Mathematics - art or science?

Din Taylor

I remember many a heated debate about this when I was a maths researcher. On the one hand you have Carl Friedrich Gauss calling it the "queen of the sciences" and on the other hand the renowned number theorist G. H. Hardy argues that it is an art in A Mathematician's Apology. (Well pure maths anyway.)

It would be interesting to get the view of the mathematicians on boards.

Fremen

Being a mathematician, it's nice to see things clearly defined. The answer to this question depends what is meant by "art" (and to some extent, what is meant by mathematics). If you define art as something which is manmade and aesthetically pleasing, then you could easily argue that mathematics is art. Of course, some artists would argue that art only needs to provoke an emotional response, not necessarily a pleasant one. Still, the latter definition includes the former.

The definition of a science is a bit easier to tackle. Karl Popper defined a science as an intellectual discipline which makes falsifiable predictions. Maths goes one step further, in that the predictions (conjectures) are both falsifiable and verifiable. On those grounds, you can call maths a science.

I think it's a false dichotomy to split the world into arts and science. A subject can be one or the other, or both, or neither.

Eliot Rosewater

A lecturer of mine once remarked, "Mathematics is like poetry: it is worthy of study for its own sake".

My Oxford Concise English Dictionary defines art as "the expression or application of creative skill and imagination, especially through a visual medium such as painting or sculpture". I think that mathematics requires creativity and imagination.

equivariant

IMO maths shares elements of both art and science but is neither. Anyway mathematics as a human endeavour by far predates science (at least in the sense that word is used nowadays) and is probably at least as old as anything that would be generally recognised as art. So why should it be classified as one of these?

PS I think that mathematics is far more worthy of study for its own sake than poetry is, but then I am biased

Kazmandu

I agree with equivariant. No need to call math art. Besides there is one big difference between the two. Art is an expression of culture (anthropological definition of culture) and math is cultureless. Example pascals triangle is an expression of what culture French? Chinese? Persian? :rolleyes:

hint: all of them means none of them.

Catsmokinpot

Eliot Rosewater wrote: »

A lecturer of mine once remarked, "Mathematics is like poetry: it is worthy of study for its own sake".

My Oxford Concise English Dictionary defines art as "the expression or application of creative skill and imagination, especially through a visual medium such as painting or sculpture". I think that mathematics requires creativity and imagination.

Yes but it has to be right or its bad Maths

It's a science, if its wrong even though it looks nice it gets thrown out and replaced with new Maths.

1 +(-1) doesn't equal 0 because it looks pretty, it's because it does.

Pythagoras didn't just invent his theory in his mind, it took his brilliant mind to realise what was already staring him in the face.

Just a few thoughts, that's how I see it anyway.

equivariant

Kazmandu wrote: »

I agree with equivariant. No need to call math art. Besides there is one big difference between the two. Art is an expression of culture (anthropological definition of culture) and math is cultureless. Example pascals triangle is an expression of what culture French? Chinese? Persian? :rolleyes:

hint: all of them means none of them.

I'm not sure I agree that mathematics is cultureless. Certain types of mathematics are clearly identified with certain cultures. For example the ancient greeks and geometry, or bourbaki and french mathematics. If mathematics and culture are independent why is it that the Chinese did not develop geometry to the same level as the greeks?

Kazmandu

Hi Equavariant

Here is a pretty good debate on that issue.:rolleyes: If you want to add more - I would be interested in what you have to say.

http://mathematicalpoetry.blogspot.com/2009/12/math-art-moment-13.html


Cheers!:)

scallioneater

I think that mathematics is the language of science and therefore as a language it is an art. Over the millenia and centuries the language of math has adapted and changed to fit the needs of its practicioners, developing new expressions and combinations just as all languages have.

Some have argued that there is an underlying logic to math that makes it a science. I agree that we all see logic in math expressions, but we see the same logic in a well fromed sentence of any language. Also, if the logic of math makes it a science, then philosophy is a science.

Science requires art, Art requires science. I think math is sublime because it is a major foundation of most (if not all) of the arts and the sciences.

The subsets science and art do not form a partition on the set of all subjects. Indeed, they are not even disjoint.

Anybody who takes a look at the Project Euler problems or does a course in computer computation in college, or who just remembers forgetting some algebraic rule in school and scrawling a few numeric examples to try to jog their memory, will know that experimentation is very much a part of mathematics. I don't think anybody could argue that it isn't a science.

On the other hand, problem solving, sketching out a proof, and writing about and explaining mathematics to other people are very much arts. mathematicians have quoted as saying they like another mathematician's "style".

I guess it's not so much a question as a topic to stimulate discussion about maths anyway.

Ruski

More of a language.

c-note

numbering letters a to z, 1 to 26 respectivly;

we find the sum of math to be
13+1+20+8 = 42
reducing this to a single digit 4+2 =6

doing the same with art we find
1+18+20 = 39...3+9 = 12... 1+2=3

clearly art(3) not equal math(6)

***********HOWEVER***********

if we take PAINT
16+1+9+14+20 = 60 ... 6+0 = 6

here we see that math(6) = paint(6)

what we can conclude from this is either;

A: NOTHING, if you believe there is no art in math

B: Math is a subset of Art (namely paint)

QED

hope that clears it up

gosplan

This answer sucks but it's quite clearly both.

elementary

Din Taylor wrote: »

I remember many a heated debate about this when I was a maths researcher. On the one hand you have Carl Friedrich Gauss calling it the "queen of the sciences" and on the other hand the renowned number theorist G. H. Hardy argues that it is an art in A Mathematician's Apology. (Well pure maths anyway.)

It would be interesting to get the view of the mathematicians on boards.

In Gauss' time 'science' would have had a more broad meaning than it does today. Nowadays science is associated with barbarism and a vulgar, unimaginative type of intellect:pac: so I'd say it's an art.