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/sci/ - Science & Math

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2572940 No.2572940 [Reply] [Original]

Which one of the millennium problems would be easiest for someone to solve without any high level mathematics background? I am not asking which is easiest, I am asking which one covers the narrowest scope so that I can solve it without having to read up on 1,000 different topics.

>> No.2572980

>>2572940
1/10.

>> No.2572990

>>2572980
>implying i'm a troll
Someone on here has to have experience with these problems.

>> No.2573002

Some problems in math can be attacked by people with no background in the subject. Progress can be made with new ideas. By not knowing what everyone else done incorrectly you may have a better way of thinking and be able to solve the problems. If you proved N=/=NP then you'd know a lot about all the other problems on the list.

>> No.2573026

well there's not knowing high level mathematics, and there's not knowing low-level mathematics.

You won't be able to solve math problems if you don't know how to do math itself

>> No.2573028

> Birch and Swinnerton-Dyer Conjecture
Number theory

> Hodge Conjecture
Geometry, Algebra

> Navier-Stokes Equations
motion of fluids, high adventures in differentials

> P vs NP
Computation and complexity theory

> Poincaré Conjecture
Topology and differential geometry, but you are late

> Riemann Hypothesis
number theory, analysis, infinite series

> Yang-Mills Theory
geometry

>> No.2573041

I know I have a better chance of winning the lottery than solving it, but what is the harm in trying? I have solved problems without entirely knowing the concepts before so why not at least attempt it?

>> No.2573043
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2573043

which of the 8000ers is the easiest mountain to climb for someone with no legs or arms?

>> No.2573047

>>2573041
what problems have you solved?

>> No.2573064
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2573064

>>2573043

>> No.2573068

>>2573047

He's obviously solved the
Poincaré Conjecture

It has to be that because what moron would solve a simple high school problem by chance and then be stupid enough to believe that their experience is analogous to solving the toughest problems in all mathematics.

>> No.2573083

>>2573028
Thank you very much.

Best geometry/number theory textbooks?

>> No.2573086
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2573086

people that have failed to solve any of these problems include the most brilliant mathematicians out there, with decades of experience doing analysis, they are professionals at it, they get payed a lot of money just to analyze math problems.

Now, you are telling me, that you, a fucking high schooler from shittyville kentucky with shacky knowledge of basic algebra would come and seriously attempt to solve any of these problems?

you make my day op

>> No.2573090

>>2573068
grigori perelman is OP?

cooool!

>> No.2573109

Hey OP,
Go to the wiki article for one of the problems. Start clicking on terms you don't understand and go to their articles. You'll have a whole bunch of windows opened up soon.
Lots of times you need a doctorate just to really understand what the problems are asking and the full complexities of their details.
Do something productive with your time, like ride a bicycle.

>> No.2573113

>>2573086
>>2573068
What's with the hate?

Didn't you guys hear about the college undergrad that solved one of his fields "impossible" problems? He was in class and copied the problem down and thought it was HW. He did it and handed it in one night and handed it in to his professor, not knowing that he had just solved one of the hardest problems.

>> No.2573125

http://www.claymath.org/millennium/P_vs_NP/Official_Problem_Description.pdf

>> No.2573129

>>2573113
he was a PhD student

george dantzig

>> No.2573137

>>2573113
ahhahah lets see the source, sounds interesting

>> No.2573156

>>2573129
My point still stands. Had he known what the problem was labeled as, do you think he would have solved it?

Do you think that he was smarter than everyone else that had tried to solve it or that he worked harder because he thought to himself "this is just a simple homework problem"? You don't have to smarter than everyone else who has attempted the problem to solve it; maybe my unique point of view is what was missing, probably not but why would people rage over this?

>> No.2573167

>>2573137
http://www.snopes.com/college/homework/unsolvable.asp

>> No.2573188

>>2573156
because your are insulting those mathematicians that dedicate their lives to it, by being so fucking naive and ignorant.

Stating that you may be able to solve the MPs with 0 experience in analysis, and reading fucking basic geometry books pisses anyone off.

>> No.2573200
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2573200

Even though none are solvable without studying math at a minimum time of 3-5 years just to get into the subjects, probably the "easiest" is the Yang-Mills Theory problem.
The algebra related ones carry an enourmous baggage of abstract formalism which you can't learn without spending many years (it's probably just not possible in a "short time" to learn it), the Riemann Hypothesis is just over ninethousand years old and it's just not probable that there is a solution which can be reached with current math anytime soon the P vs NP and the Stokes problems as tideous existence problems of the worst kind, and the Yang Mills problem also hasn't been solved even though there is enourmous interest in it from many sides.
BUT the point is that the Yang Mills problem is about Fibre Bundles, Fields and related geometrical concepts and it's possible that someone who for example grasps general relativity very easy, who's good at visualizing can see the problem in some way.
From time to time there are normal humans who are good at geometry or number theory, so you have your best "chances" there.

>> No.2573214

>>2573156
>>2573156
> Do you think that he was smarter than everyone else that had tried to solve it

yes, or very close.

you may also be as smart but if you want to solve these, here is the proven method of doing it, the one your hero george dantzig took

get into a university and study maths

>> No.2573216

>>2573156
> Do you think that he was smarter than everyone else that had tried to solve it
yes

>> No.2573228

>>2573200
and by fields I mean gauge fields, not rings with inverses

>> No.2573230

>>2573167
it wasnt a "unsolvable" problem. it only lacked of a proof, its very fucking different than the millennium problems. besides he hold a BS and MS degree in math.

>> No.2573231

Are you trying to say that I have NO chance whatsoever at solving those problems? There was nothing wrong with my statement; sure, my chances are almost 0, but I still
>may
be able to solve the MPs with 0 experience in analysis, and reading fucking basic geometry books


Any recommendations on those books?

>> No.2573233

>>2573156
> Had he known what the problem was labeled as, do you think he would have solved it?

well, i guess as you know how these problems are labelled, you aren't going to solve them

>> No.2573245

>>2573231
the chance is about that of a quadriplegic climbing Everest unassisted.

thing is you won't even be able to understand the problems.

i have a degree in maths and i don't understand some of them.

how can you solve a problem you don't understand?

>> No.2573246

>>2573156

He might not have been smarter than anyone else who had tried to solve the problem, but he was a PhD student and had all the necessary tools to do it. He at least knew what the questions were asking him to do and didn't need to spend much time reading books to learn the concepts one needs to understand to be able to solve them.

The problems you're thinking of solving are orders of magnitude more complex and you have nowhere near the same amount of knowledge that Danzig had when he solved two easier problems.

You sound as deluded as those people we had on a few weeks ago who thought they could beat a gorilla in a fight armed with no more than a baseball bat.

It's interesting that the pic in your OP is from a Hollywood film, because that's the only place where someone with no high-level mathematics background could solve one of those problems.

>> No.2573254

>>2573231
Ok kid, solve the MPs, stop wasting your time stating that "you can do it" and start doing something about it.

Good luck :)

>> No.2573263

>Hi. I'm a retard.

>how do I stop being a retard without actually >stopping being a retard?

>> No.2573286

>>2573245
That's why I'm asking for textbook reccomendations so that I can read up on the topics that I need to. You don't need to completely understand a topic to solve it.

I can take a 3rd grader and give him the books with the steps to solve a polynomial and then give him a polynomial and, with enough, time.... ta-daaaa he solved the problem. Does that mean he completely understands why everything works or that his math is at high school level? No.

Infinite monkeys on infinite type-writers will eventually type out shakespeare

all it takes is time

>> No.2573292
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2573292

OP, one problem with this is probably that you have kind of a wrong perception of these kind of problems. You say you have solved problems before but this just means these where problems formulated in terms you already know.
But for example one of the problems is related to elliptic curves, take a brieve look at that page and read the intros of the chapters

http://en.wikipedia.org/wiki/Elliptic_curves

the definition of the thing itself might be relatively easy but as it turns out this objects has unexpected properties you can't "see" from looking at it.

Or these

http://en.wikipedia.org/wiki/Elliptic_integral

See, you can't just read a book and solve the problem, because you'd have to study math from scratch just to get the question.

It's like you just learned all the rules for intergration and someone says integrate x^x. you won't instantanously know the answer

>> No.2573308

>>2573286

>Infinite monkeys on infinite type-writers will eventually type out shakespeare

There isn't an infinite number of you and you don't have infinite time. Although it is technically possible for you to solve one of these problems, you'd be much better off buying a lottery ticket or running for president/prime minister/king in whatever country you live in.

>> No.2573312

>>2573263
advance

>> No.2573323

I fucking love Navier-Stokes.

>> No.2573325

>>2573286
galois showed almost all polynomials can't be solved

lol at captcha BIRKHOFF Creli

http://en.wikipedia.org/wiki/Garrett_Birkhoff

i swear someone manipulates these captures for comedy effect

>> No.2573330
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2573330

There is a nice documentary online which is about the man who solved Fermats Last Theorem in the 90s

http://www.youtube.com/watch?v=SVXB5zuZRcM

cheerz

>>2573292
btw. the two links aren't really related but both are examples for mathematical objects which carry some secrets

>> No.2573331

>>2573286

>That's why I'm asking for textbook reccomendations so that I can read up on the topics that I need to. You don't need to completely understand a topic to solve it.

This is not fucking true. That analogy you gave with the third grader is mechanical than anything else. As a Mathematics tutor, I see people attempting to learn Mathematics in a mechanical manner and it just doesn't work. Even if that 3rd Grader could solve that specific polynomial, it doesn't mean he can solve several others which have differing properties.

In order to solve some of these problems, or even one, you need to comprehend the basic structure/foundations which underlie them. You can't just buy a shitload of books, read snippets of them and say, ''oh I comprehend this lol.''

There are people who dedicate their entire lives to these problems, and many more have died in VAIN to fucking solve them. Can you imagine living your entire life in an attempt to solve a problem, and never doing so? That's an excruciating way to die and many have felt that anguish. That original post you made is flying in the face of every Mathematician who has ever attempted solving one of those MP problems. You're getting a pissed off reaction by the denizens of /sci/ because of this. You're shitting on them tremendously. You also said, "all it takes is time." While that is true, it's not like human life is infinite. It could take the next 500 years for another solution to come about.

>> No.2573337

lol delusions of grandeur big time

>> No.2573346

>>2573200

Yangs mills is the fucking hardest of the problems. You got a shit ton of Mathematical Physicists working on it. The problem is complex as fuck.

RH is way more easier to understand as you just need two years of uni. Not fucking five years of uni and deep understanding of mathematical physics.

>> No.2573351

>>2573325
every individual polynomial can be solved since C is algebraically closed.
what you mean is that for polynomials of almost all degrees there can't be given a closed formula for the solution

>> No.2573368
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2573368

>>2573346
I gave an argumentation why it might be solvable for someone. I know that it's "fucking hard" but all the problems are.
If this formulation even makes sense, I'd say the Stokes Problem is the hardest. Well that's the one I'd not want to work on at least.

>> No.2573369

>>2572940

If you are serious about solving them, you're going to have to buckle down and get serious. Be prepared to literally spend all your free time learning mathematics. The people who are best at subjects spend all their time focused on that one subject, so you'll have to quit your job and do nothing but math.

You should also be doing the problems for their own sake, not for the money. It's the only way you'll be motivated.

http://www.ted.com/talks/dan_pink_on_motivation.html

These two go without question. Finally, I suggest you enroll at a university to learn math. Having friends and faculty around to go to and ask questions will make your life infinitely easier. But if you do want to go solo, I'd suggest looking at MIT opencourseware. You could also look at the required textbooks for a random top 10 undergraduate math curriculum and find them here http://bib.tiera.ru/ and spend all your time reading through them.

By the way, I wouldn't go for the "easiest" problem. Instead I'd suggest reading up all the problems until you understand them fully, then choosing the one that interests you the most. It will be the one easiest for YOU.

Good luck OP, I believe in you!

>> No.2573377

>>2572940

None.

Trolls on here might say P versus NP. But, lets me real here. You aren't going to solve it.

>> No.2573396

>>2573368

Yangs mill isn't about GR. You are a fucking idiot who doesn't know what Yang mill is. Fourth year Mathematical Physics student and like no one I know understand Yangs mills. So to claim someone with no Physics will understand it is stupid.

The point is you need atleast grasp what field theories are. Which, take about 30-60 hard books assuming you are self teaching.

>> No.2573413

>>2573351
>>2573351
> inappropriate pedantry alert

you sound like a fun kind of guy

>> No.2573422

Seriously OP, don't waste your time.

>> No.2573443

Putting the shitstorm that is this thread to one side, which of the MPs would bear the most fruit if solved?

>> No.2573450

>>2573396
>Fourth year Mathematical Physics student and like no one I know understand Yangs mills.
?

I think my understanding of Yang Mills Theory is not too bad. I don't quite get what you're saying, of course it's very hard and it is different from general relativity.

>> No.2573470
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2573470

>>2573443
define.
there are some other proofs relying on these conjectures and these people would be happy.
The "wrong" answer to the NP question would have catastrophic results since then people would heavily investigate how to fuck other people up.
The Yang Mills problem is very physics related, but it would not change much in the real world in the sense that physicists do pertubation theory anyway. The Navier-Stokes Equations Problem is pretty similar, a prove would be nice, but it probably won't solve anything else.
Besides the first point I made, the other problems are of very academic interest.

>> No.2573499

>>2573396
>Fourth year Mathematical Physics student and like no one I know understand Yangs mills

What? Its not exactly difficult to get the basic idea of Yang-Mill theory, Im a third year student and I understand the basics just fine.

>> No.2573519

>>2573450

Got nothing to do with GR. You need to understand QM, so you would need to have good foundation in functional analysis. Which, imples you know basic analysis.

Herp derp OP doesn't want to read books.

>> No.2573573

>>2573519
all this time I've been asking for textbook recommendations.

Can /sci/ decide on easiest one to solve already?

>> No.2573585

0th: I just took gr as an example of a geometric problem in my first post, I don't know where the rage comes from, as if I'd implied they were closer related than they are
>>2573519
okay, now that's just not true.
firstly both theories can be understood in terms of fibre bundles, both are in the realm of Cartan Geometry with a little more structure thrown in (little differential calculus or a metric strucure). I'd argue that knowing gr gives you a better basis than knowing QM. In any case you seem to be far on the physics side if you imply that you have to quantize the "fields" to work with yang mills theory.
Classical Electromagnetism is a Yang Mills theory with an 1-dimensional bundle and the usual F=dA field strength. If you work with U(1) for starters, I don't see why QM would really come in handy here. If you don't need QM, then you don't need too much functional analysis eighter.

>> No.2573591

>>2573470
The proof of consistency of Navier-Stokes would be very nice, it'll probably show us some way to actually solve them.

>> No.2573598

>>2573499

Third year fag. Lol that reminds me when I thought I knew the basics of QM, then I hit fourth year.

>> No.2573630

Math major here, how hard can a math problem be to understand?
>Yang–Mills theory is a gauge theory
wat
>In physics, a gauge theory is a type of field theory
wat
>Quantum field theory (QFT)[1] provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized (represented) by an infinite number of dynamical degrees of freedom, that is, fields and (in a condensed matter context) many-body systems.
wat
>A conceptual framework is used in research to outline possible courses of action or to present a preferred approach to an idea or thought.
Oh I see.