A trivial exercise in mathematics

Let P(f)=0 be an elliptic system of partial differential equations defined over a closed, smooth, oriented n-dimensional manifold X. then:

Topological index of P = Analytical index of P = (-1)^n <ch(s(P)) . td(T_C X), [X]>

where
n is the dimension of the space
s(P) is the symbol of the system
ch is the Chern character
T_C X is the complexified tangent bundle on X
td is the Todd class
. is the cup product
[X] is the fundamental class of X
<a,b> is the Kronecker pairing

<^_^> >_> [-_-]

*yawn*

<(`___`)> kloombarg?

>>1
There:
n=X=0
ch=s=T_C=lambda x:x
class pp(int):
 td=lambda x,y:y
P=pp()

P = (-1)^n <ch(s(P)) . td(T_C(X)), [X]>X
I had to fix it, it was full of errors

Oh, I forgot,

P = (True, True)

Problem solved

ENGLISH MOTHERFUCKER

>>5
n=X=0
ch=s=T_C=lambda ^___^
class pp(int):
 td=lambda,kiirbius x,y:y
P=pp()

P = (-1)^n <(`___`)>(s(P)) . td(9>_>)9), [X]>X

fix'd

SCIIIIEEEEEENNNNNCNCCCCCE!

Oh, and >>7 probably didn't even realize >>5-6 was trolling

too many nerds, needs more cool science not useless crap

>>10
all i see is envy

>>11
Because the mathematicians OBVIOUSLY get all the chicks.

I must say, beyond dirac delta functions and fourier transforms, mathematics are fucking useless, as non-integer numbers have no objective existence and mathematics is an axiomatic science.

Philosophy >> Physics >>>>>>> Maths.

>>12
hahahahaha philosophy hahaha

>>13
hahahaha, dumbass who thinks maths and physics sprung out of someone's asshole and threw a clump of shit at him.

>>14
ahahahahahahhahah philosophy hahahahhahhahahaha gb2/noobs/

non-integer numbers have no objective existence
Are you by any chance Australian?

>>16
British.

>>14
so what you're saying is that we should return to our roots? we should've just stayed in the trees, right? moron.

philosophy is greater than physics is greater than math.
Sounds entirely correct, where are you people having the problem?

philsophy == physics == maths

More like

***   Philosophy ***
        /     |      \
Physics Maths etc...

clearly no. i am a mathematician, but i strongly dislike philosophy (hint: ad hoc crap)

Hint: physics used to be called natural philosophy.
Hint: large amounts of maths started life as footnotes in philosophical works.

In england, science (physics, astrology or maths) are popular dual degrees in good universities. They're pretty hard too.

I do physics and philosophy, but the two maths and philosophy students I know got a total of three yearly prizes for best marks between the both of them. And they're pretty good with analytical philosophy.

Abductively, I infer that >>22 must be a pretty shit academic to be so categorical about something he doesn't know.

However, if >>22 is basing his statement on his experience of emo/goth kids or stoners who think they are 'philosophizing' when they're talking crap, then I retract my statement, and will just conclude that >>22 is very, very naive.

>>23
Indeed. Physics means nature in greek, after all. It is a formalized form of a branch of philosophy called teleology, which has pretty much become entirely formal and merged with physics. But back in the days where physics was being born, teleology was quite central to philosophical thought, and sought to describe the world, its creations, and its mechanics.

Likewise, a lot of these early philosophers were also the forefathers of modern mathematics (thales, pythagora), a trend which continued until Descartes, and arguably, Carroll and Russell.

Science == productive endeavour that has given us the modern world.

Philosophy == mental masturbation that after three thousand years has still failed to give definitive final answers to the questions Plato was asking.  What's the point, other than "oo er I'm so clever, look at me, oo?"

>>25 tells the truth

>>24
you must be a pretty pimp philosopher to assume such things about me.

maybe it's just easier for me to see it's bullshit because i began reading philosophical works early (when i was around 12. that was 8 years ago).

have fun drowning your infantile critical thinking skills in loopy contradiction-full tripe of Kant, Jacobi, Rousseau, etc. while i spend my time working in rigorous systems that actually lead somewhere!

>>25
>>26
I have the feeling that not much I can say will change your mind, given how infantile you guys are being. It's not like we're saying what you guys are doing is crap, so why are you so fuckin infantile.

My original statement was that mathematics and physics emanated from philosophy. That doesn't mean philosophy is better, because maths and physics are pretty fucking hard.

On the other hand, philosophy has a lot of useful stuff too, these days. It's not just Plato and Kant. We have stuff like Frege, Russell, Searle and Minsky. In fact, ask any person doing computer science, and who is over 30, what they did as an undergrad. If they work in NLP or Machine learning, odds are they did maths and philosophy.

>>27
Because crap != non-crap.  Go peddle that in the "humanities," where everything and its opposite are true.  In the sciences, there is truth and there is falsehood and there is an empirically demonstrable difference between the two.

>>28
Bullshit, just look at QM, and things like string theory. I'm a physicist, so I don't know too much beyond that, but I'm sure there are similar controversial areas in mathematics, and 'unprovables'. Haven't you read any of Godel's work? I thought he was quite popular amongst mathematicians.

Then again, the more you post, the more ignorant you seem to me. So I wouldn't really expect you to know.

T_C=3 I am sad because someone is fucking my eye socket.

>>29
String theory attempts to explain unprovables.

>>29
Quantum mechanics provides mathematical models that work and give usable concrete results in the real world.  Transistors, for instance, could not have been created without solid state physics requiring the ground work laid out by people like Niels Bohr.

Your unwillingness to accept this fact is your problem, not science's.

String theory attempts to explain unprovables.
Like religion.

>>32
Muppet. I completely agree with the fact that, as Feynman points out, quantum mechanics may be unprovable but it just works (for now).

You see, wherever you turn, you make a jackass out of yourself.

none of you even know what a rigged hilbert space is. so just stop mentioning quantum theory. please. for fucks sake. you clueless dolts.

>>35
It's a thought experiment-come-mathematical model used in spectral theory to solve problems with generalized eigenfunctions. Theoretical Physicists learn that in their third year. Other than that, anyone with university entry-level physics knowledge could read about it by picking up a book on QM that's more than 50 pages long.

You've been proven wrong. So put your e-cock away and go back to your job as a failed physicist. The grown-ups are debating here.

>>36
Agreed. The only thing that pisses me off with QM is how the media portray it as a science that one day will allow us to travel back in time, or how some philosophy postgrads write papers on how it proves anti-realism. But I think some of the people in the thread know what they're talking about.

really shitheads? seems like all you know is pasting from wikipedia.

answer this then: if D=-id/dx on C^k[a,b]. what are the eigenfunctions at different boundry conditions?

this is one is a classic. I miss the [SHITHEAD] mathematician, it is a shame that he leaved us wiht the crackpot philosophy string theory and shits lik 0.9 = 1
btw, lets do >>38 problem as it make 1 year or so that he leaved us : ((

>>39 dont forget about all that astral projection bushIT

When I read >>36, the grown-ups are debating statement. I laughed. Then I remember this was a year ago when such a statement wasn't ridiculous. Thanks a lot, moot.

RAMANUCHAN, U WIN A MANIGOLD LOL

lol @ "u r infantile, I r adult"

>>37
stupid media is stupid

I left when people stopped pasting SCIIIIEEEEEENNNNNCNCCCCCE! And it got boring.
You want me to post? I can but I don't remember calling myself a mathmetician, more a philosopher if you remember correctly. I'm so happy that someone remembers me though, really, I'm touched.

>>44 please post more trivial exercise in mathematics

lol @ homos flamewarzing

One s, seven c's, four i's, seven e's and six n's

>>47
*applauds*

I feel the need, the need for weed!

Marijuana MUST be legalized.