Art and Mathematics - the two sisters

Yesterday I came across this interesting blog where there was a discussion on whether there is Art in Maths and vice-versa. Now this was a topic on which I have done some thinking in the past. So I decided to share my two cents.

The opinion in the post was that (quote) Art has a lot of Maths in it but there's no Art in Maths (unquote). Then there was this suggestion that (quote)there is a certain degree of talent as well as skill needed to be good at both Maths and Art.(unquote).

We had a good discussion on this topic.

Karthik :
Interestingly, with minimal knowledge of math, you can deduce and reach upto advanced math by pure logic and intelligence.So it is probably incorrect to say that math requires prior knowledge. Infact, any creation of new field of math is an art.There is tremendous creativity involved. Ramanujan came up with close to 4000 formulae in math purely through intuition without furnishing the proofs for many of them.

ME :
Art by definition is possibly the only thing that springs from an innate source. There is little or no skill involved except for expression of the gift and the honing (or adulteration) of it to conform to popular taste. Mathematics on the other hand is a skill , to develop it you have to walk down the path.

One might say that with minimal knowledge of math, you can deduce and reach upto advanced math by pure logic and intelligence.So it is probably incorrect to say that math requires prior knowledge. But from minimal knowledge when you deduce and reach advanced logic, you are actually treading this very path and developing your skill. Also, Ramanujan surely worked a lot on his math, he only was not schooled in the formal system of expressing it for which Hardy bailed him out.

But interestingly, Math is nothing but the modelling of what already exists in nature. Its modelling and simulating natural phenomenon and axioms so as to enable objective analysis and prediction of cause and effect. Its all for "automatic" processing. Art is the creative expression of nature "as is" but as perceived by the artist. It is this subjectivity that you pay a premium for. The very thing which you seek to eliminate as a mathematician. How ironic ! When all they seek to do is the same. Also paradoxically, the have-nots in Art, need to "cultivate" the taste to appreciate it, while the have-nots in maths can easily comprehend the results of maths through plain logic and elementary education.

One more thought...often enough great mathematicians are able to see through the veneer of objectivity and perceive the beauty of nature in their mathematical derivations and observations. That is when I think there is art in maths and you need a practitioner of the highest order, a true artist to appreciate this. Also, history shows that highly skilled mathematicians and scientific minds have been 'gifted' artists too, in music, painting or any of the other forms of creativity. Da Vinci, Bertrand Russell, CV Raman and others were all great artists or patrons of art.

Sujith :
To add to your points. Mathematicians wouldn't be happy if you say that math is just about modelling the real world. You might well be aware about Platonism, the school of metaphysicists who believe that 'mathematical objects' reside in a world of their own. Another way to say this is that Math would have been there even if this world hadn't.

Mathematicians wouldn't also be happy if you say that it's all about skills. Math has no more to do with skill than art has. Again invoking metaphysics, there's a strong school of thoughts of 'rationalists' who believe that there are a set of innate or a priori knowledge that we are endowed with. Knowledge about math is one such thing, according to them. Math is more about discovering that innate knowledge. The skill part of it just a practice with symbols so that they don't come in our way of understanding what we already seem to know!

ME :

Platonism is a refuge of the mathematicians who are more than a trifle uncomfortable with the pure objectivity in maths. ;-)

There is really a choice to be made in maths and art, also the aims are different. In one you seek to understand and PREDICT natural world, so you want hard theoretical models which are objective and most importantly replicable. The other is a choice where you dont seek to predict or really understand but just PERCEIVE and express. For eg. its most important in the derivations of maths that be used in applications without really needing to understand the real root of the derivation and how it was arrived at. Whereas in art, a person without the necessary understanding and perception wont be able to appreciate the work of art.

To wind up a lot of my babbling, I would say that I would respect a great mathematician and I would be in awe of a great artist. I hope I make sense.


Credits & Thanks To : All the bloggers mentioned in the post, Pritesh and her original post.