Math Useless Without Applications?

[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.

 

[Pinu7]

If pure mathematics is useless, then so is any other art. Therefore, why do it? The answer is because we enjoy it. Applications follow naturally, but pure mathematicians never think to themselves how this will benefit mankind.

 

[Rasalhague]

http://www.bbc.co.uk/programmes/b00qj2nq

A recent radio programme from the BBC.

In Our Time: Unintended Consequences of Mathematics

"Melvyn Bragg and guests John Barrow, Colva Roney-Dougal and Marcus du Sautoy explore the unintended consequences of mathematical discoveries, from the computer to online encryption, to alternating current and predicting the path of asteroids."

 

[epenguin]

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.

I suspect in a lot of Uni science/eng/econ etc. depts. you'd find the anti-pure argument put a lot more aggressively than the OP or anyone has here.

I don't think the argument of the 1st para above will cut much ice there - these applied-from-very-pure activities surely involve quite a small number of people? Much more the departments will be concerned with the inadequate mathematical preparation of their greater mass of students to deal with the phys/chem/biol/econ etc. (not enough 'dull' math). They'd prefer someone else to do the job but are often wondering couldn't we do it better ourselves? And sometimes they actually do, so if you push purism too far you can put math profs. and depts. out of a job!

 

[pslarsen]

I think it is one of most beautiful things in life when math finds it real world application - and especially if it is something you discover yourself (ehh rediscover). What I find sad is that math has become so complex and crazy. Simple, but nonintuitive math is so beautiful.

Take for instance the proof of Andrew Wiles.. I believe that there exist some very nice and beautiful mathematics which yet haven't been discovered, that can proof Fermat's last theorem in a very simple way - and this math will definitely have some stunning physical applications. The proof of Wiles was so complex that he even couldn't discover his own mistake in the first place.. advanced yes.. but beautiful.. no way!

Pure mathematicians use to much energy on complexity. We need people like Ramanujan who can describe complexity with simple math..

So is math useless? Some of it... DEFINITELY !

 

[dacruick]

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

Of course pure non-applied math is useless. Thats in the definition of non-applied. I don't even think that it exists though. all math can be applied in some way, and if it is unable to be applied currently, then it has the potential to be applied later. But if you can't apply it, you can't use it, it is useless

 

[Dembadon]

How are we defining "useless" here? Useless for what?

Something which is generally and utterly useless, to me, means that it cannot be used in any way for one's benefit. In that sense, let's suppose that pure maths is only useful for providing those who like to solve problems a hobby. It is then useful, is it not? I would also argue that pure maths has supplied applied maths with useful information before.

 

[RazorRose]

well... ummm for me like... i'll read something sometimes and divide individual words into numbers and just go on reading lalaala and its like a calming exercise for my brain. i'll read a word like for example. potato. which is a 3.5 so now everytime that word happens in the book i'll just think to myself 3.5. and so on and so form. it just seems to still my mind especially when reading something i don't find particularly beneficial or interesting.
to most people converting letters into numbers would be useless. but to me helpful.

-emphasizing dembadon point.

 

[Pinu7]

http://abstrusegoose.com/strips/pure_mathematics.JPG

 

[freydawg56]

If you do not mind doing some math, but really want to apply it, go for Engineering,
Besides, they make fun of mathematicians all the time. (at the same time respecting it)
Well, I'm in Electrical Engineering, and this year I've started my study of Electromagnetic Waves, and thanks to all those guys that thought up a bunch of vector calculus and vector analysis, we can handle EM waves in a meaningful way.

One of my favorite sayings in engineering, is For all practical purposes.
This allows us to use the things that are finite, but pretend they go to infinity.
Example, electrons on a power line. Sure the power line is 500 some miles long, but we can pretend it is infinity in an applicable way.

So in summary, if you want to design things using math, try engineering. It is a lot of work, but it is satisfying and less boring than doing proofs all day (we do derive a bunch of stuff though, kinda boring)

 

[Studiot]

I read this thread and laughed, but also shook my head sadly.

May I offer my congratulations to the OP as the only contributor who appears to have learned anything.

As far as I can see he is the only one to have the guts to have stood up and admitted to a change of opinion. Every other contributor, except the humorous ones which I cannot gauge, appears to have left the thread with the same entrenched opinion as (s)he arrived with.

What a sorry exercise in communication.

 

[sponsoredwalk]

except the humorous ones which I cannot gauge,

If you attempted to gauge them you'd get shot at (i.e. get vocally confronted) by the comic-strip math professor hunting for math students looking for real-world applications (i.e. the "pure" mathematicians on PF who are so pure as to spend their time here arguing about math's purity instead of actually doing any math).

 

[Studiot]

I laughed at the comic strip.
I also laughed at the humurous comment by a real maths professor earlier on.

Rock on baby.

 

[freydawg56]

I read this thread and laughed, but also shook my head sadly.

May I offer my congratulations to the OP as the only contributor who appears to have learned anything.

As far as I can see he is the only one to have the guts to have stood up and admitted to a change of opinion. Every other contributor, except the humorous ones which I cannot gauge, appears to have left the thread with the same entrenched opinion as (s)he arrived with.

What a sorry exercise in communication.

Off topic:
but, i don't change my opinion every time i read something and most people don't either.
I do however consider new ideas and the possibility of adjusting my own opinions.
**no harshness intended, and there are reasons these kind of jokes exist

http://www.farmdale.com/emp-jokes.shtml

 

[Dembadon]

I read this thread and laughed, but also shook my head sadly.

May I offer my congratulations to the OP as the only contributor who appears to have learned anything.

As far as I can see he is the only one to have the guts to have stood up and admitted to a change of opinion. Every other contributor, except the humorous ones which I cannot gauge, appears to have left the thread with the same entrenched opinion as (s)he arrived with.

What a sorry exercise in communication.

Care to elaborate on this, or share your own opinion? Please, enlighten us! Given your attitude towards the thread and everyone who has posted in it, I'm sure we could all glean some useful information from your superior understanding.

 

[HallsofIvy]

I read this thread and laughed, but also shook my head sadly.

May I offer my congratulations to the OP as the only contributor who appears to have learned anything.

As far as I can see he is the only one to have the guts to have stood up and admitted to a change of opinion. Every other contributor, except the humorous ones which I cannot gauge, appears to have left the thread with the same entrenched opinion as (s)he arrived with.

What a sorry exercise in communication.

And by that you mean "the only one who agreed with me"?

 

[pawan_ctn]

nothing is useless in maths... math is the subject of arts and science both.
we always use it as tool to calculate and evaluate the science theories but it is not limited upto there only. see the mathematics by the eyes of maths not by the science. if u ll see it as a science tool then u can say, but the mathematics is a alone subject , it has own thinking

 

[Studiot]

And by that you mean "the only one who agreed with me"?

Of course not.

In fact the post immediately prior to the source of this quote takes me to task for not venturing any opinion.

I thought I had clearly congratulated the OP on openly saying he had disagreed with his teacher, but listened to her, thought about it, and turned again, like Dick Whittington.

BTW your earlier post was one of those I found humorous rather than lining up with one side or the other.

 

[Dembadon]

The reason I asked you to elaborate is because your post does not address the OP’s question.

… I thought I had clearly congratulated the OP on openly saying he had disagreed with his teacher, but listened to her, thought about it, and turned again, like Dick Whittington. …

You still avoid taking a personal stance regarding the OP's question. Congratulating someone else on their thought process does not have anything to do with whether or not you think math is useless, which is the question that is being asked by the OP. In other words, we would be wrong to assume anything about your position without a more direct statement from you.

Also, you do not know whether or not the posters have done as you suggest here. I’m sure most, if not all, read the post, thought about it, and then responded with their opinion.

As far as I can see he is the only one to have the guts to have stood up and admitted to a change of opinion. Every other contributor, except the humorous ones which I cannot gauge, appears to have left the thread with the same entrenched opinion as (s)he arrived with.

Here, you seem to be implying that, "Every other contributor..." should have changed their minds after reading the first post; which I guess is the entrenched opinion with which you arrived? If it's not, please elaborate.

May I offer my congratulations to the OP as the only contributor who appears to have learned anything.

Learned anything? The position of superiority you take here leads me to believe that you have a full understanding of what one should have said. If my assumption is incorrect, please elaborate.

What a sorry exercise in communication.

I thought the goal of a forum was to stimulate discussion between all opinions, not just one. I’d say it’s working as intended; quite well, even. If you agree with that, please elaborate on what you meant by this statement.

 

[Studiot]

You still avoid taking a personal stance regarding the OP's question. Congratulating someone else on their thought process does not have anything to do with whether or not you think math is useless, which is the question that is being asked by the OP. In other words, we would be wrong to assume anything about your position without a more direct statement from you.

Agreed, although since this is a math sub-forum I wonder if it has to be one or the other? Perhaps there is a third, fourth, fifth... way?

As an applied mathematician I have no desire to get into a war with someone with a shotgun.

Take a look at this thread. My curt comment quickly stimulated further thought and discourse rather better than my just 'pronouncing from on high' might have done.

https://www.physicsforums.com/showthread.php?t=381546

Not that I'm here from on high - I'm here to learn like everyone else.

 

[Dembadon]

Agreed, although since this is a math sub-forum I wonder if it has to be one or the other? Perhaps there is a third, fourth, fifth... way? ...

I didn't place a limit on how many solutions/opinions one could offer, either. I just asked if you had one.

... As an applied mathematician I have no desire to get into a war with someone with a shotgun. ...

Good. I have no desire to start a war, nor did I intend to portray myself as a shotgun-wielding applied mathematician slayer. I am seeking understanding; nothing more.

 

[George Jones]

http://abstrusegoose.com/strips/pure_mathematics.JPG

[/URL]

Notice that in the second-last panel, the applied mathematicians say "X ... ," and, in the last panel, X satisfies Killing's equations, so X is a killing vector (field).