Mathematics possesses not only truth, but supreme beauty

nautilus_withoverlay“Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry” Bertrand Russell 

The idea that mathmatical truths have an inherent beauty is not a new one.

  • Contrast and compare notions of beauty in both the Arts and Mathematics? In what way is the appreciation of beauty different and similar in both areas of knowledge?
  • To what extent are divisions between disciplines, or domains of knowledge, natural or cultural?
  • What is the essential (not subjective) difference between an ugly and a beautiful equation?

Neuroscience and the appreciation of Mathematical beauty

Maybe neuroscience can help us engage with these questions? In a recent BBC essay James Gallagher discusses recent research which suggests that “beautiful” maths creates activity in the same emotional brain centres that are stimulated by beautiful artworks or music.

“One of the researchers, Prof Semir Zeki, told the BBC: “A large number of areas of the brain are involved when viewing equations, but when one looks at a formula rated as beautiful it activates the emotional brain – the medial orbito-frontal cortex – like looking at a great painting or listening to a piece of music.”

The more beautiful they rated the formula, the greater the surge in activity detected during the fMRI (functional magnetic resonance imaging) scans.”

Read more in this article on the BBC website

Edward Frenkel and the beauty of abstraction

Frenkel argues that there are established links and similarities between social and cultural processes of abstraction, the evolution of the use of money for instance, and Maths.

Read the full ‘Big Think’ “The Beauty of Abstraction” article here

Find out more about Mathematical Beauty here

I love this very short TED talk from Arthur Benjamin who very entertainingly describes the significance of the Fibonacci Series and relates it to both nature and humans desire to appreciate beauty. He also calls for greater levels of aesthetic appreciation in the teaching of high school maths and that there needs to be a stronger emphasis on the application of mathematical knowledge. He humorously says we should spend time, not just working out ‘x’, but also reflecting on the ‘why’!

Other links

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One Response to Mathematics possesses not only truth, but supreme beauty

  1. danieltrump says:

    Great post, it will be of great value to many non-mathsy ToK teachers. Love the fMRI research on equations, I know that my emotion centres are certainly triggered when faced with Maths problems ! Thanks Mr Stevens !

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