>During the first half of the twentieth century, mathematicians

>>58798580
Yes, and if you're interested in this here's a set of lectures that explain exactly these kinds of problems that can't be solved by computation

http://scs.hosted.panopto.com/Panopto/Podcast/Podcast.ashx?courseid=bcf8243e-cf18-481f-960f-3c5b26fbb69b&type=mp4

Lecture one, talks about this very same thing.

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>>58798635
Does this fall under the P versus NP problem?

>>58798635
Oops, here is the streaming version but you should download these in case they disappear https://scs.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=e4e4c48c-dc8a-4775-b1c8-a6dfb08303e5

>>58798635
Thanks, will check them out. But, pardon the inexperience, how do we even accept true or false in programming, why doesn't 1 and 0 count as a predicament? What am I missing?

Yes, i also heard that Noam Chomsky proved that no computer model can prove that 1+1 is really 2, because computers only deal with approximiations due to the IEEE floating point data types, meaning that no computer can even display the number 2, only 1.99999...

>>58798580
You've slightly misunderstood what they proved. It's not that computers can't determine the truth of a statement. For example, any computer could determine the truth of "4 == 2 + 2". Computers can even prove theorems. There's actually a lot of effort going into automating mathematical research.

What the mathematicians you mentioned showed was that there's no guarantee that computers (or mathematicians) will be able to determine the truth of *arbitrary* statements (more precisely: with a finite number of computational steps). Basically this means that there will always be some true propositions than cannot be logically proven to be true (by mathematician or machine).

>>58798681
>To view this content install or enable:
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Dropped

>unironically discussing philosophy of math

lad...

>>58798794
So, the paragraph refers to the integrity of axioms? Is that what the computers cannot determine as 'true' or 'false'?

>>58798815
Just trying to figure out what the theory of computation is about.

>>58798797
That's why I posted the download links too >>58798635

It's a Carnagie Mellon course on theoretical computer science math/intro

>>58798698
You would know all this if you watched the lectures. Some of your questions require a 20 minute presentation by a professor to show you as they are not easy answers since whatever answer I give you will just produce more questions as you don't have the background.

The second and third lecture covers 'truth' by discovering it through propositional calculus, formal axioms ect.

>>58798828
Not the integrity of the axioms, but their reach. For any axiomatic system, the set of true propositions in that system is not wholly covered by the set of true propositions that can be logically proved based on the founding axioms.

In the case of computers, there are true equations that cannot be proven to be true with the arithmetic axioms.

>>58798667
Go fuck yourself. Stop pretending to know things you have no clue about, you dirty piece of shit.

Computers actually cannot prove that pi is a finite number because it requires 12 years of computation power to solve that problem, and computer scientists aren't very patient

>>58798954
>In the case of computers, there are true equations that cannot be proven to be true with the arithmetic axioms.

Sorry, this is badly worded. Here's better:
there are true equations that cannot be proven to have solutions with the arithmetic axioms (i.e. can't be solved with the algebra maneuvers you learned in high school).

>To view this content install or enable: Adobe Flash Player
>*disables umatrix*
>To view this content install or enable: Adobe Flash Player

what

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>>58798975
I asked a simple question, you dumb nigger. I don't pretend to know anything, that's why I asked.

>>58798794
Hilbert's 10th problem to be exact, which he added in 1928 to ask "Is there a finite procedure to determine the validity of a given logical expression?" meaning a Betrand Russell type expression such as "In this set, there exists A such that..".

Finite procedure meaning, an algorithm. This was proven no by Church-Turing and the rest of the lectures in that series show you exactly why it was proven no and other problems that have no computational solution outside of approximations such as Max Cut.

>>58799061
It's related but since it's an undecided problem it isn't considered NP-complete (being both NP plus NP-hard). http://cs.stackexchange.com/a/1888

This explains how the definition of NP is that it consists of all problems that are decidable (not just verifiable) in polynomial time and Hilbert's 10th question is undecided

Of course all these terms in that answer would make sense if you saw all the lectures. You really only need high school algebra to understand it.