/sci/ - Science & Math

>>5941882
Are you good at maths? Do you know how to construct proofs?

Yes, spend 10 years on becoming a talented mathematician, then you would have about the same chance as any other talented mathematician.

>>5941883
i'm good at it and I visualize concepts and numbers very well but I don't really know anything complicated.

>>5941887
it must be easier than that. there was on college kid that solved a unproved statistics thing that he mistook for homework

>>5941917
Not many college kids could do that, though. And not on just any problem. Most require an understanding of the language mathematicians use for proofs.

Are you at uni?

>>5941882

For the most part they're solved... you just have to work out the finer details. For example P!=NP... everyone knows it but the mathematics don't exist yet to prove it.

>>5941917
>there was on college kid that solved a unproved statistics thing that he mistook for homework
the cases where something like that happened the guy is usually one of the most brilliant mathematicians of his time.

quick, what do you understand related to <span class="math"> e^{i\pi} + 1 = 0 [/spoiler] (This is the international Gauss test of mathematical ability)

>>5941882

Just FYI even if you solve one you have to publish it, have it peer reviewed and accepted to the point where the mainstream media is tossing articles around about your breakthrough, then you have to wait a few years for no refutation to come up, THEN you're awarded the prize.

>>5941945
The Birch and Swinnerton-Dyer conjecture never gets any attention :(

They aren't difficult problems, just require a bit of abstract thinking for a bit. For example, fermats last theorem, a problem which awarded $1mil (iirc), say that a^n + b^n != c^n where they are all positive integers and n >= 3, The solution is based around elliptic curves, and is quite interesting. The current guy working on the ABC conjecture, has basically invented a whole new field of math, just to try to answer the question. Also, he spent like ten years on it. For example, with the reimann hypothesis, you can assume it to be true, and most people do, because several hundred thousand numbers have in fact been tested through it. But if you can find one number that disproves the reimann hypothesis, the entire thing is false, and you get the moneys. Finding one mere example, no mathematical proofs necessary.

>>5941952

I'd also like to point out that you never actually submit the solution to the institute: they literally hear about it from the media then put you on hold for a few years. It says this all on their website.

>>5941957
>They aren't difficult problems
be more pedantic and condescending if you can.

>The solution is based around elliptic curves, and is quite interesting
Oh, you can.

What are you waiting, then ? Go for the millions !

>>5941951
>what do you understand related to euler's identity
What do you mean, understand related to it? I can explain why it's true if that's what you mean..

>>5941987
Explain it to me. With basic tools.
For now, I just now what is Pi, that's all

>>5941954
Hey, that one's my favorite!

>>5942006
Cool story bro

Do you know my faorite tree is the oak ?

>>5942022
Really? That's my favorite too!!!

"If P = NP, then the world would be a profoundly different place than we usually assume it to be. There would be no special value in 'creative leaps,' no fundamental gap between solving a problem and recognizing the solution once it’s found. Everyone who could appreciate a symphony would be Mozart; everyone who could follow a step-by-step argument would be Gauss..."

I hate this kind of stupid shit. It's completely misleading.

Let's look at what this is based on: "Cobham's thesis holds that P is the class of computational problems that are "efficiently solvable" or "tractable"; in practice, some problems not known to be in P have practical solutions, and some that are in P do not, but this is a useful rule of thumb."

This is the primary significance of P: a rule of thumb, which we know isn't generally true, equates P with tractability.

Because we know Cobham's thesis is actually false in any formal sense, the primary consequence of proving that P = NP would almost certainly be the replacement of Cobham's thesis with the rule of thumb that "more tractable problems are easier to recognize as P".

In other words, proving that P = NP would probably not make more problems tractable, but demonstrate that P contains many more intractable problems than we believed.

>>5942046
It's like those nitwits who go on and on about how terribly significant it is to practical computer programming that you provably can't make an algorithm to determine whether any given algorithm will halt.

This is an academic curiosity based on fantastical assumptions about the computer. Real computers aren't infinite-storage turing machines at all, but finite state machines, and it is quite trivial to prove that an algorithm *is* possible to determine whether any given real computer program will halt when run on any given real computer.

>>5942022
>implying the oak choice of the Millenium problems isn't either P = NP or Riemann Hypothesis

>>5942059
you dunno the oak's conjecture ? It's damn hard.
It'll be on the list of Billeniums problems

>>5942069
Proving oak's conjecture would make it possible to develop technology to control pokemon.

>>5942071
Grmmmm !!!
rule /1/ of the Great Oaks Book !

>>5942069
oh fugg the billeniums broblems sorry I forgot :DDD

>>5942071
oak for bresident!!

>>5942080
Painting is hard with branches

But soon we'll run the world

OWWWK

>>5941993
That would take a long ass time, especially considering I'd have to explain about taylor series, complex numbers and all sorts of other shit too. No thanks.

>>5942114
No, you didn't understand what I mean. Imagine I'm a MS intersted in math. I just know Pi, Ok.

How can you "explain" me the equation ?
Here is the real difficulty. Make that thing understandable.

>>5942122
What the hell is a MS? Medical student?

In that case there is no hope.

>>5942134
obvious man, if needed :
Middle School I guess

>>5942122
That only *really* (as in, you absolutely get what's going on there) works if you know those concepts I mentioned. I'd start with explaining the complex plane, and then introduce Euler's formula. But seriously, you can't explain Euler's identity to someone who doesn't know about complex numbers without them being confused about some part of it.

>>5942145
There is a french guy (mathematician), I don't remember his name.

He's known to be the best talker ever.(in math field, of course)

Because on every subject, he can speak in such a way that everybody has the feeling to learn something, and to see the things in a new angle.
10 years old don't get the full math, but they see images, they "feel" stgh
And the old mathematicians are always impressed by how he can link apparently different subjects, using the right methaphor.

There is no "absolute comprehension" of euler formula. The way you see it is not the way you'll in 10 years and so on. All the great mathematicians say that. Even for the concepts which seem really basic.

Maybe.

Definitely.
But I'd need a lot of time. A lot.

>>5942122
Explaining why <span class="math">e^{i\pi} + 1 = 0[/spoiler] requires accepting two things:

1. You'll never be a first class mathematician (according to Gauss, god of math), and
2. Much of it will fly over your head due to a lack of familiarity with the mathematical jargon required to truly prove its truth.

>>5941993
i*i is -1, even though it seems impossible. If we think of the real numbers on one line, and the imaginary numbers on a perpendicular plane, with 1 as a real unit and i as an imaginary unit, then look at the angle of i and the angle of negative 1, we see that i acts quite like an angle, rather than acting like a real number when multiplied.
e is the number where the slope of e^x is always e^x. It is essentially a perfect exponential curve unit.
Because i acts like an angle, e^xi curves around in a circle rather than tending towards infinity. Its angle is always e^xi, but xi is circular. We might think it would always tend towards infinity, but that would be an incorrect way of looking at i, since we are mixing it with real numbers on the opposite angle.
So e^xi is essentially an angle.
You said you know what pi is, so what is it in radians? It's the leftmost angle. If we consider i to be as far away from 0 as 1 and -1 and -i (which we can't do completely, but we are thinking in two separate units), we see -1 is where pi would normally be if we were working with angles. Therefore e^ipi = -1, or e^ipi +1 = 0.
I'm very inexperienced sorry, I'm sure this is wrong.

>>5942163
you live in 19th century ?

{math]\exp(z) = \sum_{n = 0}^{\infty} {z^n \over n!}[/math]
is a correct definition of complex exponential function.
Separate. You have cos and sin (that's also a possible definition of sin and cos, the most used actually)

cos(Pi)=-1
sin(Pi)=0

and you're done.

Math have changed, you know... It was maybe hard, it's now just beautiful

>>5942180
Apparently you never passed through the 19th century, because everything you just did is completely unjustified - until you prove that each of those series converges absolutely and that rearranging an absolutely convergent sum does not change its value.

>>5942179
Oh shit, a circle has constant rate of change. Definitely wrong. Oh well

>>5942191
which is completely basic. Every term is absolutely convergent, and the fact that in this case you can rearrange is proved in 10 lines.

>>5942190
Wait, no... I was thinking of how you go a little bit and turn the same amount. It's not a constant rate of change at all.
Tell me how wrong I am

>>5942224
just in case : <span class="math"> \frac{r^n}{n!} [/spoiler] obviously converge to zero in C, so R=infinity and the exp serie converges

>>5942224
>every term is absolutely convergent

Oh, so you want to prove that if a series of analytic functions converges uniformly then their limit is also analytic?

>>5942237
wat ? are you dumb ?
<span class="math">\exp(z) = \sum_{n = 0}^{\infty} {z^n \over n!}[/spoiler] is absolutely convergent. What's your problem with that.

In many books that's even the definition of the complex exponential function.

I don't understand what's wrong with you. Euler identity was maybe hard in the past. Now, you can clearly prove it without any difficulty at HS+2 (two years of uni, dunno the name)

>>5942244
You were saying "every term is absolutely convergent" which doesn't make any sense. I was trying to figure out what you were getting at, and the closest guess I could come up with was a series of polynomial functions converging uniformly to the exponential function (which is what is happening).

I'm not saying it's hard to prove; I'm saying there are a lot of subtle points that people like to throw under the rug because "Oh look it's beautiful!"

>>5942245
ok, my bad, it's because I'm not a native speaker and I was refering to
>until you prove that each of those series converges absolutely

each of those series <-> every term is convergent (bad formulation)

Ok for your point, but don't go too much on the other side (that's verrrry complicated....esoteric and shit). It's just series.

For instance, dominated convergence theorem, less sexy, is far more hard to prove (if you speak of riemann integrability, not lebesgue one).

>>5941957
>implying you understand modularity

>>5942262
>implying Andrew Wiles understands modularity

>>5942275
>implying the oak's king understand modularity
>>5942099
>>5942099
>>5942099
of course HE DOES

>>5942298
>Andrew Wiles
>king of oak
>not Perelman

>>5942302

>Perelman

He said King of Oak, not King of Autism.

>>5942302
uhm... Perelman is the king of bears I would say

>>5942308
>king of autism
>not Ramanujan

Get your shit together

>implying Gauss was a good mathematician

>But if you can find one number that disproves the reimann hypothesis, the entire thing is false, and you get the moneys.

Not necessarily the Millennium Prize. If you find a counterexample the CMI will check if it totally breaks the conjecture (meaning you are awarded the million), or if its usefulness will be only slightly weakened by excluding your case (meaning you get only parts of the prize money).

>>5942308

>>5942317
But if there's one counterexample then there's automatically four from symmetry, and each of those have four, and so on. Checkmate atheists.

>>5942323
Doesn't mean shit. The Zeta function already has infinitely many non-critical zeroes (the trivial ones). If you show, say, that there is a zero with real part 1/2 + 1/|z| for a sufficiently large z, then the main implications of the RH about the distribution of primes are virtually unaffected.

>>5941882

yes a 5y old can solve them too

I think the p=np will be the last of the millennium problems to be solved, if it is ever solved.

>>5942329
Then I will show there is a zero <span class="math">\zeta(s) = 0[/spoiler] with s = 7/8 + it. :)

>>5942179
Please respond

>>5941882

>given enough time, monkeys could write shakespeare
>still no monkey shakespeare

I doubt it.

>>5942311

Is that Bill Hicks?

Where are the Asians in math going? What the fuck is going on?

Gauss, Von Neumann, Euler, Perelman, etc.

See any Asians among the greatest mathematicians?

>>5942394
Ramanujan, Mochizuki, Tao...

>>5942394
Asians have a subservient culture not suitable for challenge like math/science promotes.
Gauss and Galois were both misbehaving assholes in school not having an ounce of respect for authority.
In asia this is looked down upon. In the west, this makes you a badass.

>>5942336
>dat pic

it's been three weeks since I saw the video and I still cringed.

>>5942398
>Tao

>>5942156
There is still a big difference between making someone feel he understanded concept and actually make him understand it in at least one interpretation.

There is also difference between explaining a new view on the subject to someone already experienced with it and introducing a new concept to a freshman.

>>5942438
http://www.youtube.com/watch?v=pVSj8vYFlFg&

>>5942446
yeah, sure.
I believe (but not 100% sure) that he is the guy who was in charge of this : http://www.dimensions-math.org/Dim_E.htm

I think it's great vulgarization. I remember I was not even in middle-school when the teacher showed us the first part of it. And I had to wait until uni to "fully" (notic the quotes") understand the whole subject.

But anyway, when I was in HS, I watched the whole thing, it was still interesting and beautiful, and I wanted to know more. That's why I think this movie is a "great one". He gave me the will to study math deeper.