Monday, 12 April 2010
Maths is beautiful
A bar somewhere in Scotland at the end of the second sunny day of the year. A group of teachers round the table.
Stephanie pushed the Guardian newspaper across the table. “Have you seen this today?” she asked, excitement in her voice. Dot scanned the article and then sighed.
“The ten greatest mathematicians? There's something wrong with me. I just can't get excited about the achievements of these apparently great minds. Look at this one – guy called Tao gets a prize for finding out that you can find sequences of primes of any length in which every number in the sequence is a fixed distance apart. Um. Good.” It was clear that she was seriously underwhelmed.
“If we forget that maths underpins science, nature and the whole world we live in, we'll be in trouble. It's all exciting!” suggested Stephanie, while Nick spluttered and banged his glass down on the table, almost spilling the contents.
“Are you kidding? Euler and Gauss must be two of the greatest ever minds in history!” he said loudly.
Dot looked incredulous. “So tell me something they found out that will excite me,” she challenged.
Nick picked up the paper, gesticulating wildly as he talked “Gauss gave us the basis for models of how the universe works from the petals on a flower to variations in star cluster to finance. Euler, complex numbers, without which no electronics nor even a.c. power. His maths give you the light you read by. He discovered the square root of negative numbers, Gauss, curved space-time - both new dimensions - literally - of thought.”
He looked around the table. “A fine argument, well made,” said Stephanie with an admiring smile. Robert sitting sleepily in the corner raised his glass in approval.
Dot raised her own glass and one eyebrow “Good with the light thing - that's persuasive. Square root of negative numbers though. Why would that affect me?”
Stephanie nodded “You make a fair point - it's our biggest barrier to teaching and learning sometimes…but Miss, Whyyyyy? Have a look at this video as a start” She scribbled down a web address.
Nick searched for an apt analogy “It's like when your language isn't enough to express an idea, so you resort to painting and music to make your point.”
Robert stirred once more. He swirled his whisky gently round the glass, and spoke with reverence. “It's more than just important. It's… beautiful.”
Dot nodded vigorously “I liked that and I can understand that analogy, Nick. I wish,” she added wistfully, “I wish I could see numbers as beautiful.”
Kenny leaned over from the next table “I'm with Dot on the maths. I once watched a programme though about a guy who could remember pi by visualising it as a landscape…”
Nick looked sympathetic “Dot, you don't need to have all the maths to get it: just listen to people who have the math and the passion like Richard Feynman.”
The musician who’d been playing soothing airs in the corner put down his fiddle and joined them. “JS Bach did,” he said simply.
Dot looked doubtful. “JS Bach created some music that stirs the soul. Numbers themselves don't do that.”
“It's not the numbers, so much.” Nick waved his arms again. “It's the beauty of the universe. When you get it, even the striking of a match is an amazing thing...”
The violin player continued “Bach’s music was maths and maths is music. Literally.”
Dot was not convinced. “Some of it is, Gordon yes. But not the best stuff.”
Gordon pointed to the strings on his violin “Music is sound waves and frequencies. Chords are combinations of these and so on.”
Nick nodded vigorously “The relationships are the textures and the rhythm of the music. The numbers are the score on the page.”
Dot frowned “But I don't need to know that in order to create beautiful sounds, or an emotional response. Maybe maths describes phenomena in a way that appeals to one kind of mind?” she suggested
Nick nodded again “I think it adds depth of understanding. Feynman again, asserting that the scientist can appreciate a flower no less than an artist.
Dot couldn’t help pointing out glumly “The "maths" we do in school isn't like this though.”
Nick grimaced. “It is when I do it,” he asserted. “A suggestion for your kids is to get them solving puzzles: shapes, patterns, connecting ideas, words, sequences. For fun. That’s maths”
Dot smiled. “I understand that maths learning is not linear, so would you say that playing with numbers is as important as playing with language?”
Nick responded, “Both are symbols of something else. Connections and connectedness. That's not just maths, that's knowledge.”
With this profound thought, we leave them and ponder how to reconcile this inspiring and lively concept of maths with the pressures of everyday teaching, and the HMIE requirement for evidence of pace and challenge through test results.
Of course this conversation could not really have taken place in one cosy bar, as Stephanie is in Thurso, Nick is in Edinburgh, Gordon the violin player and Kenny are in Glasgow, Robert (who had his mandolin beside him but was too tired to play it) is in North Berwick and Dot is in the Scottish Borders. North, South, East and West mean nothing to Twitter however, and 140 characters mean everything.
Thanks to @sdisbury (Stephanie), @cullaloe (Nick), @gbrown057 (Gordon), @Kenny73 (Kenny), @jonesieboy (Robert)