He Unreasonable Effectiveness of Pure Mathematics

[k3N70n]

Hi.

I have to write a paper (about 20-25 pages) and I'm likely going to choose the topic 'The Unreasonable Effectiveness of Pure Mathematics' as was suggested by one my prof's (of course, I'm familiar with Eugene Wigner's article). I was curious if anyone could point me towards more modern journal articles on similar topics? My paper has to be presented to a group of peers which will include mostly natural science students who are 4th & 3rd year students, thus, it has to be reasonably accessible to those less mathematically inclined.
Thank you kindly for any help.

-kentt
(I hate writing papers)

 

[Gib Z]

I don't have a journal article, but I may lend my view on the matter at hand.

In my personal view, I find it quite obvious why Mathematics and physics go so well together. It is because Physics describes the Universe, and because the Universe as well as everything in it, follows mathematics, inherently. It can't not follow mathematics, no matter how it tries. Either, there is some nice pattern where a physicist finds a mathematical model to represent the pattern, or there is no pattern and we label it to be 'random', another mathematical concept, and then we study the probabilities of the random outcomes. Or, we can't do either, but only because the mathematical tools are our disposal are too weak, and some brilliant genius must make their own.

 

[arildno]

Hmm..I'd rather say that the world cannot be self-contradictory, and hence there will be some type of underlying "logic" to which it adheres.

On the assumption that any type of logic can give rise to its own mathematics, it follows that the world should be mathematizable in some shape.

That the "world logic" might be very different from our own immediately accessible logic(s) is, of course, a very real possibility..

 

[MathematicalPhysicist]

as i see it this "world logic" doesn't make sense, if it's not accessible to our logic we can not talk about it, and thus it's just a nice term, a superficial one that no human at least can acsertain it validity or not.

 

[arildno]

as i see it this "world logic" doesn't make sense, if it's not accessible to our logic we can not talk about it, and thus it's just a nice term, a superficial one that no human at least can acsertain it validity or not.

It doesn't mean much else than non-selfcontradictoriness.

I.e, either the world contradicts itself, or it doesn't. If it doesn't contradict itself, there is a "logic" of some sorts that underlies it.

 

[Kummer]

Write the paper on Georg Riemann and his ideas of Differential Geometery. When he first discovered it as a pure area of mathematics it had little effect. 70 years later E'nstein found how to apply it.

 

[k3N70n]

Thanks Kummer. I had ran into that in my research but it definatly sounds like one of the more interesting applications of pure math.