is pure math useless?

babysnatcher

I was not too sure what to title this but I just skimmed through a thread with the same title so I just used this. I am not sure whether to go into math or physics. I would prefer math but how will I ever know if I "know" something. This is a troubling thought that discourages me from math. On a side note, that foreign language requirement for math is annoying. Anyways, physics seems safer. Its hard to argue that one does not know how to produce a product if they physically made it. But with math it seems very difficult to "know" that you "know" - I actually do not "believe" in 100% "knowability", which leads to the "belief" chance for any possibilities at any time which leads to the "belief" of "unknowability". It has not been proven that the uncomprehendable is impossible. The perception or reasoning ability of the spectator does not change what is already there, could be there, or is not there. I hope you can see the evidence I provided in the context I wanted it instead of literally what the words say because everything I have said does not agree from the beginning but the "opposite" is unprovable. Regardless of my "belief", I am willing to go along with "2 can only be 2, and no other number at the same time" for now. Does more relativly solid evidence like this come up in pure math? I do not care if math is applicable or not, and I do not care about producing products at all, but I just want to "know" I "know" - and I think something intangible like math seems difficult to "know" I "know" it. One of my main goals is to attempt to "know" as much as I can, and/or spend the rest of my life attempting to maximize an impression of "truth". Another goal of mine is to continuously raise my reasoning skill as high as I can. Heck, I might even do philosophy. I can correct relatively inaccurate statements all day because it is just fun. I get nervous when I communicate because I'm an unconfident person, because of my "beliefs", so I'm not sure how accurate this is. Also, I forgot to include more "things" so ask questions!

micromass

I recommend that you go into philosophy.

rollingstein

Hardy said the more useless it was he felt purer. Or something like it.

"A Mathematicians Apology"

micromass

That's Hardy's opinion. Not all mathematicians think that way.

rollingstein

Sure. I didn't say they do.

OTOH, Hardy was important enough in pure math to give his opinion some weight (IMHO).

I look forward to contrary quotes from other noteworthy pure mathematicians, if you have any.

babysnatcher

Wow! You guys are really gonna have this pissing contest on my post? Why.......

Sankaku

While an entertaining read, I think that book has done more damage to the social culture of mathematics than other single book I know. There is nothing wrong with Hardy's opinions, just that people take them way too seriously.

micromass

Just look at the following interview with some Fields medalists: http://www.ams.org/notices/200703/co...interviews.pdf All seem to be implying that applied mathematics is important one way or another. While they might not particularly care much about applications, they don't seem to be very much adverse to it, unlike Hardy.

rollingstein

Thanks! Great reading.

babysnatcher

Eh, guess ill give my opinion on something on my post, even though y'all aren't helping. So yeah, the one talking isn't the problem. Problems occur when people take actions, that cause harmful results, based on another persons speech.

Robert1986

I think the important thing to remember is that even the parts of math that seem the most "useless" can turn out to be very practical. There is a lot of interplay between various branches of math. For example, stat is a pretty applied branch of math, I think most people will agree. On the other hand, many people might think that algebra is a branch of math that is less "applied" than other areas - and I would agree. Yet, there is an entire area of research known as algebraic statistics where "useless" stuff from algebra is used to do stat stuff. This has the advantage of advancing both statistics and algebra. This kind of thing happens all the time, and I didn't really notice it until I started grad school and began attending seminars and such.

babysnatcher

K. I'm sure I did said I do not care about applicability. Just about "knowing". I suppose I could learn all the math and then apply it every now and then just to satisfy this "knowing".

joeblow

What do you want to do with your life?

If you want to do anything other than be a professor who researches, I would strongly discourage a pure math major. I would also discourage an applied math major, since the theory being taught is presented better in engineering courses where you will actually experience countless applications of what you're learning. If you want to teach, most math programs have an education emphasis.

At one point in my career, I was into pure math. However, after reaching the 700 level in Algebra and finding very few true applications, I totally lost the motivation to learn it.

Maybe theoretical computer science would be up your alley... but good luck finding a job where you'll be able to do anything other than programming.

WannabeNewton

I'm curious as to how you people figured out what in god's name post #1 was actually saying.

babysnatcher

Ima be a teacher ,no matter what I major in(including engineering), to reinforce my knowledge. So if I learn the math in engineering anyway then ima do engineering. I just wanted math/physics for a dramatic understanding so I won't miss anything but if engineering encompasses enough math/physics understanding to be very competent then ill do engineering. And if I can build it then I "know" something. I didn't want to multi phd major anyway because I like to overanalyze and there isn't enough time to overanalyze all these fields.

Wait but I'm still confused on this. I'm doing ChE, btw. What am I missing from the physics classes that are named "solids" ,and "eletricity and magnetism"? What am I missing from advanced organic chemistry and inorganic chemsitry classes? What am I missing from math classes I am not taking? I am just convinced that all of these upper division and grad school course versions of my foundations of ChE(chem, math, phys) cannot be for nothing. Is there really no reason to further my physics/math/chem education beyond those basic lower division undergrad courses? Will extra classes just be a waste of time? Should I just stick to the ChE classes now? Will I learn everything I need to know and build up my intuition of theoretical possibilities to an optimum level with just that?

Robert1986

I have no idea what the ramblings in post #1 were saying. I guess I was just answering the title of the thread.

Whovian

I know you said you were willing to go along with that, but the only thing I could make sense of in the OP was something along the lines of "how do we prove something like this."

The short answer is, we don't. Unfortunately, in mathematics, there are a few things we just have to take for granted. For instance, I don't think we can provide an entirely rigorous definition of equality, other than "two numbers are equal if it's obvious they're the same number" and "two numbers are nonequal if it's obvious they're not the same number." Or the fact that 1+1=2, it's difficult to define addition unless we define it with respect to "adding 1," but then we need to define adding 1. And so on.

If you're confused, don't be surprised. My point is, we can't prove or define anything in maths from scratch, we have to take some things for granted. 2=4 if our number system is based on modulo 2, for example, so it's possible to design systems where almost any axioms break down.