What do you like best - pure or applied?

But if you think about it, isn't maths applied philosophy?

no.

When I say pure maths I mean proper pure maths e.g. number theory, not core maths 1-4 a level stuff (with the exception of possibly proof by induction).

I personally like applied maths way more because it seems more creative and you can see how it can be used.

What do you think?

But concepts such as Infinity and Zero are also philosophical. Maths itself is an abstraction: we define 5 as 5 of something, but equally any symbol could represent 5, etc.

number theory, analysis, geometry, proofs and logic? that is what I thought pure maths was. maybe I missed a few things. and am I correct in thinking that calculus is completely applied maths except for studying it through analysis?

But concepts such as Infinity and Zero are also philosophical. Maths itself is an abstraction: we define 5 as 5 of something, but equally any symbol could represent 5, etc.

But if you think about it, isn't maths applied philosophy?

Subtract the total amount of money that mathematicians have to spend on philosophy textbooks, from the total amount of money that physicists have to spend on mathematics textbooks, and you get the total amount of money that physicists have to spend on mathematics textbooks.

It would be better to add a poll to this thread.

done

Pure.

Out of interest, what is calculus classed as?

Or better yet, divide the amount Physicists spend on Mathematics texbooks by the amount Mathematicians spend on Philosophy texbooks and you get an a problem!

Calculus is applied - It was primarily invented under the motivation to study motion. Although the more recent area of maths known as Analysis studies the same concepts as calculus as a pure branch.

But if you think about it, isn't maths applied philosophy?

Subtract the total amount of money that mathematicians have to spend on philosophy textbooks, from the total amount of money that physicists have to spend on mathematics textbooks, and you get the total amount of money that physicists have to spend on mathematics textbooks.

There's no absolute distinction. There are clues.

For instance, if a textbook or lecture starts with "let X bet a set..." there's a good chance that it is a textbook or lecture on pure mathematics. Also pure mathematics tends to contain more words and definitions and applied mathematics tends to contain more numbers and equations.

Of course that's not universally true, for example analytic number theory is pure mathematics but consists of many estimates.

But in any case I think the fact that you can write a page of words and paragraphs, with almost no equations, and it still be mathematics has the potential to befuddle A-level students. Sometimes people say something like "that's not maths, it's logic", but it is very much mathematics and should be called as such. By that I mean, it has as much right to be called "mathematics" as anything else!

Pure mathematics tends to be organised (not separated) according to the two pillars of algebra and analysis. There is sort of a third wheel called "topology". Then there is geometry and number theory, the two topics that can perhaps be understood at a rudimentary level. Number theory might be considered as the application of algebra, analysis, and topology (and other mathematics) to "elementary number theory". Geometry is the application of algebra, analysis, and topology (and other mathematics) to situations where geometric/physical intuition holds some sway and is of some interest. Finally there is the "rising bin" of combinatorics. It's "rising" because it's getting more important all the time, and it's a "bin" because lots of other stuff that doesn't fit into anywhere else goes into it.