What are some interesting open questions in mathematics?

>>>/global/rules/3
>You will not post any of the following outside of /b/: Trolls, flames, *RACISM*, off-topic replies, uncalled for catchphrases, macro image replies, indecipherable text (example: "lol u tk him 2da bar|?"), anthropomorphic ("furry") or grotesque ("guro") images, post number GETs ("dubs"), or loli/shota pornography.

>*RACISM*

What I said is not racist though. Nowhere in my post did I say that I hate niggers or that I think niggers are inferior.

Also, I'm hispanic so take your white privilege off this campus.

Not the same user, but using nigger is racist.

>Can you reduce the black population of your nation to just one with this method?
Your question literally implies mass deportation and ethnic cleansing.

And yes, hispanics can be racist.

>using nigger is racist.

Says who?

Fucking white cavemen, could you stop being offended on behalf of other people?

This is why I fucking hate white people.

Please rephrase my problem by changing the word nigger with the phrase 'fucking white devil'

Well, that is the actual Collatz Conjecture.

>hypothetically deporting people is RAYCISS

I'm actually arab.

It would be racist either way, plus completely offtopic. This isn't /b/. Go act like a schoolchild over there.

Then lets hate on white people together, my nigga.

No, hating white people is reverse-racism.

Do you EVEN know anything?

Stfu and leave the thread, go back to /pol/ or /b/

Wait, are you deporting a racial minority out of your board?

Ironic, isn't it?

It must be lonely, and here you are seeking attention from a few anons in Veeky Forums.
This is the last (you) I'm giving you, cya

>oh no, muh racism that is completely harmless because this is just a retarded message board

>better go completely apeshit!

doesn't it only imply mass deportation if the collatz conjecture is true? otherwise you won't get rid of them

You guys are shit

> literally cannot produce a problem that is interesting and not outside the few mentioned on wikipedia

nigger

is it your homework to find an open problem and describe it to your classmates or something? can you not use google or something? there's whole books on this topic, people have better things to do than copy them out to you

maybe I'm just interested and have already looked into most of the popular ones

Say you're somewhat good at math and can study any graduate book without much trouble. Now, you fantasize about solving a very difficult problem.

How do you know if someone is already working on it if you're not an academic? You catalog and study all the papers regarding the problem?

trip fags are the worst.

>How do you know if someone is already working on it if you're not an academic?
If you know it's a 'very difficult' problem that's probably because many other people have tried and failed. You should assume someone if already working on it.

And how about easier problems? There's a book called Open problems in topology II - Elliott Pearl (2007). But it's 2016 now. How does one know if a problem has been solved?
>Picture from: Open problems in topology I (2003).
A lot of these problems get solved apparently.

>How does one know if a problem has been solved?
hope that the literature is available and up-to-date

>hope that the literature is available and up-to-date
Thank you.

Is it possible to use chords to divide a circle into equal-area pieces, none of which are congruent?

When does 0.9 repeating round up to 1?

Interesting

Well there is a proof that .999... = 1 in the sticky, but I personally don't buy it and would say that .999... is 1 - an infinitesimal and does not have a fractional representation

However this problem is of absolutely 0 consequence so I don't care

>there is a proof that .999... = 1 in the sticky, but I personally don't buy it
Nobody cares what you think, bitch.

If a proof is logically valid, it is a valid proof. Zip, zero, nada. No ifs, ands, or butts.

0.999.... is exactly the same as saying [math]\lim_{n\to\infty}\sum_{k=1}^{n}\frac{9}{10^k}[/math] which is PRECISELY equal to 1, and there is nothing you can do about so you better start crying now.

I don't give a fuck who cares what I think, that is not an argument.

I think not all numbers have a fractional representation just like not all numbers have a digit representation. 0.999... repeating is what I know to be the first number less than 1. 1/3*3 = 1 because we know through the definition of division that .333... defined by 1/3 is not the first number less than .333..., but .333.., however .333... - the smallest number greater than 0 is also a valid number

the nearest integer to e^n is prime for infinitely many values

>the smallest number greater than 0

You're essentially talking about nonstandard real numbers.

Can one define limits in nonstandard reals in such a way that what you're saying becomes true? I don't care enough to check atm. In any case, if you define numbers like everyone else does, .999... = 1.

>the smallest number greater than 0

You have much to learn, my friend. I implore you to consider defining such an object. Without, of course, worrying about the fact that any value x which satisfies this assumption is trumped by x/2 ad infinitum. This is essentially a proof by contradiction that no such smallest number greater than zero can exist--you've constructed a set with a greatest lower bound/infimum yet this minimum is never achieved.

Why do you 'think' that not all numbers have a fractional representation? This is, in fact, true. There are irrational numbers, and those have even nastier numbers contained within them known as transcendental numbers. None of these have an exact fractional form. You should realize, however, that a decimal expansion is defined by a power series much like provides. It's a recursive construction based on remainders in base 10, and so you get a power series where each next term is of order 1 but contains a power of 10^(-1) compared to the previous term. Since the decimal expansion can be realized by this power series, and this series has a known value, the decimal expansion is equal to this value.

Healthy skepticism is warranted, but just denying things because of your feelings is almost as bad as believing everything without proof anyway.

If it's interesting it'll probably be one of the ones mentioned on wikipedia. I don't get why that's surprising.

If it's an "open" problem then someone's studying it. If it's not a recognized unfilled hole yet it's not really open, it's just not addressed yet.

The quick way would be to see if Erdos ever offered someone 20 bucks to solve it. That'll cover most unsolved problems. Beyond that you'd have to ask around on stackexchange or something.

What I'm talking about is still a number without a digit representation.

I don't have the standards for interesting a normal person does

What's your background? Most open problems in mathematics that are "interesting" are "interesting" because they're relatively easy for laymen to get the gist of. Further questions, resting on current research, will be far more niche. I'm a published mathematician (main author) and 99% of the questions I could find would be outside my field and pretty close to gibberish to me.

Coming from a faggot I think you're a raging homosexual but that's not a bad thing is it?

My background is NEET

I enjoy trying to understand/apply my problem solving skills to hard problems because I end up learning a lot.

It's hope of actually getting it that keeps me interested

reread what I wrote, m8. Your current issue with the standard proof essentially 'I don't believe in it, because I don't like the idea of it.' A digit representation is an algorithmic way to express a number--independent of what that number is. Some expressions are finite like 3,4,5, or 6.28. Some are infinite like 1/3=0.333... or e. Some are redundant like 1 = 0.999... . This ties back, again, to your lack of understanding about the real numbers themselves--like claiming a smallest real number greater than zero. Yeah, if you Google around you might find something like the construction of hyper-reals, but this isn't actually what they're meant to solve. It's more of a concrete algebra of differentials.

Seriously, is not an excuse to blindly be upset by things but should be a motivator to actually learn about them--rather than just nitpick, incorrectly, the semantics.

There's not many other open problems you'll be able to understand then. It's not just the difficulty, it's understanding the basic concepts involved and the language used. You'd need to get an early graduate level survey of all normal fields under your belt and then pick an area to study heavily. There's still a lot of open questions in logic/computability theory and in the modern tendrils of analysis. I'm not sure about how deeply populated the other major areas are but I have a general impression that they're still fruitful but less populated.

I'm taking "open" questions here to be questions that people have wondered about and worked on for 10+ years but for which no proof has been found yet.

The question was can you reduce the nigger population to one. The answer is yes, but then it cycles, but the answer is yes, but then it cycles. So really, you get waves of high and low populations, it's kinda cool actually.

what if it's 4 niggers where 3 of them just keep walking back and forth between the US and Canada?

Could you please post your proof that it gets to 1 for any starting number?

ERDOS GO HOME

let f be an irreducible polynomial of degree n.
let v(f, p) be the number of distinct values that f can take mod p
p_i is the sequence of prime numbers
then
[eqn] lim_{i \rightarrow \infty} v(f, p) = \sum_{k=1}^n (-1)^{k-1}\frac{1}{k!} [/eqn]

...

Reeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee NORMIE !!!!!!!!!!!!!

Then go back to raping some white woman, or oppress some jews. Whatever you do get the fuck out normie

1220496076800.

Now fuck off.

[eqn]\lim_{i \rightarrow \infty}[/eqn]

sofa problem, RH, an Erdos conjecture (with someone else) relating to Egyptian fractions, and a personal favorite:

does a perfect cuboid exist?

I've done some very basic (read: babby) research on this one, proving a few easy lemmas for myself. Basically just gathering information relating to the problem.

Some interesting problems have come up on stackexchange:

math.stackexchange.com/unanswered/tagged/?tab=votes

Nigger

The permutations may overlap but must be contiguous.

How can Hispanics be racist if they don't have power?

Tacos seems to have a lot of power in Mexico and Central and South America.

Yeah but these rules should be broken if it is funny to do so.

>It only implies mass deportation of the Collatz conjecture is true

Brainlet detected.

It could also mean below replacement level birthrates, which are already happening to blacks in the United States, as well as whites and Asians, and soon Hispanics will be under too.