What Are the Most Fascinating Aspects of Purely Theoretical Mathematics?

[Shahil]

Can somebody please help me out!

I was just wondering if anybody can give me any website links or information on a branch of mathematics which is purely and utterly theoretical and has no practical usage and value whatsoever.

I know that this sounds a bit odd as maths is suppose to help us out but I'm just interested in pure theoretical maths.

Thanks

 

[lethe]

Originally posted by Shahil

I know that this sounds a bit odd as maths is suppose to help us out but I'm just interested in pure theoretical maths.

Thanks

mathworld

there is no such thing as theoretical math, though... only theoretical science...

 

[Shahil]

Does that mean all mathematics has to have a meaning?

I remember when I was in school, my maths teacher (who is quite brilliant) said that geometry and riders have no practical purpose?

 

[lethe]

Originally posted by Shahil
Does that mean all mathematics has to have a meaning?

what is meaningful to me might not be meaningful to you. meaning is relative.

mathematics doesn t have to have a meaning to little league pitchers.

I remember when I was in school, my maths teacher (who is quite brilliant) said that geometry and riders have no practical purpose?

geometry clearly has practical uses. i don t know what "riders" is.

 

[Shahil]

You do make sense!

I'll get a .jpeg and attach it tomorrow. I know we call them riders here in south africa, maybe you have a different name for them!

 

[Shahil]

Actually here's an example. It's for the final examination for grade 12 level.

I really hope something attaches!

 

[uart]

what is meaningful to me might not be meaningful to you. meaning is relative.

Yes hehe, I once remeber the father of a friend of mine at school (long ago) who swore that "negative numbers had no practical purpose". :) No joke.


I have to admit that I find it very interesting to see results that might have sat as little more than a mathematical curiosity for hundreds of years and then suddenly find a valuable application. One in particular that springs to mind is the "modulo prime" result that

$$a^{p-1} = 1 : {\rm modulo}\ p$$.

Where p is a prime and a is any integer which is not equal to zero (all math done in modulo p).

This result was established a long time ago (I think it was by Fermat but I'm not sure, it was about that era anyway.) After sitting as nothing more than a curious result for hundreds of years it suddenly became extremely important as the one of the underlying mechanisms of the "RSA" public key encryption that is now routinely used in millions of secure internet transactions daily. :)

 

[selfAdjoint]

There is a famous story about the great English mathematician Hardy. He was very radical and anti-authoritarian, sort of the Chomsky of his day, and on one occasion having proved a particular theorem in number theory he said, "There, at least that will never be of any practical use to anybody". This was in about 1936, and four years later his students were using his theorem to plan the hunt for Nazi U-boats.

People in the US Navy learned this story, and for about ten years after WWII they funded number theory research hoping for another miracle theorem. None came.

 

[robert Ihnot]

Another matter is "casting out nines," which deals with the sum of the digits of a number. Well, if you think it is rather useless to worry about the remainder modulo nine, or the sum of the digits; I was surprised to learn in accounting that, at least before computers, accountants frequently checked their work by "casting out nines," which is not foolproof, but is an easy check on their arithmetic.