What is your motivation for studying mathematics?

[ajb]

Just a general question, may be practical or philosophical, what is your motivation for studying mathematics?

 

My motivation is that I believe that a deeper understanding of nature can only be archived by understanding (and generalising) the mathematical structures found in theoretical physics.

 

Much like category theory studies via abstraction the "mathematics of mathematics", mathematical physics deals with the mathematical structures found in theoretical physics without direct reference to the original physical systems. The generic idea is that we learn more about nature by abstraction. This I believe will become more and more true as time goes on and the tools of theoretical physics will embrace areas of mathematics formally restricted to pure mathematics.

 

A further, but to me secondary motivation is for the simple sake of discovering new mathematical structures and further developing pure mathematics.

 

So, what about you?

[Mr Skeptic]

I like math because of its usefulness to understanding science, especially physics.

[ajb]

I like math because of its usefulness to understanding science, especially physics.

 

A necessary evil? or part of science?

 

Either way, it looks like physics is both our main motivations.

[DJBruce]

For me I study math becuase in my opinion math is the language in which the truths of the universe are written and one day I hope that math will help me discover these truths. As a side note, I find it fun and I need it in order to enter a good university.

[ajb]

"truths of the Universe"- another vote for physics?

[Mr Skeptic]

A necessary evil? or part of science?

 

Uncertain. Some maths are interesting in and of themselves, some maths are annoying but necessary.

 

Either way, it looks like physics is both our main motivations.

 

Yup!

[npts2020]

I was dragged kicking and screaming to do math, probably because of bad instruction early on. After 10th grade geometry class, I had hoped that I was done having to learn math but in 12th grade the astronomy class I took required fairly advanced algebra and basic calculus. I muddled my way through and managed to get a "B" but was obviously handicapped by not knowing enough math. The same thing was happening when training to be an engineer but I managed to pick up enough to at least understand more than not. So I guess you can put me in the "necessary evil for learning physics" category.

[ajb]

A related but different question. Is mathematics an art (thus things are created) or is it a science (things are discovered)?

 

I think it is a science as a whole.

[abskebabs]

Hi ajb, I caught sight of your question and it definitely intrigued me, as i have wondered about this before. I think I find a lot in common, with the sensation you refer to and generally, the feeling of exploration that is gained during the study and thought process while trying to gain cognition fo mathematical systems. One particular example, came from reading the vector calculus chapter and gasping in wonder at the way things developed out of a simple notion considering a vector travelling along a curve.

 

Personally, in order to answer your question, I remember a conversation with some friends from school a while back about this. I remember the question of whether mathematics was a science, and I disagreed interjecting that it was a language.

 

My views have differed since then, but this core insight has been influential in forming my own views on the matter. Mathematics itself may be categorised into boxes like "applied", "pure", geometry and algebra, though i see it much more broadly as a system of thinking and means of application to solve problems. I guess it depends on where you draw the line between mathematics, logic, and even perhaps analytical philosophy.

 

I have recently been reading a lot of economics, and especially that of the Austrian school, and strangely enough, this has reinforced my perception of the importance of logic, and understanding deduction while causing me to become more skeptical of transplanting methods of induction from the natural sciences in order to reason the social sciences.

 

In short, I'm still fascinated by mathematics and mathematical thinking, I guess my general philosophy nowadays is a lot less straightforward. I also think mathematics has artistic elements to it, but thankfully, like with the natural sciences, this is not used to rule out theorems in it, though I guess some may be considered so "pathological" and far from th core or application to be deemed worthy of study. What do you think?

 

I find I get an aesthetic appeal to elegance, when I read a certain tract of mathematics, or even a few pages from a maths or physics textbook, when I feel both the prose and the maths combine to produce this kind of appeal. I guess in this way, it shares a similiar aspect to me in the way words canombine to produce a beautiful book, reinforcing the entire language notion.

[Mr Skeptic]

Interesting point, abskebabs. I think math can be considered a language of formal thought. Like other languages, it can be used aesthetically.

[ecoli]

application to biological and social phenomenon.

[Shadow]

Pure human curiosity. I just love finding out how things work. (Un)fortunately, that sets cardinality is finite; I hate proofs (among other things) )

 

Cheers,

 

Gabe

[fredrik]

I've never been interested in so called pure mathematics, but my motivation for mathematics has always been the same that motivates me to understand the world I live in (My focus has been natural science: physics but also biology). As an efficient language to describe what I see in a rational manner. So I see the development of mathematics as going hand in hand with the development of science. For me, one without the other is unthinkable.

 

What can you rationally express without efficient language?

But also, what to do with a language, if you have nothing to say?

 

As has been been the case in the history of physics, to see the simplicity of nature has been closely related to "inventing the language in which it gets simple". That's what "economy of language means to me". Simplicity is relative.

 

/Fredrik

[Petanquell]

I'm just very often bored and I chosed mathematics to fill my long days because it seems much more logical and easier than nature...

[Shadow]

how can it be more logical and easier than nature if mathematics are, at least according to me, the most fundamental laws by which nature must abide, thus being an integral part of nature itself? )

[Petanquell]

in math, always [math] 1+1=2 [/math]

in nature, sometimes [math]\mbox{male} \bigcap \mbox{female} = \begin{cases} \mbox{boy} & \mbox{if } \mathbb{R^+} \\ \mbox{girl} & \mbox{if } \mathbb{R^-} \\ 0 & \mbox{if } \varnothing \\ \mbox{something else}&\mbox{if something else} \end{cases}[/math]

Do you see it??

[ajb]

I don't think mathematics is just a language, but it is true that language/notation is an important part of mathematics.

 

So, it seems that natural philosophy is the main driving force on this thread. Maybe with the exception of Shadow and Petanquell.

 

Does anyone have any thing to add about pure mathematics as an intellectual pursuit and the benefit of knowledge for mankind?

[hell_ever]

I believe pure math is an art form very much like music and painting. As G H Hardy said (don't remember exact phrase) "May Math never be of any use." Very sad to see no number theory subforum on this website dedicated to science. Physics, chemistry and other subjects simply use math as a tool, for their own development and contribute nothing to math itself.

[Shadow]

I missed your art/science question ajb. I believe it is a point of view. One can think of the universe in a way that suggests 1+1 always equaled two, and it just took humankind time before they figured it out. And it's true; one atom and another atom always made two atoms, regardless of whether some race on a blue planet knew about it or not.

 

Or, one can again think of the universe as a fixed thing, but there being an infinite way of expressing the laws by which it is governed. For example, humans created the number one, the number two, the signs plus and equals, and then described this mathematical relation in this way. While it was always true, we created the notation and the system by which this is expressed.

 

I like to think of it as a combination of the two; creating on the basis of discovery.

 

Cheers,

 

Gabe

 

PS.: hell_ever, I believe the "General Mathematics" sub-forum is suitable for discussions regarding Number Theory )

Edited December 28, 2008 by Shadow

[DJBruce]

In my opinion the basic ideas for math are universal. Like Shadow said 1+1=2 no matter if we knew it or not. So since the ideas for math are universal math is not so much an art like painting but is more like a coloring book where we can only draw inside the lines already given to use.

[ajb]

Physics, chemistry and other subjects simply use math as a tool, for their own development and contribute nothing to math itself.

 

That is not true at all. Many developments in mathematics go in hand with discoveries in the natural world. A good example is operator algebras and quantum mechanics.

 

Also, the contrary is true, developments in pure mathematics feed back into the other sciences allowing further development. This is especially true of mathematical physics and theoretical physics.

 

 

I have recently come across a mathematical structure that I have not seen in the literature. I think I discovered it, yet some of the opinion here is that I created/invented it. Very interesting. (It may be already know and studied somewhere).

 

Another point is that it came from work very much rooted in physics. Again, negating hell-ever's statment. Again, very interesting.

Edited December 29, 2008 by ajb

[Shadow]

I have recently come across a mathematical structure that I have not seen in the literature.

 

Not to go off topic here, but care to share? I probably won't understand, but...well, I am a curious person

 

Cheers,

 

Gabe

[ajb]

I am not going to share right now. I will as soon as I have announced my results officially at a meeting/seminar series or a preprint. I have been invited to give an informal seminar at King's College, so once I have done that...

 

Watch this space.

[Shadow]

Thanks, will do.

 

Good luck )

[ajb]

I will tell you that it is related to [math]L_{\infty}[/math]-algebras , homotopy B.V.-algebras and odd symplectic geometry.