Math Useless Without Applications?

[matt grime]

Your response to what you consider to be a stupid question is to be condecending?? That's just plain rude.

My response to a stupid question is not going to be nice. You are the person who chose to argue a position, one in which you presmably believe, one that you were prepared to assert against your teacher. Well, you did argue it, and you got a response. I don't care what your personal opinions are about it, or about me. I have no patience with people who hold patently idiotic positions, especially those that are prepared to air them in public. Sorry.

 

[wolram]

Well, for the general public, I'd say it is formally useful to discipline your mind in such a way as to minimize making logical mistakes.

Maths is an excellent way to develop structured, logical thinking.

You think so, in cosmology mathematicians generate all kinds of possibilities, if it is mathematically possible observationist have to prove it wrong, in this case why is maths more powerful than observation.

 

[mathwonk]

why is this thread tolerated? there is no math in it.

 

[wolram]

why is this thread tolerated? there is no math in it.

I guess it is a problem that science can not yet solve, if a mathematician comes up with
an equation that is possible, then it may take obserationalists hundreds of years to prove it wrong, just tell me how many possibilities are mathematically correct and observable, when it comes to cosmology.

 

[mathwonk]

i rest my case.

 

[PowerIso]

why is this thread tolerated? there is no math in it.

In that case, find the limit of (1 + 1/n)^n as n approaches infinity.

=-o
=-o Math!

 

[tony873004]

why is this thread tolerated? there is no math in it.

There might not be an x, or a y, or a root symbol, but it's a question about math in a sub-forum entitled "Math".

You are the person who chose to argue a position, one in which you presmably believe, one that you were prepared to assert against your teacher.

I don't think my teacher thought I asserted anything against her. It was a very light-hearted discussion. She seemed to welcome my comment as it allowed her to explain the other point of view, a point of view I've never really thought about before. Her response was enlightening. 10 minutes later, we passed each other in the hall, smiled and waved.

I didn't come in here to start a debate. If I did, I'd be defending my so-called position. But you won't find anywhere in this thread where I've rebutted any of the points people have made. To this forum, it was phrased as a question (read the last line of my OP), not a point of view, and the responses have been received as replies to the question. Thus far, people have responded:

• Math is a beautiful thing (I can appreciate that.)

• Some people derive pleasure from math (to a limited extent, I do too, but I derive more pleasure from science, especially science that relies on math)

• Some scientific breakthroughs used math that was once only non-applied math (I never knew this. Prior to this discussion, I always figured the math followed the science, such as Newton inventing Calculus to prove his intuition that Earth can be accurately approximated as a point mass)

• Math trains your mind to think logically (I never thought about it like that before, but I can see where that makes sense).

These are great replies. I'm glad I asked the question. It's opening my eyes to a new way of thinking. This is what I was hoping for... answers to my question. I didn't reply to these reasons by disagreeing, hence I don't know why you feel I am arguing a position. I simply asked a question.

Well, you did argue it.

Please show me where. It was phrased as a question, and I never rebutted any of the responses.

My response to a stupid question is not going to be nice.

If it's such a stupid question, why did Timothy Gowers choose to devote an entire key-note speech to the subject, as seen in links in Morphism's reply? Gowers states: "If I fail to convince you that mathamatics is important and wortwhile, I will be letting down the mathamatics community... Unfortunately, if one surveys in a superficial way the vast activities of mathamaticians around the world, it is easy to come away with the impression that mathamatics is not actually that important."

Some people are of the impression that there's no such thing as a stupid question. Obviously you're not among them. So please tell me (2nd time I've asked you this), if I have a question that some might perceive as a stupid question, what should I do? Continue wondering, or ask?

I have no patience with people who hold patently idiotic positions, especially those that are prepared to air them in public. Sorry.

A question is not a position. I light-heartedly phrased it as an "off-the-top-of-my-head" position to my teacher in response to her deciding to skip an application section. Her rebuttal was very interesting. It dealt with the history of math, and gave me some insight into the minds of those who enjoy math. But her time was limited. So I posted it here, along with some of the reasons I question its importance, as a question, hoping for more insight. I'm mostly happy with responses. I got a lot of insight, unfortunately, along with some attitude.

 

[leon1127]

The most useless maths topic was said to be number theory. And now, you don't even dare to get online without it!
think about your computer games without mathematics... FFT in signal processing etc.
You can live without maths, but you can't live luxurious without maths!

 

[tony873004]

But using math to write computer games is an example of applied math. We could, however, debate the usefullness of computer games :)

 

[phoenixthoth]

Too vague to give a yes or no answer, even if you change it to "is pure math useless?"

Is math useless to X?

Is the criteria that something is useful if at least one person is entertained by it? That at least one person makes money off it? That it trains brains to think analytically? That it may not be itself useful but in turn is used in something that is?

It's useful to me because I use it to make money, brain training, and entertainment (as well as exquisite agony).

In fact, monetarily speaking, everything that isn't math is completely useless to me, because my job depends on it and pretty much exclusively it.

I think the question needs to have the "to X." I'm sure that even something that most consider very useful is useless to someone, like condoms and Stephen Hawking. To him, they're utterly useless (unless he blows them up to make art or something, which is the implication that some people are making about pure math--it's entertaining).

An Amish person finds this laptop I'm using utterly useless, I imagine.

Is pure math useless to you? Probably. Is (insert any subject besides math) useless to me? Most likely. Does that mean math is useless? Does that mean any subject besides math is useless? Ultimately, given the universally relative nature of a branch of knowledge's utility (especially considering those that have no use for it), can anything at all be said to be useless or useful without adding "to X?"



One time I had a teacher who labeled his office hours as "no question too dumb office hours." Lovely ambiguity, isn't it? Well, I suppose some people define themselves to be a good teacher when they laugh in a students face when they ask what the teacher thinks is a dumb question, hoping that his or her inability to answer the question, masked with ridicule, will emotionally cripple the student enough so that the suffering will motivate the student to stop pestering the teacher as well as be a "better" student that stops asking questions.

 

[robert Ihnot]

It seems that only man has much ability to understand the symbol of a thing--such as a map. This, has great value for the tribe, and it certainly has a social advantage. While writing, counting, are valuable and were practiced by the scribes of Egypt, is there anything in the quality of genius, such as Gauss, which would be useful in a less developed society, one concerned mainly with farming? (He might have been able to straighten the Egyptians out on fractions.)

Since people differ widely in their innate ability to understand abstract math, it might have not had much survival value throughout History. I have to wonder about Einstein, what "survival value," if any, his abilities would have if he had been a simple farmer, one with 20 acres and a mule?

At the time of Luther, few could read, but learning was certainly prized. Luther was on a crusade to translate the Bible into German, so that every German could understand scripture when spoken. Thus. he was taking the scriptures away from the privilaged domain of the high Priesthood. Funny, Grace Hopper wanted to do the same thing, about the computer, using COBOL.

Perhaps then someday the Great Emancipator will come, like Isaac Asimov, and make complex math understandable to all. And if he did, would people then call it useless?

 

[Cookie_1993]

when the teacher tells you tht so-on-so is the stuff.. u get the theory but i hardly understand it unless she puts it on a good practicle example!
sometimes techers just say," u need it to pass the examination!" well.. what is much of use learning it, if u use it only for the tests.. where does this part of fundamental thinking help me!? (simple question i asked all my math teachers!)

 

[symbolipoint]

when the teacher tells you tht so-on-so is the stuff.. u get the theory but i hardly understand it unless she puts it on a good practicle example!
sometimes techers just say," u need it to pass the examination!" well.. what is much of use learning it, if u use it only for the tests.. where does this part of fundamental thinking help me!? (simple question i asked all my math teachers!)

This topic has now been discussed generally enough; but your question can be restated like this:

"Which mathematics topics and skills that you studied in school have you used in your work?" At least the responses that readers offer will be realistic. When I quote, "used in your work", I do not mean just within the study of Mathematics; I mean how people APPLIED the mathematics concepts and skills. From my own experience, I could say much more about the use of simple Algebra than of any other areas of Mathematics.

 

[tony873004]

Are significant figures used much in non-applied math? Thus far I have seen them come into play in applied-math word problems. For example, questions containing: "The Earth is 150 million km from the Sun, how fast..." pretty much limits the answer to 2 significant figures. But how about in non-applied math? I don't even see decimal numbers appearing that often in Calc class, so I would guess it's not nearly as common.

 

[mathwonk]

please kill this thread. it makes us look stupid as a forum.

 

[MaWM]

I don't believe in pure math. Some people prefer to pursue mathematics as a mental challenge without any concern for any applications it may have. That doesn't mean that it doesn't have applications. It has been my experience that, whenever I study a distant and esoteric branch of pure mathematics, I find an application for it soon after. In fact, the more pure the math is initially, the more profound the applications.

Right now I'm doing exterior forms algebra, some of the most abstract math I've studied.. and wow is it ever useful!

 

[arildno]

Are significant figures used much in non-applied math? Thus far I have seen them come into play in applied-math word problems. For example, questions containing: "The Earth is 150 million km from the Sun, how fast..." pretty much limits the answer to 2 significant figures. But how about in non-applied math? I don't even see decimal numbers appearing that often in Calc class, so I would guess it's not nearly as common.

Well, in some numerical courses, you'd be interested in developing maths concerning finite-precision aritmetic, i.e predict and model exactly how a computer calculates.
In that respect, "significant digits" DOES become an important concern, in particular how you might lose them..

 

[Gib Z]

and I wouldn't call calculus non-applied math :( Some of it is, some of it isn't, but a lot of it can be applied.

 

[CRGreathouse]

Right now I'm doing exterior forms algebra, some of the most abstract math I've studied.. and wow is it ever useful!

How do you find them useful?

 

[MaWM]

How do you find them useful?

You can use it to put physics into a dimensionally independent form. Alot of the laws we study in elementary calculus turn out to be special cases of exterior forms calculus applied to a universe of three spatial dimensions. Stating physical laws in terms of exterior calulus makes transitioning from classical physics to special relativity (and, I suspect, string theory) much easier.

Additionally, certain structures in physics can be translated into elements of an exterior algebra. The algebra is closed with respect to the represtations of such objects. That is to say, using the alegraic properties on a list of representations generates new algebraic objects which are also representations of phyical structures in the same category. That is to say, new previously unknown structures in the category can be generated from the known ones. In their raw physical realization, these structures may appear entirely unrelated.

 

[kev1829]

No, math is not useless. Unfortunately many students (myself included) resist the fact that it is like any other skill. You need the basics to be able to perform the advanced, but the more advanced the math the less opportunity to apply the skill.

As for decimals in calculus, in my experience decimals are considered an approximation. They were never accepted for an answer outside "real world application" problems. Fractions and symbols are exact.

 

[Cookie_1993]

please kill this thread. it makes us look stupid as a forum.

I think its a really interesting topic becoz this qustion always pops up in a teenager's head or any student's head!

 

[alphachapmtl]

"...that math is useless if its never applied to anything..."

In a way this is certainly true, but this can be said of almost anything.

What good is a picture, a movie, a painting, a baby, a girlfriend ?

I guess if you enjoy it its useful to you, if you don't its not.

And then we die.

 

[yasiru89]

Pure mathematics is not exactly useless just because it has no applications.

Rather paradoxial when you consider that the main classification is pure mathematics and applied mathematics. Without addressing this ambiguity immediately I must first offer a reluctant apology that I believed women in mathematics was a bad idea from the outset, though your teacher's comment may have been one of habit rather than conviction. 'Mental masturbation' may have been a bit much but it does bluntly get a point through.

I will undoubtedly have to study both pure and applied branches of mathematics through my life, this shall not be because I hold all that much interest in physical application but rather that pure mathematics is a constantly(yet never predictably) evolving creature. It seems inevitable that any chosen part of pure mathematics shall eventually succumb to application and hence 'cease to be' pure mathematics. However by this time there shall be other outlets of pure mathematics available that have not met their fate as yet. Therefore for as long as intellectual effort soldiers on, pure mathematics shall survive. If I choose to study what has been branded applied mathematics it is not because I enjoy the real world curiosities it extends to but rather because I find worth study the conceptual element that sparked the whole branch. Then there are those fields that are interesting in themselves, such as quantum mechanics. It must be noted that quantum mechanics is not the precise picture, rather a very good approximation of it and the mathematics associated with it(which to support my claim seems very distant at first glance to what we use it for)spans over probability theory, perturbations and vector fields. Incentive to but not directly of the realm of applied mathematics.

If anyone really bothered to read 'A Mathematician's apology' by Hardy, they will notice that the man held no regret at his or his peers pursuit of mathematics, the entire work merely serves his need to justify it on the grounds that while it may have been useless (a secondary importance) there came no harm out of it. A point that is all too often brushed aside, since applied mathematics constitues more to good and evil than pure mathematics ever will.
Yet it is more than anything a matter of preference, as it always is in the subjective world of mathematics. No matter how uninteresting your trivial mathematics may be we still need the majority to go with it, for the sake of the survival of pure mathematics if nothing else. Hence perhaps in your case applications need indeed be treated seriously. It is also an illusion that discipline is all that mathematics encompasses; intuition and sometimes even the mundane elements of logic(for their lack of extension) really have no place in serious mathematics and to plough on for the sake of grades is indeed appalling.

Applied mathematics is all too often an uninteresting and dismissable consequence of our efforts in pure mathematics, it is useful, and without even defining the word useful I shall accept that, but to me this 'consequence' only serves best to broaden the reach of pure mathematics and in general to make our lives easier with the mundane, yet 'useful' conveniences it shall have to(by collaboration with other sciences and industry)offer.

 

[Gib Z]

Rather paradoxial when you consider that the main classification is pure mathematics and applied mathematics

In modern mathematics the distinction between the two classifications is becoming more and more obscure.

I must first offer a reluctant apology that I believed women in mathematics was a bad idea from the outset

I'm a bit confused on that. Are you apologizing about a previous view that women in mathematics was a bad idea, but reluctantly? Now that is paradoxical. Mathematics should be available to everyone who wants access to it; rich or poor, purists and appliers; females or males. In deed the fact that this is that is one of the attractions to mathematics for me, I find it very amazing that a bankrupt Middle aged man living in his moms attic can make as large a contribution to mathematics as proving the Pioncare conjecture (I'm almost certain I spelled that wrong).

If anyone really bothered to read 'A Mathematician's apology' by Hardy

What makes you think we haven't? Some of us have, some of us haven't.

No matter how uninteresting your trivial mathematics may be we still need the majority to go with it, for the sake of the survival of pure mathematics if nothing else.

I don't understand what you are saying there, sorry :(

Applied mathematics is all too often an uninteresting and dismissable consequence of our efforts in pure mathematics

You say that like you're stating a fact when really it's your closed minded opinion. The OP make it very clear he finds the applications interesting, though finds the pure parts not so much. Who are you to directly say he's wrong?

In my opinion, all mathematics is interesting and beautiful, just different aspects are so to different people and tastes. Personally, I prefer more "pure" things, but many wouldn't consider a lot of analysis as Pure, though I still love that.

 

[yasiru89]

One by one then,

It is the obscurity that I wished to clear up.

My replies can be cruel and opinionated and I often do not give up a stance, but equality comes not from ignoring our differences but from embracing them, for they make us who we are and certain mentalities are truly(yet regrettably at times) hardwired into our brains. Counter-intuitive? Very, and that is what I meant earlier; women do incredibly well in physical sciences but not all that well in mathematics with almost none prominent in pure mathematics. This is because as anyone involved in psychology will tell you women more than men function on the basis of intuition very often and when the lack of it becomes prominent the 'extinction' occurs. However it must be understood that I am not telling certain people to stay away from mathematics but rather making the observation and remarking that intuition-promoting teachers may not be the best choice for teaching 'serious' mathematics. Then again in applied mathematics it is the case that 'more the merrier'.

And it's Poincare with the last accented.

I didn't mean the reading thing harshly, only that half-baked quotations, especially from this book are becoming more and more popular for the 'case' of applied mathematics vs. pure mathematics.

As I said earlier pure mathematics evolves as applications gobble up certain parts of it. This phenomenon is crucial for its development and when applied mathematics is pursued the best 'use' it is put to is the broadening of pure mathematics.

And it is as good as a fact that 'Applied mathematics is all too often an uninteresting and dismissable consequence of our efforts in pure mathematics', why? Because nowadays the most important applications are derived from the most abstract of branches of mathematics, some people on this thread have agreed with this to some extent too.
I take it OP is the original poster, he summarises that while he gains some pleasure from mathematics the uses are what he is really after(the applied bit)
So on the intellectual context that I am addressing the matter applied mathematics is indeed trivial and uninteresting. Yet I do not relegate the originators opinion quite the way that I am accused of doing. I simply assert that applied mathematics fulfils its usefulness mainly in acting as a catalyst for pure mathematics and secondarily to bring about the simple conveniences of life.

 

[Gib Z]

Reasonable arguments (and hence a good post), though I'm not sure why you don't like intuition in mathematics, Terrence Tao says that to truly understand a concept you have to be able to understand it algebraically, geometrically and intuitively.

 

[yasiru89]

My thanks for the unbiased consideration.
I must say that intuition while of tremendous utility towards a complete grasp sometimes can and will, as the contexts become more abstract, lead us astray. It is by no means a fault of intuition, it is the minimalistic thinking process that we unwittingly find quite handy in day to day problems. More twisted yet elegant approaches belie the greater truths and hence those of us not blessed with the gift of omniscience(or intelligence somewhere asymptotic to such) can only rely upon the constructs of rigour.

 

[titaniumx3]

The way I see it is that pure math, analysis, abstraction, theoretical math, mental masturbation or whatever you want to call it, is the medium in which new discoveries in mathematics are made. Hopefully, some of these discoveries are then applied elsewhere at which point you can probably consider them as being "applied math".

Wasn't all applied mathematics born out of mental masturbation at some point?

 

[Dragonfall]

The division between pure and applied maths is an administrative one.