What is your motivation for studying mathematics?

[Shadow]

That was a little bit more information than I needed to know, but go right ahead.

 

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[ajb]

On the question of mathematics being a science or an art. In my experience mathematics is a science, however doing mathematics can be an art.

 

I mean, having the initial creative thought or idea is more like art, but the implementation of that said idea is analytical, logical and scientific.

 

Any more thoughts?

[Petanquell]

More than art, it's a toy.

[ajb]

Care to explain that remark further Petanquell?

 

It is true that one can spend a lot of time "playing" with things until you find (or stumble in to) something interesting and on value.

[Shadow]

Knowing Pq, I believe he means it can be a source of fun, much like a toy.

 

Also, I disagree with the implementation of an idea not being an art. I believe it is as much an art to find a solution as it is to implement it in a correct, efficient, elegant and robust way. But that's just me

[ajb]

Certainly an art in constructing proofs.

[Shadow]

I'll second that. And an art I'm not at all good at I might add

[doG]

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

 

To better understand nature and our Universe. Effectively another vote for physics.

 

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

 

Science. Arts are open to creative definition. Math is not, it is itself definitive.

[ajb]

I'll second that. And an art I'm not at all good at I might add

 

I have a couple of things I need to construct proofs for. They are "obviously" true and I can show via examples they are true, but I need to construct a more water-tight proof. That is where the "art" comes in. Trying to cut out the irrelevant and highlight the important.

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To better understand nature and our Universe. Effectively another vote for physics.

 

Science. Arts are open to creative definition. Math is not, it is itself definitive.

 

Thank you for your input. Again, natural philosophy seems to be the main motivation.

[Shadow]

I have a couple of things I need to construct proofs for. They are "obviously" true and I can show via examples they are true, but I need to construct a more water-tight proof. That is where the "art" comes in. Trying to cut out the irrelevant and highlight the important.

 

Proofs are part of what I call "formal mathematics", because for the most part, they're just that; a formality. I know math couldn't exist without them, but it will never cease to irritate me that, as you said, even though we know something to be true, we still have to find the right words to express that truth, so that it can be considered valid and be built upon (excluding axioms, obviously). And that, from my point of view, is just so bureaucratic...

[Mr Skeptic]

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

 

I'd say that doing math is a science, and discovering/creating new math is an art.

[Shadow]

Isn't that true with everything?

[Petanquell]

I'll try it explain with my words despite my level of english.

I have three very related reasons:

 

The first reason should be clear, I'm bored and curious. In a curious-period I wonder how things work and how they were invented. In a bored-period I just sit and read, or work on a book I'm writing for my schoolmates, because they complain about the speed of our math teacher (she's really fast, I guess it's about 180 words per minute ).

 

The second reason is a little related to the book I write. I want to motivate others to do mathematics because I consider mathematics as a basic knowledge which builds you among others a useful logic."I believe everyone has some measure of talent for mathematics in them, it's just that many don't know about that, which is what I try to change. I'm also convinced that while I'm not inteligent enough to invent something great, I might be "inteligent" enough to find someone who can.

 

The third reason is that mathematics is something like meassure of intelligence for others (I really don't know why). And it gives you the respect needed to be listened to by others.

 

In a nutshell, I study to relax and to motivate others to be better then me.

 

All those things I very enjoy. When I'm writing that book or teaching my schoolmate (sometimes more then 6 hour a day) it gives me feel, that I'm useful for others. Sometimes I regret that my father forbid me to study mathematics at the university

 

Pq

 

Google dofinition of toy: "An artifact designed to be played with."

Richard P. Feynman's did exactly what i want to do . His quotation express it nicely: "Physics is like sex: sure, it may give some practical results, but that's not why we do it."

[ajb]

Proofs are part of what I call "formal mathematics", because for the most part, they're just that; a formality. I know math couldn't exist without them, but it will never cease to irritate me that, as you said, even though we know something to be true, we still have to find the right words to express that truth, so that it can be considered valid and be built upon (excluding axioms, obviously). And that, from my point of view, is just so bureaucratic...

 

Well, I do have proofs of what I claim, just I am sure I can make them much neater, easier to follow even though for the most part they are what I call "brute force" calculations as opposed to some clever argument. Proofs of a theorem can be interesting sometimes, and sometimes more interesting than the theorems, but not usually!

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I'd say that doing math is a science, and discovering/creating new math is an art.

 

I think I can understand that point of view. However, the "new structures" I have found have come about in trying to do something else. In particular I have only partially achieved what I set out to do, but along the way I have found some interesting structures. What is that saying about the journey being more important than the destination?

 

Therefore, I am not sure I can claim that my artistic creativeness led to these things. It was more spotting interesting structures in what I am trying to do.

 

I am sure some mathematicians have better luck in working out what they initially set out prove/construct etc.

[Shadow]

What did you set out to prove/construct? Is it that thing you're giving a seminar for at Kings College, the stuff related to [lot's of long words here]?

[ajb]

I wanted to understand more about odd symplectic geometry and differential forms. In particular the de Rham complex has more symmetries than just Diff. These symmetries have odd symplectic geometry as their origin. Originally, all I wanted was some useful examples. So far I don't really have much on that front, but by trying to do so I have found some interesting algebraic structures. These were known more generally, but I have found a very geometric setting for them.

 

I have found a possible use and subsequently I have discovered some related structures on higher Poisson manifolds. That is manifolds that have an [math]L_{\infty}[/math]-algebra structure on there space of functions that is a multiderivation.

 

I have shown that some of the structures on classical Poisson manifolds generalises. An open question is if this is useful in physics.

 

My work is based on three papers I would say;

 

A. S. Schwarz. Geometry of the Batalin-Vilkovisky quantization. Commun. Math. Phys. 155:249-260, 1993.

 

H. M. Khudaverdian and Th. Th. Voronov. Differential forms and odd symplectic Geometry, 2006.

 

Th. Th. Voronov. Higher derived brackets and homotopy algebras. 2004.

[ajb]

This is an interesting article Constructive mathematics by Phil Wilson in the Plus magazine.

 

It questions the philosophy of "existence" and "constructive" proofs. In the first you prove the existence of something, but don't say how to find/construct etc the thing in question. The example they use is that of the fixed point theorem. The proof states the existence of such a point, but does not say how to find that point.

 

This leads to constructivism, which is the philosophy that only by finding/constructing an object does it exist.

 

In particular, this means that mathematics does not exist independent of the human mind.

 

Personally, I don't fully subscribe to constructivism. However, I do see the attraction in construct proof and algorithms for actually finding objects. In some sense this is very close to my "gut feeling" that once should be able to provide at least one fully worked out example of any construction/theorem/definition etc. Otherwise mathematics can appear to be very "empty".

 

Any further thoughts?

[devrimci_kürt]

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

 

I concur with your opinion. ...

[Syntho-sis]

Mathematics is a science in itself. Constantly new discoveries are being made in this field.

 

Numbers have properties that are both fascinating and mind-numbing.

 

It is the language that we speak when we are discussing the universe around us.

[ajb]

Mathematics is a science in itself. Constantly new discoveries are being made in this field.

 

Thanks for your input.

 

Just have a look at the ArXiv and you will see many papers representing progress and further understanding of mathematics.

 

Numbers have properties that are both fascinating and mind-numbing.

 

True, but lets not forget objects that are not numbers.

 

It is the language that we speak when we are discussing the universe around us.

 

This seems to be the strongest motivation for most of the people who have posted here.

[Syntho-sis]

Just have a look at the ArXiv and you will see many papers representing progress and further understanding of mathematics.

 

 

Wow...Thank you for the the site. Very, very much appreciated...

 

*Adds to bookmarks*

 

[ajb]

Well I did say I would link to preprints. So, if anyone is interested

 

"Graded manifolds and Lie algebroids" arXiv:0910.1243v1 [math-ph]

"On higher Poisson and Koszul--Schouten brackets" arXiv:0910.1992v1 [math-ph]

 

___________________________________________________________

 

Lets see if we can get this thread going again.

 

Anyone else like to comment on

 

1) Why do you study mathematics? What is your motivation?

 

2) Is mathematics science or art?