Non euclidian geometry is still based in the real world. its a matter of euclids 5th postualte and attempted to discern if the universe is governed by euclidian or non euclidian geometry.

it is not possible to decide through mathematical reasoning alone if the geometry of the physical universe is Euclidean or non-Euclidean; this is a task for the physical sciences. János Bolyai



so we can conclude that all math has some application o the real world or its useless. aswell its often times based off of other math rooted in the real world as an attempt to simplyfy or improve upon the math.

This post was edited by Ylem122 on May 6 2013 11:36pm

Of course it is, but the reality is that Euclidean and some non-Euclidean geometries have been shown to both be used as good models for different physical phenomena. Given that these basic axioms do seem to fit reality in some specific realms, mathematical reasoning alone can lead to great insights. I don't care if the entire universe is non-Euclidean, I care if a model based on non-Euclidean geometry produces good predictions about some specific phenomenon.



Well, it could be useless for now, and I don't put any stock in the alleged beauty of pure mathematics, but we can't tell if it will be useless forever. Oftentimes, it hasn't turned out this way (see Hardy, number theory, and the other things we've discussed). I don't think it's so hard to understand why -- it will necessarily be at least tangentially related to useful areas of mathematics, and if it leads to linkages between these areas (as it often does), there's a high propensity for that sort of thing to lead to something useful.

We have to remember that, unlike sciences, the math doesn't care what it's describing -- sometimes we find the same math is good for very unrelated phenomena (e.g. compound interest and radioactive decay behave almost identically from a mathematical standpoint as I mentioned above).

pure mathmatics were never useless, and allways had real world applications.

it was not so much how math effected the real world that hardy seperated himself from, but how it effected humanity. it was still very much connected to reality.

This post was edited by Ylem122 on May 6 2013 11:56pm

Not necessarily, quite a lot of theory on primes were established before they were really used for anything.



I don't see how it would be connected to reality but have no effect on humans. He didn't only say it had no bad effects, he said no good or bad effects:



This post was edited by N1ccolo on May 7 2013 12:09am

such as?

1

direct application to humanity in good or bad? no.

direct applcation to most anything that exists? yes

no direct application to humanity, an undeniable relation ship with the real world.

This post was edited by Ylem122 on May 7 2013 12:15am

I don't know what you're asking for, theory on primes before they were used for much? Euclid showed there are infinitely many primes, showed that any natural number can be written as a product of primes, Eratosthenes showed how to compute primes. Fermat, Marsenne, Euler, Gauss all studied and found results on primes.

This post was edited by N1ccolo on May 7 2013 12:20am

I don't understand what you're talking about. The number 1? Obviously it helped us with things.. o_O

how so?

what about graph theory? started off as purely recreational mathematics and now is essential for many fields
and how much application did boolean logic have when it was establsihed?



is music useless? is philosophy useless?
mathematics as a research field are self-sufficient and often l'art pour l'art
and quite frankly i don't care if you consider it useless
because with so many at the time useless results mathematics have helped more to advance science and technology than anything else

you can put alot of real world data on a graph.

An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, seems kinda real world appliciable.

while they maybe useless at the time math, in respect to humanity, in my reguards what makes it useless is the lack of real world application, and none have shown this yet. a math not based in the real world or not appliciable to the real world, dosnt seem to exist.

though if it did, it would be useless.

cept for maybe primes, cant find a single use of them aside from the coming of cryptography 2 millenia+ after they were first talked about. perhaps its more a case of recognizing them and thus working to avoid them in real world applications, as a number undividible by any number other then itself and 1 might cause issues, that brought about their study.

This post was edited by Ylem122 on May 7 2013 04:25am