Exploring Pure Mathematics: What Does it Describe & What are its Laws?

[Imparcticle]

What does pure mathematics describe exactly? What are its laws based on?

Recall the psi beta function. It was used for purely mathematical persuits and it was believed it did not pertain to our physical reality. In 1969, Venetziano observed a relationship between the behavior of particles (or strings) and the mathematical properties of the psi beta function. Could it also be that other aspects of pure mathematics describe the most abstract aspects of this universe and we are unaware of it? After all, mathematics is based on physical law right? If we build on the physical law, logically, we will come to a point where we exit the realm of what has been discovered and confirmed and enter one that has not been investigated by experimentation or physical theory--but instead mathematical theory which appears to have no relations to our physical reality.

What is your take on this? If I have made errors please do the honors of correcting me. Is my understanding of what "pure mathematics" is incorrect? Please tell me if this is so.

 

[matt grime]

You've not said what you think pure mathematics is, so it's hard to say if you're incorrect. The distinction between pure and applied is largely arbitrary and not particularly important. A reasonable rule of thumb is that in applied the result is what counts, in pure it is how you obtain the result that matters.

 

[Imparcticle]

Pure mathematics is supposedly a description that does not apply to our universe AFIK. Like the psi beta function.

 

[matt grime]

Then I would suggest as far as you know, you know incorrectly. What is more pure than the study of prime numbers? WHy does their description not apply to our universe? What does apply mean? More subjective illdefined terms.

 

[stefanfuglsang]

See these links

http://en.wikipedia.org/wiki/Pure_mathematics
http://en.wikipedia.org/wiki/Applied_mathematics

 

[Gza]

What does apply mean? More subjective illdefined terms.

The English language, and all language for that matter is simply not as concise, well defined and self consistent as that of mathematics unfortunately. So you can really attack any distinction between "pure" and "applied" math without much trouble, since language has a nasty habit of "crumbling in on itself," due to its lack of axiomatic foundations. And I was curious about your statement:

What is more pure than the study of prime numbers? WHy does their description not apply to our universe?

The question I would ask, would be, "What are the properties of prime numbers that do apply to our universe?" You being more mathematically minded than I, seek to apply what you know about these abstract properties of these special numbers to the universe. I from my experimental background, seek to find the pattern "out there", not to force a pre-conceived notion on the universe. I'm just curious what your answer to my question posed above would be.

 

[loseyourname]

Imparticle, I'm pretty sure "pure mathematics" does not refer to math that has no application. It refers to the study of mathematics without regard to application. That is, if I simply add 2 + 2, I am practicing pure mathematics. If I add 2 hot dogs to 2 hot dogs, then I am practicing applied mathematics.

 

[homology]

There is a pretty good book (so far anyway I'm half way through it) by Mark Steiner called:

"The Applicability of Mathematics as a Philosophical Problem"

In which he considers the way in which mathematics and physics tend to jive (my word, not Steiner's).

It's philosophy, however he assumes a science and math audience (i.e. doesn't expect you to be an expert on Heidegger, Kant, etc...)

Kevin

 

[rayjohn01]

First I would say that applied maths is a subset of pure maths, and is important since in many applied science courses that means that the maths is often limited to what is deemed relevant or useful to the discipline and more general ideas are lacking.
In pure maths it is not necessary to refer to specific physical objects for the logic to be applied to a set of axioms , but that in no way implies that it cannot be used in practical situations.
Having said that there are many areas of pure maths which at present have no or little application to physical sciences -- they are like answers awaiting a problem.
To the person who said that that maths is derived from physical law -- I would agree but it is an idealised form of observation and as such may suffer from our imperfect way of seeing things. I do not know of an equation which adequately describes a feeling of pain -- but maybe someday.