The beauty of mathematics

THE EDITOR, Madam:

A former colleague of mine, a famous teacher of mathematics, told me as he was approaching retirement that he felt that his biggest failure was not communicating the beauty of mathematics to his students. When I told my own students this story, they scoffed at the idea that there could be beauty in a subject they associated with pain, suffering, defeat and enduring humiliation.

I responded by showing them beautiful examples of mathematics in nature as well as in art: the geometry in jewels, honeycomb, spirals in shells and galaxies, the golden rectangle in famous paintings and masterpieces of architecture and engineering, and the wonders of the invention of perspective in visual art. We discussed what Galileo meant when he said the book of nature is written in the language of mathematics, and what Edna St Vincent Milay meant when, in a famous poem, she said that Euclid alone has looked on beauty bare. There is an austere beauty in mathematics that some have likened to sculpture and music.

Perhaps if schools take a ‘mathematics without tears’ approach to teaching the subject, this would improve both student performance as well as a deeper appreciation for it. It is important to stress its utilitarian value, certainly, but if this is accompanied by some emphasis on its aesthetic, humanistic and spiritual dimensions; this will give them a more rounded and richer educational experience. Children love stories, and there are some famous ones about mathematical inventions, such as the one about Pythagoras and his students killing a cow for a feast to celebrate the proving of his famous theorem. The success of Euclid’s geometry inspired theologians to construct similar arguments for the existence of God. Number mysticism contributed significantly to the development of mathematics in Russia. Mathematicians claim that nothing that they have proven has ever been unproven, and this partly explains the high regard for mathematical knowledge traditionally held by many philosophers.

Some educators regard reading, writing and reasoning as the ‘three Rs’ that should form the basis of education, with mathematics as the chief but not the sole arm of the development of reasoning ability. It is also necessary to learn to reason with the natural languages. And all activities that encourage reasoning, such as critical thinking, debating and taking divergent approaches to problem-solving, can aid mathematical reasoning. There is also empirical evidence for the view that introducing philosophical reasoning in schools can improve performance in mathematics and language arts.

EARL MCKENZIE