What is the point in pure maths?

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?

You know what, you're smarter than you look.

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.

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

He may be very naive, but I doubt mocking him will make him understand any quicker.

Pascal was quite young when he made all of those discoveries about maths.

...and you come across as a complete dickhead. Young people are often better equipped to do something that will actually change the world than closed-minded old people with your attitude as they have not been indoctrinated with the etiquette and conventions/routines of their discipline or society in general. Joan of Arc was like 13 when she kicked the English army's arse. Pascal was quite young when he made all of those discoveries about maths. Hitler was grown up when he started Nazism. I think you are the one who needs to grow up and accept that sometimes people disagree with you.

...and you come across as a complete dickhead. Young people are often better equipped to do something that will actually change the world than closed-minded old people with your attitude as they have not been indoctrinated with the etiquette and conventions/routines of their discipline or society in general. Joan of Arc was like 13 when she kicked the English army's arse. Pascal was quite young when he made all of those discoveries about maths. Hitler was grown up when he started Nazism. I think you are the one who needs to grow up and accept that sometimes people disagree with you.

Hitler was grown up when he started Nazism. I think you are the one who needs to grow up and accept that sometimes people disagree with you..

Just to clarify my stance, I think if something has real-world application, I no longer consider it to be 'pure maths'.

Dafuq? Are you trying to imply you're a genius?!

Oh dear, Godwin's Law. You've just forfeited your entire argument and forever more you will have to accept that you can't justify your ludicrous claims of pure maths lacking a meaningful existence or practical use. That's just the way it is I'm afraid.

The difference is, you haven't seen a lot of people like me, but I've seen a lot of people like you. As such I can identify a common thread. It's not that these people don't recognise that they are wrong - nothing wrong with that. It's the refusal to even consider the possibility. To not even consider it as worthy of a second thought.

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!

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.

Finding the dot product of two vectors isn't pure maths

As for the OP, if pure maths is no longer allowed to be classed as such when it starts being useful, obviously no pure maths will be 'useful' by your definition.

Well you may need to speak to the department of education because they have it in C4 pure maths A2 level XD

(And out of interest, what defines pure maths?)

While I agree with many sentiments from your post, this one is a bit dubious. We shouldn't forget Gödel's lesson that every set of proofs always has to have some axioma's that cannot be proven, but are rather assumed. Of course, they are often very plausible and agreeable, but it's an illusion to consider it some form of "pure truth" that is completely without assumption. Of course it's silly to suggest that proofs as such are 'silly' though.