Monday, November 7, 2011

Beautiful Maths

I'm very proud to post here a really interesting essay written  by John O'Donnell comparing the beauty of Mathematics and Poetry.
I hope you'll enjoy reading as much as I did.
John, thanks for sharing.


Are the great mathematical and scientific theories works of art?

Beauty, harmony, elegance.  These are words that we normally associate with what is best in the arts. It may surprise some to hear that these terms are also used in fields where dispassionate logic is often assumed to hold sway – physics and mathematics.
It has even been said that equations are the poetry of science.

The great physicists almost invariably used standards of beauty and elegance to help them formulate their best theories. It was only after these theories had been created that the hard graft of comparing them with experiment was undertaken by other talented if less original minds.

The phrase “it must be beautiful” has been attributed to two of the greatest scientists – Einstein and Dirac - when describing how they arrived at their extraordinarily successful equations.  Einstein went so far as to say- when an early experiment seemed to contradict his theory of relativity – that he felt sorry for the experimenter because he must have made a mistake, his theory was too beautiful to be wrong.

The same is true in pure mathematics, an activity where we would assume that logic and rigour are the most important factors. Take this quote from the great Irish mathematician William Rowan Hamilton:

“Mathematics is an aesthethic creation, akin to poetry with its own mysteries and moments of profound revelation”

The process of coming up with a great scientific or mathematical theory is remarkably similar to the process of creating a work of art. Surely this cannot be a coincidence. Why should powerful theories in mathematics and science also be beautiful? Why are the beautiful theories often (though not always) correct while “uglier” theories are more often wrong? This is a profound question that nobody has adequately answered up to now.

What makes something beautiful or elegant? Are there objective criteria to decide this? I am only raising the questions. Maybe you readers out there can provide some answers?


4 comments:

  1. thats a very interesting way of looking at it.

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  2. I don't really have answer to this, but I think there is a kind of balance in the world where the human mind craves knowledge of certian things and we are drawn to beauty and symmetry. I can't really explain my thoughts, but it just makes sense to me that something beautiful would "work". I don't know if that's instinct or carnal or what, but I'm not really the type to obsess over it :)

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  3. Beauty: I'd say equal parts proportion, completeness, and unexpectedness. As a start. But then I always find people's faces more beautiful when they have a flaw -- I like the surprise element. Same thing with art.

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  4. @Sweet Pea, Thanks JOD will be pleased.
    @J.A, I think i do know what you mean.
    @ Gail, I agree with you. I like that element of surprise in people, life and everything in general, beyond the given, the expected.

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