Maths vs. Art: Objective vs. Subjective????

The title sounds hi-funda, eh? B-)

I feel great about having been a part of this discussion. Not only because it sounds hi-funda but because this is one of my favourite topics. Abstract vs. precise…….

It started off with someone saying “Art has a lot of Maths in it but there’s no Art in Maths”. Now, the discussion lasted for aboutt two hours with two of the members against the statement and the third one (the one who made the statement) in favour. Let’s name the ones in favour as F and the ones against as A. There were points after points made for and against the statement and I can possibly never remember all that was said. So, I shall list the most important ones and at the end of it a quote that sprang to my mind as a result of the discussion (improvised by the one who made the statement)…..

The points are:

1. Art is supposed to be subjective where there’s nothing like correct or wrong. There’s only a good or bad and THAT too is heavily dependent on the perception of an individual. On the other hand, Maths is either correct or wrong. There’s a proof for everything and the proof can be verified by anyone who expresses and doubt.

2. In deciding whether the Art is good or not, the steps taken while creating it are not of as much importance as the final result. Whereas in maths, the steps taken are of importance for they are under scrutiny and are available even after the proof is completed. Not only that, there may be more than one proofs and hence, every proof is to be checked.

3. There’s this creativity element involved in Art that may or may not need any prior information/knowledge. Whereas in Maths, you need apriori knowledge database.

4. There’s no talent needed for Maths, it’s about skill and practice (something the A strongly disagreed with). Whereas for Art, there’s talent needed along with skill and practice. The “A”s feel that there is something called an aptitude/talent for Maths too. And by the way, we ended up reading up a lot of definitions from the dictionary. I list them here as one needs to know these definitions before one conlcudes whether one’s in favour of this statement or against it.

(a) Talent: Natural or innate qualities
(b) Innate: From birth, Inbuilt (without teaching)
(c) Skill: An ability that has been acquired by training
(d) Art: The products of human creativity; works of art collectively, The creation of beautiful or significant things

So, we deduced that there is a certain degree of talent as well as skill needed to be good at both Maths and Art.

5. Art has this humane element to it whereas Maths is free of that humane touch, Creativity being the only human link between the two. The “A”s strongly disagreed again.

If you read the statement, there’s this humane element to it. “Art has a lot of Maths in it but there’s no Art in Maths”. The word ART there brings about the humane nature to the whole thing. What is Art to one is not Art to the others. I know people who call Maths “Beautiful”. So, beauty can’t be unless that ONE person sees it. So, if someone finds Maths beautiful, it becomes a form of Art. So, Art can not be free of Maths (for some people) and Maths can be an Art (to some other people)…….

At the end of this all, I came up with a quote (with a slight change brought about by the “F” of our discussion Group and create a balance between the aesthetic and precise element of the quote)…….

The truth of subatomic Physics is not Maths, it’s Art

For those who wish to understand it, please meet me for a coffee at Coffee Board, I shall elaborate……….:)




  1. Karthik said,

    June 15, 2006 at 2:27 am

    Interesting discussion. would have liked to write on this. but you beat me to it πŸ™‚
    A few comments

    point 3: 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.

    4. Talent can be created with proper guidance and practise.

    5) Art in its most familiar form perhaps has the human touch. Not everyone understands modern art or instrumental music. We need to train and condition ourselves to understand them. So, in that sense, some amount of prior knowledge and training is alway useful to appreciate something, math included.

    Finally to quote hamming ‘ The purpose of computation is insight, not numbers’.

    I feel creating anything new through pure thinking in any field , not just fine arts, is art.

  2. Pritesh said,

    June 15, 2006 at 10:03 pm

    Thanks Karthik. I was of the same opinion. Creating something new is Art. Even if it’s Mathematics formulae………

  3. sathya said,

    June 19, 2006 at 9:23 am

    I wrote a pretty long comment on Mathematics being a language and hence an art, but the site refused to save it, so I’ll be glad to discuss this over a coffee.

  4. sathya said,

    June 19, 2006 at 9:25 am

    I wrote a pretty long comment about Mathematics being a language and hence an art, but the site refused to save it, so I’ll discuss it over a coffee.

  5. Sree said,

    June 22, 2006 at 4:48 am

    good read again!:)
    as a student of music, n classical music at that, I realise how crucial is maths for art too…i guess its the definitions that trap us- of art being subjective n maths the other way….arts do have a high quotient of individuality, but any form of arts has its own set of rules, techniques etc.
    may be an artist manages to keep the painful process to himself/herself n let the world relish the end product?
    well, these days, defining arts only thru the beauty angle is also being widely questioned…so even this idea seems to fall on its face!

  6. sp said,

    June 22, 2006 at 10:29 pm

    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.

    @karthik : 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.

    Anyway I can ramble on and on…On a digressing note, it is interesting to wonder about what really is innate? Is there anything that is really inborn? Where do you draw the line? Every second after the child is born, his faculties are shaped by the environment he is in. I sometimes wonder if the genes are slowly and gradually hardcoded after birth. πŸ™‚

    @Pritesh : Very interesting topic. I once had a discussion with a friend of mine on something similar and my take on it was somewhat on lines of what I have posted here.

    Happy Blogging!

  7. sp said,

    June 22, 2006 at 10:41 pm

    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 there is Art in Maths. πŸ™‚

    Da vinci, Bertrand Russell, many other great minds have been most creative too.

  8. June 22, 2006 at 10:54 pm

    Hi SP,

    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!

    The last part of your comment is what we all must agree with, because, it’s a question — the right thing to do on this topic is to question! I don’t think we have many real answers on this question. πŸ™‚


  9. Pritesh said,

    June 22, 2006 at 11:10 pm

    Well, I am happy with the discussion here. Sujit and SP, thanks for dropping by and reading the blog and commenting on it.

    It’s actually very hard to say whether Maths is an Art or not. Our discussion was mostly centred around whether Maths has any Art in it and since Art WORD itself is a subjective, one can never really SAY whether it is or isn’t!

    And I kind of agree with Sujju. Training in maths has somewhat to do with the training in symbols and numbers to put yourself across to the world. There are ideas that may or may not be innate! This is too complicated a topic for me to say ANYTHING conclusive! I can only express MY opinions here…..

    Thanks Sujit and SP again for giving valuable replies to the blog…..

  10. sp said,

    June 23, 2006 at 9:08 am

    @sujit: Platonism is a refuge of the mathematicians who are more than a trifle uncomfortable with the pure objectivity in maths. πŸ˜‰

    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.

    Anyways, I am just rambling along. Its just that I have given a lot of thought to this earlier and was happy to find this discussion here.

    To wind up a lot of 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.

  11. sathya said,

    June 24, 2006 at 12:29 am

    Most of the current day mathematics is centred around explaining physical phenomenon. This probably creates an expectation for mathematics to be logical in all aspects (after all people would like to believe the world is in order)!

    My profession happens to be financial mathematics. Usage of mathematics in the current day is greatly centred round this with ever increasing commercialism. A great deal of this branch only deals with things going out of logic. Obviously this cannot be put in the normal framework of ‘classical mathematics’ (if I may borrow the usage!). This leads to contemporary mathematics – frankly speaking this is merely built to the whims of those who already have a result. In my own work, I often know the answers, but seldom a way to express them mathematically and end up cooking a nice new concept to prove it! There is nothing binding to express these in common mathematical notations as long as you can communicate your idea. The current set of notation in use just lays a platform for easier communication.–>

  12. Nissim said,

    January 22, 2007 at 10:19 pm

    Godel,Escher,Bach(by Hofstadter)(saw it in Tata book house).
    A mathematician(logician), an artist and a musician. Gr8 book I hear…read a bit of it once and was impressed.
    Fractals are found in Escher’s paintings and people have found abstract Algebra useful to deal with them.
    Math is Art.

    I am interested in mathematics only as a creative art.
    A Mathematician’s Apology (London 1941).G.H.Hardy

    The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas, like the colours or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics.
    A Mathematician’s Apology.

    A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.
    A Mathematician’s Apology

    Sorry for such a long comment.

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