Math Useless Without Applications?

[tony873004]

In my teacher's office hours, I expressed some disappointment that she was going to skip one of the "application" sections, which are my favorites. I complained that math is useless if its never applied to anything. And I tend to quickly forget math unless I see it applied to real world applications because it helps me visualize the math in a way that pure memorization can never achieve.

I was surprised that she disagreed. She told me that "back-in-the-day", non-applied mathamaticians looked down upon applied mathamaticians as the working class. She told me that she was about halfway inbetween the 2 opinions, although the sections in the book she is choosing to skip tell a different story. She referred to math as "mental msturb...ion" (I would hope this word is censored in the forum). It's not hard to see her point. I get that warm fuzzy feeling too, every time I struggle for a half hour on a problem and finally figure it out. But that said, I have to admit I would have zero interest in math if math could not be applied to solve real world problems. If 2 dollars + 2 dollars didn't equal 4 dollars, I wouldn't even have an interest to know simple addition.

I was just interested in the opinions of others on this issue. Is pure non-applied math useless?

 

[morphism]

Is pure non-applied math useless?

In a word: No.

 

[morphism]

Here is a post I made which I think could be relevant to this discussion.

(And here's the thread that post came from.)

 

[bob1182006]

pure non-applied math isn't useless I think, but for some people like me it's pretty hard to learn without the applications, or graphs.

When I took linear algebra I had NO idea exactly what was going on I was passing but I didn't understand. Until I did some of the applications and graphed some of the matrices...

 

[bassplayer142]

Most math has to be applied. How do you get the pytagorean Theorem without a physical triangle?

 

[morphism]

Most math has to be applied. How do you get the pytagorean Theorem without a physical triangle?

Like http://planetmath.org/encyclopedia/PythagoreanTheoremInInnerProductSpaces.html !

 

[tony873004]

Thanks, morph, for the links. It's very interesting stuff. I'm like bob1182006. I need to know why, and I'm not a very good math student until I do know why. In calc I, we didn't touch applications until the last week of the course. I wish they were integrated throughout the course, because as a result, I struggled through the course. It seems that math classes are designed for diciplined students, rather than intuitive thinkers. For example, I got C in Calc I the first time I took it. Three of my friends, over the years, got A's. Unlike me, they were very diciplined students: no partying until the homework is finished. But a few weeks ago, I gave all of them the same challenge: create a word problem that requires Calc I material to solve. You do not have to solve the problem. Just come up with one. I only got answers like "well, its the slope of the curve...". I'd respond with "why might I want to know that?" But not one of the A students could come up with a real-life application, while I, the C student, can come up with hundreds.

 

[robert Ihnot]

I have heard another women describe it as "mental masturbation," which makes no sense since it is definitively not a flight of fantasy. "Back in the days" when some looked down on applied math, that was definitively not the attitude of the Government, who used a lot around the time of the moon shot. Similarly for employers like life insurance companies and advertisers needing statistical analysis.

 

[Chronos]

Pure mathematics does not always agree with observation. That might mean the universe is sitting in the back row of class, or, it might mean we do not sufficiently understand how to apply it. Our math might be better than our understanding of its implications.

 

[ice109]

In my teacher's office hours, I expressed some disappointment that she was going to skip one of the "application" sections, which are my favorites. I complained that math is useless if its never applied to anything. And I tend to quickly forget math unless I see it applied to real world applications because it helps me visualize the math in a way that pure memorization can never achieve.

I was surprised that she disagreed. She told me that "back-in-the-day", non-applied mathamaticians looked down upon applied mathamaticians as the working class. She told me that she was about halfway inbetween the 2 opinions, although the sections in the book she is choosing to skip tell a different story. She referred to math as "mental msturb...ion" (I would hope this word is censored in the forum). It's not hard to see her point. I get that warm fuzzy feeling too, every time I struggle for a half hour on a problem and finally figure it out. But that said, I have to admit I would have zero interest in math if math could not be applied to solve real world problems. If 2 dollars + 2 dollars didn't equal 4 dollars, I wouldn't even have an interest to know simple addition.

I was just interested in the opinions of others on this issue. Is pure non-applied math useless?

1.why in the world would a word like masturbation be censored?
2. who cares if it's useless? not everything needs utility.

 

[Maxwell]

There isn't always such a fine line between theoretical and applied math. Also, a lot of math that starts out being very theoretical can be applied over time. Basically any math is useful math.

 

[Gib Z]

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

Even if it doesn't have any clear applications at the time, even the purest of mathematics can find unexpected uses. Famous Number Theorist Hardy was a proud pure mathematician, who thought the best mathematics was the type that could not hurt or affect anyone. He took pleasure in knowing that what he was doing could not be applied and preferred math that way. I'm sure he's rolling in his grave ever since Computers started using prime number factorisation as a method of encryption.

Even something like the Riemann Zeta function, which is very deep in the purest of modern mathematics, gives useful results in string theory (where one needs to evaluate zeta(-1), and expects a finite answer on physical grounds) and deep consequences in prime numbers and hence computer security.

I myself am like the female teacher, between both grounds. I study both areas, because I find both interesting. However I find I am more on the pure side, for example the Calculus I learn is viewed by most to be a tool very applicable to many physical things, but I study it for the pure mathematics.

To me, mathematics gives me a sense of enjoyment that other people get from just as non applicable hobbies, such as stamp collecting or bird watching.

 

[tony873004]

1.why in the world would a word like masturbation be censored?

One of the biggest challenges the administrators of forum boards face is keeping spam off the board. There are many spam-bots out there that continuously try to register accounts and post garbage. The spam they post is usually porn or viagra related. Certain words raise red flags, and this is one of them. It's not too often that someone on a Math and Physics board might want to use that word.

This forum obviously does a good job, since I don't see much spam here. But on my forum board at gravitysimulator.com , until my fellow administrator and I set up some filters, we had an annoying amount of xxx-related spam, most generated by robots, and some containing that word. I just checked our filter list, and that word is not included, but many similar xxx-related and racist words are.

 

[matt grime]

In my teacher's office hours, I expressed some disappointment that she was going to skip one of the "application" sections, which are my favorites.

You can read it on your own, you know. You are not beholden to do precisely what the teacher tells you. Later on you observe that other students are 'do the homework before partying' straight A types. These two things say a hell of a lot.

I complained that math is useless if its never applied to anything.

Then apply it if it helps you. This is university right? You don't get spoon-fed.

And I tend to quickly forget math unless I see it applied to real world applications because it helps me visualize the math in a way that pure memorization can never achieve.

Again, what is stopping you going through the bit in some book that applies it? Nothing. If you don't want to do the work that helps you get an A not a C as you discuss, then why should the teacher put up with your complaints (your term). If you're not prepared to put in the effort why should she? (I await the 'oh but she's paid to line...' from someone.)

I was surprised that she disagreed.

Really?

Is pure non-applied math useless?

No, although you haven't explained what you mean by 'use'. Is literature useless?

 

[CRGreathouse]

Is pure non-applied math useless?

How do you feel about Tchaikovsky, Leonardo da Vinci, Donatello, and Poe? Did they do only 'useless' things?

 

[HallsofIvy]

You are not beholden to do precisely what the teacher tells you.

Matt, shhh! We don't want students knowing that! Next you be telling them not believe every pearl of wisdom that comes out of our mouths!

 

[bassplayer142]

I think the applications should always be added. It makes the student actually have something to learn towards. I used to be good at math but I didn't like it that much. Until Calc 1, I had learned all this math and I didn't understand the point. When we started doing applications it was like a motivational thing.

 

[tony873004]

You can read it on your own, you know

Actually, I do. I often go to the index and search for pages that apply to science and astronomy because I know they'll appeal to my intuition, and I'll have a better chance of understanding them, whether they're assigned or not. But if they're not assigned, then they won't count towards my grade. And if the teacher keeps ignoring sections that go hand-in-hand with the way my mind likes to learn, and the teachers of the other sections of the same class do not, it will have an effect on my grade, and that frusterates me.

...This is university right? You don't get spoon-fed...

When did I say I wanted to be spoon-fed? Why do all your replies to my threads contain condescending attitude?

Later on you observe that other students are 'do the homework before partying' straight A types. These two things say a hell of a lot.

By quoting this without the sentences that follow, you are quoting me out of context. Please don't do that. You give the impression that I don't understand why people who do their homework before partying get better grades than those who don't. The sentences that followed the line you quoted are important to the context. I was just trying to make the point that simply because you are a diciplined student and you can memorize your way to an A does not guarantee that you are truly grasping the material, as evidenced by the fact that 0 out of 3 former A students could not even make up a word problem based on the material, while I have no problem making up word problems. Although I got a C and they got A's, there's something I walked away with from that class that they didn't. It seems to me that a class like Calculus has two purposes, 1: make the students demonstrate that they are diciplined enough to put in the effort to pass such a class, and 2: actually teach them something useful that they can use later in life. It seems to me that classes are structured such that reason 1 is by far the higher priority. Skipping the application sections only reinforces this.

 

[arildno]

Those calling maths useless are putting up some arbitrary standard of their own, by which the designate "usefulness" to some class of activity, and "uselessness" to some other class, rarely bothering about defining what either term means.

Why should they be regarded as the hallowed possessors of objective judgment?

For example, someone with the individual quirk who gets pleased by seeing an elegant proof for some assertion, is perfectly justified in saying that maths is useful in generating personal pleasure.

And what's wrong with that?

Why is mental "masturbation" worse than fiscal masturbation?

 

[tony873004]

Those calling maths useless are putting up some arbitrary standard of their own, by which the designate "usefulness" to some class of activity, and "uselessness" to some other class, rarely bothering about defining what either term means...

Just to clarify, the title to this thread is not "Math is useless" but "Is Math useless?". It was prompted by me stating in office hours to the teacher, in a friendly context, that math without application is useless. She enlightened me that not everyone feels that way. It was a very interesting discussion that I thought I would continue here.

You and others make very good points. What does useless mean? It needs to be defined. Is a baseball game useless? To many, yes. To me, no. As long as someone is getting pleasure from it, it has purpose.

Realizing that makes me want to refine my question. Besides providing pleasure to some, is non-applied math useful. Others have responded with scientific breakthroughs that took advantage of math that was once only non-applied, and with links to video lectures discussing this in detail. This is exactly what I wanted. A week ago I was sitting in office hours thinking non-applied math was useless, not even realizing there was another side to the story.

 

[arildno]

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.

 

[matt grime]

Why am I condescending? You asked a question like 'Is maths useless (without applications)?' and wonder why I'm going to be condescending?

There is more in mathematics than you can possibly ever understand, or be aware of; it is a beautiful subject. What you're learning in those classes is the (mundane) tip of a very large iceberg, and the content frankly bears no resemblence to real mathematics.

You will have plenty of time during your degree to practise the theory with applications in your courses in Engineering, Physics, or Chemistry. In the mean time, indulge in a little intellectual rigour, sharpen your thinking, and your writing skills. Exercise that brain on difficult problems before doing tedious examples that don't educate you at all as to why something is true.

It is a different set of skills you are using, or should be using, and those students didn't get straight As 'cos they 'memorized' it; they could well have a complete and sound understanding of the mathematics, and you're the one casting aspersions on their achievements with no basis at all: your barometer of 'being able to write a word problem' is no sound test at all of the understanding of the theory.And as I pointed out, that the teacher does not assign lots of applications need have no effect on your grade at all if, as you say, you just need to do some application based examples to help you learn them. Though I must admit to being confused. You assert the examples help you understand the theory, and you say you do examples independently of the assigned work. Did you actually see your grades go up when doing this? I can't tell from what you wrote. I mean, if doing the examples really does help you understand the theory, then there is nothing lost by the teacher not doing them for you. And in fact a lot to be gained. Yet you claim that actually your grades will suffer if the practical examples are not assigned. This is contradictory in my mind.

 

[tony873004]

Why am I condescending? You asked a question like 'Is maths useless (without applications)?' and wonder why I'm going to be condescending?
...

Your response to what you consider to be a stupid question is to be condecending?? That's just plain rude. What should I do if I'm sincerely wondering if non-applied math has any usefulness? Continue wondering forever, or ask?

 

[mathwonk]

is making widgets more useful than creating beauty?

 

[Chronos]

I agree with Chris Hillman . All math is useful when correctly applied. QM is fantastically accurate on short scales, and GM is fantastically accurate at large scales. Until a TOE wanders upon the scene, that is the best we can do. The problem in not with the the math, just the applications.

 

[mathwonk]

and it keeps mathematicians off the streets, mostly.

 

[CRGreathouse]

and it keeps mathematicians off the streets, mostly.

And you know, math hooligans are the worst.

 

[arildno]

Your response to what you consider to be a stupid question is to be condecending?? That's just plain rude. What should I do if I'm sincerely wondering if non-applied math has any usefulness? Continue wondering forever, or ask?

You really need to define "usefulness" first.

Is maths useful to enhance your pleasure of watching a football game? Most likely not.
Is maths useful for getting laid? Definitely yes.

 

[dimensionless]

It's not useless, but the turn over rate for research to be applied to something, is slow. Personally, I would rather learn about real things that are not abstract. On the other hand, people have different opinions about what is and isn't abstract.

 

[Proggle]

I used to have a similar opinion to yours, that favored learning math using scenarios that my mind could visualize and understand as real, rather than with abstract symbols and concepts that my mind couldn't associate with naturally.

I held this view for Calc. 1-3, but during the course of Math. Methods for Physics 1 and 2, I realized that this wasn't true. I began looking at applications as a sort of crutch that enabled me to achieve "understanding" without really going into depth about the finer mathematical details.

As I studied more complex mathematics, I began to appreciate the power of disassociating them from anything real. I began to look differently at old applied problems, and found myself having an easier time overall.

I believe pure mathematics have a way of opening your mind to new lines of thinking. Don't make a stern judgment from Calculus courses, there are a lot more beautiful and interesting mathematics out there, and you may come to appreciate the abstract approach.

 

[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.