What is "pure math"?

Question

I know "pure math" becomes "applied math" once it becomes useful, like certain geometries used by Einstein. But MY question is, what is some OBSCURE mathematics; like the kind "Good Will Hunting" makes short rift of?

I may be no genius, haha, but I would like to take a crack at whatever the best of our Mathemeticians (Mathemagicians) have to offer.

After all, folks; they're just symbols, right? :)

Answer 1

Pure math is mathematics untainted by any hint of the real world

such as physics, money, land area, etc.



Numbers by themselves. 2, say. 2 what ? Not 2 anything. Just 2.

In geometry, for example, the idealized point and line are

part of pure math. A "line" drawn on paper is a very

crude picture of a line. No matter how sharp the pencil

point, it's still a zillion-zillion-zillion (well infinite, really)

times as thick as a mathematical line.

An atom ? HUGE, compared to a point.



Take the well known number pi.

You can approximate to any number of decimal places,

but never have the _exact_ value because the decimal

expansion is infinite.

But to the pure mathematician, pi has an exact value.

To the average Joe on the street, enh, 3 or 3.14 is close enough!

And in applications, _some_ approximation of pi IS close enough!



For obscure topics, look up things like

infinite dimension spaces

Non-Euclidean geometry

modular forms (used in the proof of Fermat's Last Theorem)

Anything in advanced Topology

Banach Spaces (Pea-Sun Theorem for example)

Galois Theory



A common property is that these things are named for someone,

and some of them are quite far removed from our nice (or not so

nice, from the pure mathematical point of view) three dimensional world.



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Answer 2

if you want to try some fun applied math then look up permutations on this site. they will have everything you want to know there



http://mathforum.org/dr.math/dr-math.html



a good question that is pretty difficult.......



how many permutations of the numerals 0-9 are there with NO nomeral being in its proper position ( ie. 0 cannot be first, 1 cannot be second, 2 cannot be third....etc. )



perms are fun and there are alot of questions on dr math involving perms that can be learned without a proffesor. not complicated math but it does require a solid understanding of numbers.



and if you want to get into derivatives and antiderivatives of complex equations, or a beautifull mind/ an uncontrolled temper type math then they will have all that jazz too.



but if you are going to ask them a question it must be very specific and you have to show all your work or you will not get a response.

Answer 3

It's really hard to make a strong distinction between "pure" and "applied" math. "Pure math" will definitely include set theory, but beyond that I don't know what either one is.



So if you want the most obscure one I know of, pick up a book on axiomatic set theory.



If you want, you can even pick up Russell and Whitehead's _Principia Mathematica [to *56]_ to look through.



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As for the math the best of the mathematicians have to offer, here are some of the most famous easy hard problems. (easy to understand, seemingly impossible to show - neither has been shown yet)

http://en.wikipedia.org/wiki/Goldbach%27s_conjecture

http://en.wikipedia.org/wiki/Twin_Prime_Conjecture



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Mathman TG: I think I would agree on most of those topics as "pure" math. However, non-euclidean geometry is a misfit in your list, seeing as how such geometries describe our world/universe.

Answer 4

"analysis"