Is there a finite amount of mathematical knowledge? Can you "solve" mathematics?

is there a finite amount of mathematical knowledge? Can you "solve" mathematics?

idk but we've made enough progress to know that noserings look like shit

pic related

If mathematics is ever solved then the mathematicians after that will generalize the problem of solving mathematics and then solve that and then generalize that problem too.

Given an infinite amount of time, an immortal being ought to have the ability to gain all knowledge, whether the total amount of possible knowledge is finite or infinite. Since mathematical knowledge is a subset of all knowledge, then this immortal being could of course gain all mathematical knowledge.

If we consider the entirety of the human race as one continuous immortal being, then if the universe never ends in time and the human race continues to exist for eternity, it may be possible for us to one day gain all mathematical knowledge.

That's the case if you take the limit, so to speak. At any specific point in the future there will be only a finite amount of mathematical knowledge.

Unlike the other faggots commenting here, whom most likely only know math from shitty Malone documentaries, the answers for this questions are crystal clear by now, thanks to the work of many people during (mostly) the 20th century.

No, there isn't a finite amount of mathematical knowledge (in the sense you would most likely define 'finite'), and no, we won't be able to "solve" mathematics.

There's a great story of how it all came down, you should start with George Cantor's foundational work on set theory, the criticism it aroused at the time and all the following work poking with some important questions arising from the Cantor set theory, and specially due to the Continuum Hypothesis, which can't be proven false nor true with "our" mathematics.
Later from that, Gödel made it worse, by proving that given any axiomatic basis on which you build your mathematics, there will be some theorems known to be true but impossible to prove as such (not all the time but at least Arithmetic is one example of such systems).
And then came Alan Turing and made it even worse, by showing that most problems are not decidable (can't be solved) and worse in the sense that there's no systematic way to tell those problems apart from those which are solvable.

The history on this subject and the story of how math was broken and then rebuilt is extremely amusing. However you will need some notions on some advanced subjects to fully understand the consequences of all of this.

>Unlike the other faggots commenting here

Ayy fuck you man.

No, math will always be incomplete as a consequence of Godel's theorem.

Build a system of maths in where Goldel's Theorem can't be proved and then we can live in blissful ignorance.

Based Godel. He took a shit on maths and left it with incompleteness, and told Einstein you can travel forward and backward in time.

Who's to say we're not already in that state of ignorance. My money is that Riemann Hypothesis is undecidable inside ZFC.

You see the number of important theorems, papers and things that start with "assume RH is true, then...", and is almost as if it was true but can't still prove it

Solving mathematics is actually a prerequisite for demonstrably proving or disproving P=NP, so it'd better be. There's a million dollars sitting in a vault not being spent on a pet monkey.

(1) It wouldn't be a system of math. Godel's incompleteness relies on logic and Peano's arithmetic.
(2) What you can do is build a mathematics where incompleteness doesn't apply, but this already exists, consider for example Presburger arithmetic.
(3) The problem is that there is no mathematic "good enough" to be both useful and decidable.

I am familiar with undecidability and I don't see how that answers the questions.

Then open your eyes and read the questions, faggot.

> Can math be solved?
No, no it can't.

Not true. There are limits to perception on both a micro and macro level. We are incapable of crafting devices that can measure or interpret phenomena on these imperceptible levels. It's foolish to think matter, energy, time, and space are all there is to perceive.

>It's foolish to think matter, energy, time, and space are all there is to perceive.
Do we have limits on our ability to conceive of abstract concepts?

>one day

you can't conclude that on the assumption. if k(t) is this person's knowledge at time t then if all knowledge is "infinite" then as the limit of k as t approaches infinity will "approach" "all knowledge" but is not reached at any particular time t. If Knowledge is infinite, it's not necessarily a "closed set" so-to-speak.

>if the universe never ends in time and the human race continues to exist for eternity
Also this

Crazy thought - if you know all math that there is to know... you basically understand everything that there is to know about logic entirely. You'd be math god of the universe - there would be no physics, chemistry, biology, etc that could confound you.

Meanwhile, I'm more interested in whether there will ever be a way to solve this problem:

Start at any number, if it's even divide by 2, if it's odd, multiply by 3 and add 1. repeat.

Every number we've tried will eventually collapse to 4 - 2 - 1 - 4 - 2 - 1 etc. But... will it always to so?

This problem annoys the crap out of me for not being solved, but FEELING like it should be trivial to solve.

Mathematics cant be solved, but Physics can be, if we can find the Grand Theory of Everything.

I feel like you can always ask "why" once more in physics, no matter how much you know. How could you possibly answer the question why the Grand Theory of Everything is the Grand Theory of Everything?

Can't 4 and 2 both be collapsed to 1... ?

define knowledge.

That's the Collatz conjecture

There's nothing to solve in Mathematics.

Mathematics mean absolutely nothing on their own.

I don't think we can get to the bottom of the definition without defining the words used in the definition.

I propose that knowledge in this context should mean that you'd get an A in a test about the matter.

Incredibly underrated post

define define

Knowledge = the number of books you have on your bookshelf in your garage next to your Ferrari.