# The End of (Mathematical) Times [closed]

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).