Creative Mathematics

spectacleinrock

I am an artist and i personally believe that mathematics is a form of art. I would like to hear the opinions of mathematicians on this matter, for research purposes. Any comments greatly appreciated

jayok

I suppose the obvious comment on this is the use of fractal graphics on computers. You can get very impressive -potentially infinite- plots from such algorithims.

For me the beauty of maths is the elegence of it. This sounds a bit silly, but calculus always looked cool to me (probably the funky symbols) then the real uses for it (I'm an electronic engineer graduate) for working out magnetic fields, etc.

Hmmm... in the art form, there's a number of different approaches you could take here. I am rambling across the keyboard now:

1. The plot of equations
2. The resolution and representation of complex problems
3. The acutal math symbols themselves uses
4. Application of maths to real live (DSP, audio/visual).

Ok enough for now, hope this ramble helps!

JayoK

popinfresh

hmm, you could always make a really cool graph in a painting, colour it up n' sh1t, then write the mathematical equation underneath it.

oq4v3ht0u76kf2

Read up on modular forms... 4 dimensions baby!! (Real x and y axis, imaginary x and y axis.)

Google for M.C. Escher's Circle Limit IV.

Modular forms are the most perfectly symmetrical objects in mathematics and they exist only in hyperbolic (that is to say, 4 dimensional) space. It is pretty much impossible to imagine such things but they do exist, at least in mathemetics. See the Taniyama-Shimura conjecture and futher see how Andrew Wiles incorporated it into his proof of Fermat's Last Theorem.

Syth

I would suggest anyone interested in this topic read Zen and the art of motorcycle maintaince by Robert Persig. In it he says that both art and science are beautiful, but in different ways. Science (and hence mathematics) is beautiful in what it means as apossed to art which is beautiful in how it looks.

Hence fractals and so forth are beautiful in the arty way, but what's really beautiful about fractals is that they are generated by one equation : z = z^2 + c. Where z and c are complex numbers. z is initally set to 0 and c is set to a point on the complex plane. then repeatable apply that forumla. If the magnitude of z goes above 2 then that point is not in the mandelbrot set, if it stays below 2 then it is in the set. Do that for all points on the plane. Put a black dot on all points in the set, a white one otherwise. (The colours are derived from how quickly z goes above 2).

That's all you need to generate the Mandelbrot fractal. One little equation and a short description. Yet look at what you get out of it. Look at the pictures. Look at the equation. That is what is beautiful about mathematics.

simu

Originally posted by Syth
I would suggest anyone interested in this topic read Zen and the art of motorcycle maintaince by Robert Persig. In it he says that both art and science are beautiful, but in different ways. Science (and hence mathematics) is beautiful in what it means as apossed to art which is beautiful in how it looks.

Yeah, but it's not as if art is devoid of meaning. IMO the best art goes beyond the initial aesthetic pleasure and reveals something new about the nature of existence. And, as regards maths, you can also experience aesthetic pleasure from maths in itself, as you work it out in your brain, before you can attach meanings to it.

Syth

And, as regards maths, you can also experience aesthetic pleasure from maths in itself, as you work it out in your brain, before you can attach meanings to it.

I don't really think that is aesthetic pleasure, more pleasure from the hunt, the feeling that you are getting near the the solution, the feeling of joy when you overcome a problem that had been bugging you. I don't really think that's aesthetic pleasure.

You could say that there are 2 kinds of beauty : 'artistic beauty' and 'mathematical beauty', and both Art and Mathematics have parts of both. (To put it simply).

Yeah, but it's not as if art is devoid of meaning

But is it that same kind of meaning that you can get from mathematics?