How do you deal with the fact that most of problems in math are either solved or really hard? There's no room for research unless you're memechizuki or you're willing to think up and solve some irrelevant problem just to publish a shitty article that no one will ever be interested in
i was thinking about a particular problem for some time, today i made a google search and some faggot wrote down the same thing 100 years ago
>>7974424
>some faggot wrote down the same thing 100 years ago
lel, 3 hours in the library will save you 3 weeks in the lab
here's tao telling you you don't have to be a yokuzuna of math to contribute to the field
https://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths/
so stop sperging and get back to work
>There's no room for research
I dont think you should be in research
>>7974424
finding a new solution to an already solved problem is just as laudable
if your solution is neater, it may even find its way into textbooks one day
What's 24 times 62?
>>7974424
I think that one of the most interesting aspects of mathematics is that problems that once seemed hard suddenly seem easy once they've been solved.
In one way, you could look at this from the perspective of a proposition of one existing hard problem: P vs NP. Godel asked von Neumann in a letter whether or not it was possible to construct an optimal Turing machine for the problem of deciding whether or not a proof exists for a prepositional logic formula F, and he posed that, if this machine operated in linear or quadratic time (though now we consider any generic polynomial amount of time to be sufficient), we can use a machine to determine whether or not it's worth our effort to continue thinking about a problem.
Now let's say we took an instance of a 'hard' problem and a valid solution. We can now verify this solution very quickly, and the question, by this fact, seems easy. The issue at hand, given an unanswered 'hard' question that is seemingly easy to verify, is whether or not finding the answer to that question can be done in an amount of time feasible to mathematicians (what Godel equated to linear or quadratic time).
If, in fact, P != NP, it's very likely that there problems out there that you can't generate a proof for in sub-exponential time, and therefore, as time continues, we'll asymptotically reach a point where all of the questions that can be answered are answered, leaving us with only the questions that can't be answered in an amount of time feasible to humans.
If P = NP, that means you're just a little bitch because you can't figure it out.
Want to know if you're a bitch? Go solve P vs NP.
>>7974424
This is why I do engineering, not only are the problems more accessible to the amateur but once you solve it you can make money from it.
>>7974424
>How do you deal with the fact that most of problems in math are either solved or really hard?
Why would you do math if you don't want to try and solve really hard problems?
Mathematics would be pretty boring if you could just look at a problem for 10 minutes and have a full solution.
>>7974424
It fills me with awe and wonder, like an infinitely complex graph is unfolding before me and it'll go on forever no matter how many patterns you find.
Then I realize I'm one of those nodes and the math collapses back into a singularity of utter simplicity.
>>7974468
>If, in fact, P != NP, it's very likely that there problems out there that you can't generate a proof for in sub-exponential time, and therefore, as time continues, we'll asymptotically reach a point where all of the questions that can be answered are answered, leaving us with only the questions that can't be answered in an amount of time feasible to humans.
>If P = NP, that means you're just a little bitch because you can't figure it out.
Fucking best way I've ever heard the implications of this problem explained. topkek
>how do you deal with the fact that most of problems in math are either solved or really hard?
That's a misconception. Seriously. People asked me the same thing when I said I wanted to do research in math.
There's plenty of room for research and new discoveries in math beyond those few super famous number theory problems. Ask your professor.
>>7974670
>tips graduation cap
>>7974616
faggot holy shit
