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When I am sufficiently content with the life I have been experiencing, I would like to think about hopeless problems so that I can start suffering again. One of those problems is related to the end of mathematical times, or say, the asymptotes of human comprehension/development of mathematics. Putting these arguably-ridiculous teasers aside, the question is more or less the following:

Would the humans be able to create (or discover) new mathematics in the (distant) future?

Let me elaborate a little with some heuristic arguments that could all perhaps be made a part of this discussion. If you were living in the ancient Greece, you would pay a visit to Euclid, and he would give you his "Elements," or better yet, you could attend his one-year lectures on geometry, and viola, you are now ready to do research (You may disagree with this oversimplification, which is fine).

Today, if you want to do math research, it seems that you should spend a considerable amount of time (assuming you know $0$ math, I think it should take on average $8$ years? of hard work) to be able to contribute to anything. Well, several counterexamples can be provided (Voltran Kerimoff knew nothing, he spent just 2 years and settled the Artichoke Conjecture), but my point still remains. The mathematical knowledge is, as I write these lines, increasing monotonically, and I guess it becomes harder to anyone "new" to catch up.

Now, think about the very far (or maybe not so-distant) future. Would the theories become so complicated that even learning them will take more than the average human life span? If that is the case, then the mathematics will cease to improve any further after some point, and we may witness dialogues like this:

Grandpa: So what do you want to do Jim?

Jim: I would like to be a mathematician like you Grandpa (I have yet to see a child say this, but anyway..)

Grandpa: Are you crazy? I was just be able to publish my first paper.

I would like to get your opinions about possible resolutions of this matter. Here is "what I have tried," or, say, my opinions on the subject:

  • Human intelligence (whatever that is) will increase as time goes on. As a result, we will be able to understand very complex things much easily. For example, a 9-year old boy in year 2651 will say: "I cannot believe those guys spent 500 years solving that Hadamard conjecture, it is just matrix fultiplication dude." (Note: Fultiplication is not a typo, that is a "high-level operation" that we do not know about for now).

  • We will learn to skip many details in between: In a number theory book to be published in 2700s, Generalized Riemann hypothesis would be stated as Lemma 1.2, and the proof will be skipped since it is trivial (perhaps via fultiplication as discussed above).

  • Computers will take over (I guess this is clear, automated theorem proving, etc.).

  • Education will be readjusted so people will learn algebraic topology (in a never-seen-before great-and-simple exposition) in primary school.

  • Don't bother as we shall destroy ourselves in the next 50-or-so years.

  • Mathematics has limits anyway (I would disagree with this).

Thanks for reading.

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closed as not constructive by Asaf Karagila, Rahul, Clayton, Micah, Apostolos Feb 2 '13 at 0:24

As it currently stands, this question is not a good fit for our Q&A format. We expect answers to be supported by facts, references, or expertise, but this question will likely solicit debate, arguments, polling, or extended discussion. If you feel that this question can be improved and possibly reopened, visit the help center for guidance.If this question can be reworded to fit the rules in the help center, please edit the question.

That's an interesting problem but I don't think it fits this website. –  Asaf Karagila Feb 2 '13 at 0:07
I agree with Asaf. The description of the close-as-not-constructive option says, "We expect answers to be supported by facts, references, or specific expertise, but this question will likely solicit debate, arguments, polling, or extended discussion." I think that applies pretty well here. –  Rahul Feb 2 '13 at 0:12
This is sad; the editorial board should sometimes leave it for the community to decide or at least wait for a few answers for the asker's sake. What is ironic is that if I were a "famous mathematician," I am sure this would not happen, and all your "criteria" would just somehow fail. I consider your decisions unfair and unjust, especially against someone who is trying to contribute. –  Anon Feb 2 '13 at 0:43
@Anon I'm sure that last bit about a famous mathematician felt good to say, but there is absolutely no historical ground for believing the staff here would behave that way. There is occasionally room for debate, but it seems like this question is as open and shut a case as there is (IMHO, of course). –  guy Feb 2 '13 at 0:55
"Besides, my question does not hurt you" But no, it does hurt the rest of us. It leaves one less spot on the front page for someone with a concrete, answerable question that will now get less attention. It leaves me with one less concrete, answerable question that I am likely to see and possibly answer. Its presence encourages more discussion-y, speculative questions to be posted in the future at the expense of concrete, answerable questions. If you want to argue that your question should not have been closed, then arguing that leaving it open has no external effects is not the way to do it. –  Rahul Feb 2 '13 at 8:38

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