8th grade
cal 2 in freshman year
cal 3 in 2nd year
linear algebra and ODE's in 3rd year
PDE's in senior year

No fucking wonder the japs are ahead of us

It's algebraic.

>>8947648
u ain't read ur quine?

>>8948692
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.

>>8948692
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

>>8948706
>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 /sci/'s wet dream society.

>>8948692
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.

>>8948692
>senior year and still no real math class
some people actually learn math in school, not pretend math.

>>8949148
>PDE's
>Not real math

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

>>8947469
Synthetic.

It's both because any human activity uses both.

>>8948704
>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.

>>8949171
good luck getting anywhere in pdes without analysis

>>8949883
But what do YOU think, anon?

>>8950071
Where in my post did I trash on analysis?

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

>>8950146
Did you just took baby's first PDE for engineers?

>>8950217
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 /sci/ alright.

>>8948732
http://www.japantimes.co.jp/news/2015/08/06/national/science-health/21st-century-nobel-rankings-japan-third-just-behind-u-k-way-back-u-s/

>>8947469
Someone explain this dichotomy in the context of math.

>>8948706
and even that was a mistake

>>8950071
linear algebra*

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

>>8951243
maybe you should go back to your containment board

>>8951389
newton more or less invented analysis. he didn't have fucking linear algebra though lol

>>8951463
lol

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

>>8952300
>if its useful it is
*flushes pure math down the toilet*

>>8947553
Underrated

>>8947469
It's synthetic a priori.

>>8951267
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.
https://plato.stanford.edu/entries/analytic-synthetic/

>>8954319
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).

>>8947469
synthetic

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

>>8948692
lmao they don't actually do this

t. jap american with family in japan

>>8947469
Analytic. Anyone who says otherwise is a filthy physicist.

>>8947469
DON'T DRAW THE INTEGRAL AS AN "S" YOU FUCKING BITCH

>>8947643
I had integrals when I was 17, including integration by parts

t. European

>>8949210

Analytic. Fight me m8.

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>>8948706
Right here

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>>8947469
axioms are synthetic.
their consequences are analytic

>>8947649
>He has never read a book in category theory.

The entire shit is:

Proof: consider the diagram.

QED

>>8957007
I graduated early and started uni at 16, taking most Maths courses
t.America

>>8947469
What's the difference between "analytic" and "synthetic"?

>>8958218
>it's an undergrad cannot do math outside undergrad maths episode

>>8947469
is analytical philosophy analytic or synthetic?

>>8947469
It's neither.

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>it's another Raphi thread

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>>8947469
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.

>>8959018
>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?

>>8959018
>There is only a single system of math
I really doubt this statement. Mind expanding on it?

>>8957007
>say junior year
>as in, 16-17
>eurofag comes in saying 17 condescendingly as if he did it earlier

>>8950238
>>8950217
Most PDE's are solved numerically these days anyway. The most important things to know are linear algebra and some functional analysis.

>>8957007
Here in the Chicago suburbs I learned this when I was 14, faggot.

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>>8957881
>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.