What is the point in pure maths?
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Original post by When you see it...
No, I'm asking what the point of it is. It seems selfish (that probably isn't the right word though) to study something just because you enjoy it.
I am well aware that eventually much pure maths has applications, but can't we just 'come up' with that mathematics when the real-world problem arises?
I am well aware that eventually much pure maths has applications, but can't we just 'come up' with that mathematics when the real-world problem arises?
As someone has already said above, it takes a lot of time to develop the correct mathematics to study different aspects of science. Some techniques have to be well-developed enough and understood enough before it can be applied. When you do science, sometimes you want the tool you use to be already available and it to be usable beyond doubt. After that you can philosophise about what it really all means.
(edited 12 years ago)
Original post by 21stcenturyphantom
I imagine he means you are saying something is only useful or worth learning when there is a direct use or objective-based purpose to it.
Yes, that is true, but how exactly did you infer that from his comment? It seems quite cryptic in what his actual point is. It actually comes across as an 'in the good old days...' comment like the sort present on the Daily Mail comments sections.
Why has the maths forum turned into a bunch of tools complaining about maths without thinking first?
Original post by Freier._.lance
As someone has already said above, it takes a lot of time to develop the correct mathematics to study different aspects of science. Some techniques have to be well-developed enough and understood enough before it can be applied. When you do science, sometimes you want the tool you use to be already available and it to be usable beyond doubt. After that you can philosophise about what it really all means.
I am arguing that the other way round would be better because existing 'real-world' problems could be dealt with more quickly and therefore the new problems could be discovered sooner, so overall the applications happen faster.
Original post by When you see it...
It has no practical application, why can't people who work (professionally I mean) in pure maths do something that actually benefits people.
Yes, I know that it helps to explain things like science which have practical application, but we don't need pure maths to help with that once the problem (or whatever it is) is found because people can work out the maths needed without worrying about the silly things like mathematical proof.
Just to clarify my stance, I think if something has real-world application, I no longer consider it to be 'pure maths'. So please don't say things like 'it is useful for solving problems in physics to do with black holes (or whatever)' because then it would no longer be pure maths.
Other than for 'fun', what is the point in pure maths?
EDIT:
Okay, to clarify further. I think 'pure maths' is when people try to prove things that, for all intents and purposes, are self-evidently true. It is impossible to prove something without making assumptions, so mathematical proof is no more valid than scientific proof just because it makes different assumptions. Also, when people work on problems with numbers or algebra (or whatever) that they can't clearly see an application for (an application being something that would benefit other people). Just because applications are often found later, that doesn't justify finding out the methods used earlier on, because those same methods could have been discovered when the real-life problem arose.
Yes, I know that it helps to explain things like science which have practical application, but we don't need pure maths to help with that once the problem (or whatever it is) is found because people can work out the maths needed without worrying about the silly things like mathematical proof.
Just to clarify my stance, I think if something has real-world application, I no longer consider it to be 'pure maths'. So please don't say things like 'it is useful for solving problems in physics to do with black holes (or whatever)' because then it would no longer be pure maths.
Other than for 'fun', what is the point in pure maths?
EDIT:
Okay, to clarify further. I think 'pure maths' is when people try to prove things that, for all intents and purposes, are self-evidently true. It is impossible to prove something without making assumptions, so mathematical proof is no more valid than scientific proof just because it makes different assumptions. Also, when people work on problems with numbers or algebra (or whatever) that they can't clearly see an application for (an application being something that would benefit other people). Just because applications are often found later, that doesn't justify finding out the methods used earlier on, because those same methods could have been discovered when the real-life problem arose.
When people criticize a discipline for not being COMPLETELY practical I can spot the stains of ignorance. OP, educate yourself.
Original post by rainbow_kisses
It is at a-level 
I can appreciate its not the same at Uni
I can appreciate its not the same at UniDamn straight it isn't. But no hard feelings.
Original post by When you see it...
I am arguing that the other way round would be better because existing 'real-world' problems could be dealt with more quickly and therefore the new problems could be discovered sooner, so overall the applications happen faster.
The other round as you say would be a lot slower. When you find something new you won't have any mathematics with a similar structure already in place and you will have no idea what you are looking at. You have two options: Either the mathematics already exists, or you have to design it yourself. The second way would be a lot slower.
Original post by When you see it...
There is a thread on here which I think is still active, arguing whether or not 0.999999.... is equal to 1. I mean WTF? If you were solving a real-life problem (I need to find some synonyms for this lol) involving these numbers, it wouldn't matter.
Oh, so you found one putative use for maths, that actually isn't very useful.
I was going through the supermarket the other day, and found something that wasn't a fruit. Does that mean that there was no fruit in the supermarket?
Original post by hassi94
Why has the maths forum turned into a bunch of tools complaining about maths without thinking first?
Why are you resorting to personal attacks? That, coupled with the fact that you are advocating not questioning the establishment and mindlessly accepting received wisdom, makes you look like the 'tool'.
Original post by When you see it...
I don't like that sort of science either, although it is more reasonable to think that discovering these planets will one day have a benefit if we discover civilisation there or visit there and find new raw materials than it is to think that some 'maths for the sake of maths' will one day have a benefit
I'm delighted to know that you have discovered a way to visit other planets without mathematics (of the kind you most detest).
Original post by Raiden10
Oh, so you found one putative use for maths, that actually isn't very useful.
I was going through the supermarket the other day, and found something that wasn't a fruit. Does that mean that there was no fruit in the supermarket?
I was going through the supermarket the other day, and found something that wasn't a fruit. Does that mean that there was no fruit in the supermarket?
Let me update my previous summary:
I speak in fundamentals.
"At least speak in specifics, otherwise I'm not going to recognise your argument."
I give a specific.
"That specific doesn't count obviously"
Why not?
"...because it is not complicated enough. A good example would be one taught at Cambridge."
"Haha, speaking in specifics proves nothing, at least talk in fundamentals, otherwise I'm not going to recognise your argument."
Dare I link you to the OP?
Original post by When you see it...
Why are you resorting to personal attacks? That, coupled with the fact that you are advocating not questioning the establishment and mindlessly accepting received wisdom, makes you look like the 'tool'.
Sorry I'm just getting irritated. It's not that I have a problem with questioning things, just that your questions are dumbfounded, and if you took time to research a bit more about maths then you might not be asking these questions.
It happened with the 0.999 thing (though that was more from posters than the thread starter) and also the discussion about 'ability' and this new one about pi. It's like people are just arguing for arguments' sake
Original post by When you see it...
Why are you resorting to personal attacks? That, coupled with the fact that you are advocating not questioning the establishment and mindlessly accepting received wisdom, makes you look like the 'tool'.
How about this for a personal attack. You're 16, I'm 23, you don't know anything, shut up and listen to what me and other people who know more than you have to say.
Original post by hassi94
Sorry I'm just getting irritated. It's not that I have a problem with questioning things, just that your questions are dumbfounded, and if you took time to research a bit more about maths then you might not be asking these questions.
It happened with the 0.999 thing (though that was more from posters than the thread starter) and also the discussion about 'ability' and this new one about pi. It's like people are just arguing for arguments' sake
It happened with the 0.999 thing (though that was more from posters than the thread starter) and also the discussion about 'ability' and this new one about pi. It's like people are just arguing for arguments' sake
Jesus don't apologize to this guy. He's an idiot.
pure maths does have lots of practical applications. Lots of things are theorised int he abstract then a very practical use is one day found.
BUT pointless things are often the most fun...
Art
Music
Cinema
Alcohol
Chocolate (unless you're actually struggling to survive)
ETC totally pointless but still very enjoyable to a lot of people...
BUT pointless things are often the most fun...
Art
Music
Cinema
Alcohol
Chocolate (unless you're actually struggling to survive)
ETC totally pointless but still very enjoyable to a lot of people...
Original post by When you see it...
Let me update my previous summary:
I speak in fundamentals.
"At least speak in specifics, otherwise I'm not going to recognise your argument."
I give a specific.
"That specific doesn't count obviously"
Why not?
"...because it is not complicated enough. A good example would be one taught at Cambridge."
"Haha, speaking in specifics proves nothing, at least talk in fundamentals, otherwise I'm not going to recognise your argument."
Dare I link you to the OP?
I speak in fundamentals.
"At least speak in specifics, otherwise I'm not going to recognise your argument."
I give a specific.
"That specific doesn't count obviously"
Why not?
"...because it is not complicated enough. A good example would be one taught at Cambridge."
"Haha, speaking in specifics proves nothing, at least talk in fundamentals, otherwise I'm not going to recognise your argument."
Dare I link you to the OP?
You can do whatever you ****ing like, mate.
Original post by Raiden10
I'm delighted to know that you have discovered a way to visit other planets without mathematics (of the kind you most detest).
So you are saying that pure maths (rather, what I am calling pure maths which it seems may not be the actual definition) is used in visiting other planets?
This thread has become ridiculous. It really is frustrating reading some of this, so I will explain a short response.
The first point to make is that there really is a point to exploring maths for the sole purpose of discovering more and developing human knowledge. The human thirst for knowledge in any area could be argued to be part of the reason for our species being so successful. This thirst, while it may not obviously lead to practical applications, in the long run may well provide a complete understanding of the world that will have an application. This again is true of any subject. The study of ancient history could be argued to have little relevance to today. Civilisation has changed lots since thousands of years ago. Yet it is still a (for want of a better word without sounding too keen) good subject to study, since it provides an insight into humanity. In the same way, the study of abstract maths, science and indeed art could perhaps provide an insight into the workings of the universe, something that will always be of interest to humanity. You can't seriously say that you have never wanted to know more about something just for the sake of knowing, even if that knowledge won't provide you with a substantial 'practical application'.
Secondly, maths can't just be developed when and if you need it. Lots of it is far too complex and would make any science (i.e. real world, practical) problem ridiculously difficult to solve. This is because science is applied mathematics. If you had to derive the mathematics from first principles whenever you wanted to use it in science, while theoretically it would be possible, it would also be ridiculously time-consuming and preposterous for other reasons. Therefore, there is a subject dedicated to deriving and developing the pure maths that constitutes the fundamentals of practical science. It isn't because someone one day decided that that was how it should be, but rather because that's the only way it can be. Without a good understanding of pure maths, hardly anything remotely interesting in science can be achieved. To really understand what I'm on about here, you probably need to think beyond your (and my, I'm only just learning A-level maths myself) understanding of maths being relatively simple problems and concepts. There is some exceptionally tricky stuff out there which does have applications in science.
Thirdly, someone did state at one point that mathematical proof is no different from scientific proof, and is just based on assumptions. This is incorrect. Mathematical proof (at least, all that I'm aware of) is based fundamentally on pure logic (scientific proof is slightly different in that it might be based somewhat on assumptions made in a commonly accepted and logical model developed from masses of experimental data). Mathematical proof is not silly. Without it, we couldn't have mathematics, since we must prove things in order to say they are true. I don't really know how better to explain it, but to describe mathematical proof as 'silly' is ridiculous, since without it there would be no 'practical' science.
Fourthly, addressing one person's point about it being selfish to study abstract maths that is of no immediate practical application, is it also selfish for the artist (poet, musician etc.) or novelist to do their work? They provide many things. They entertain, their work is a catalyst for thought and they provide extremely interesting works for people to ponder over, debate, marvel at and enjoy. The same to at least some extent (although less obviously, and often to a smaller audience) applies to mathematicians exploring extremely abstract maths.
Finally, as with all matters it is crucial to keep an open mind, and not let your immediate thoughts get in the way of things. I believe that one should try to look at philosophical problems from a variety of perspectives, and hence I would be very interested to hear any responses to what I've just written. Hopefully I haven't been spewing COMPLETE nonsense!
The first point to make is that there really is a point to exploring maths for the sole purpose of discovering more and developing human knowledge. The human thirst for knowledge in any area could be argued to be part of the reason for our species being so successful. This thirst, while it may not obviously lead to practical applications, in the long run may well provide a complete understanding of the world that will have an application. This again is true of any subject. The study of ancient history could be argued to have little relevance to today. Civilisation has changed lots since thousands of years ago. Yet it is still a (for want of a better word without sounding too keen) good subject to study, since it provides an insight into humanity. In the same way, the study of abstract maths, science and indeed art could perhaps provide an insight into the workings of the universe, something that will always be of interest to humanity. You can't seriously say that you have never wanted to know more about something just for the sake of knowing, even if that knowledge won't provide you with a substantial 'practical application'.
Secondly, maths can't just be developed when and if you need it. Lots of it is far too complex and would make any science (i.e. real world, practical) problem ridiculously difficult to solve. This is because science is applied mathematics. If you had to derive the mathematics from first principles whenever you wanted to use it in science, while theoretically it would be possible, it would also be ridiculously time-consuming and preposterous for other reasons. Therefore, there is a subject dedicated to deriving and developing the pure maths that constitutes the fundamentals of practical science. It isn't because someone one day decided that that was how it should be, but rather because that's the only way it can be. Without a good understanding of pure maths, hardly anything remotely interesting in science can be achieved. To really understand what I'm on about here, you probably need to think beyond your (and my, I'm only just learning A-level maths myself) understanding of maths being relatively simple problems and concepts. There is some exceptionally tricky stuff out there which does have applications in science.
Thirdly, someone did state at one point that mathematical proof is no different from scientific proof, and is just based on assumptions. This is incorrect. Mathematical proof (at least, all that I'm aware of) is based fundamentally on pure logic (scientific proof is slightly different in that it might be based somewhat on assumptions made in a commonly accepted and logical model developed from masses of experimental data). Mathematical proof is not silly. Without it, we couldn't have mathematics, since we must prove things in order to say they are true. I don't really know how better to explain it, but to describe mathematical proof as 'silly' is ridiculous, since without it there would be no 'practical' science.
Fourthly, addressing one person's point about it being selfish to study abstract maths that is of no immediate practical application, is it also selfish for the artist (poet, musician etc.) or novelist to do their work? They provide many things. They entertain, their work is a catalyst for thought and they provide extremely interesting works for people to ponder over, debate, marvel at and enjoy. The same to at least some extent (although less obviously, and often to a smaller audience) applies to mathematicians exploring extremely abstract maths.
Finally, as with all matters it is crucial to keep an open mind, and not let your immediate thoughts get in the way of things. I believe that one should try to look at philosophical problems from a variety of perspectives, and hence I would be very interested to hear any responses to what I've just written. Hopefully I haven't been spewing COMPLETE nonsense!
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