Mathematics, a beautiful elsewhere.

When his son Leo was small, my brother Geoff, like most parents, read him stories at night. Unlike most parents, he also lobbed his six-year-old maths problems, which Leo seemed to enjoy just as much. I once heard the two companionably solving sums together, after the light was out.

Geoff wanted Leo to know the simple pleasure of figuring stuff out, and to know that maths is not just sums, not just a language, but also a playground.

My brother does maths for a living. He teaches probability, statistics and applied mathematics at Oxford, which might sound dry. But in academia, stats is an access-all-areas lanyard. Being able to make sense of data for other researchers is a sought-after skill from science to the humanities.

“If I offer [other scientists] stats help, I get buried in the scrum,” Geoff told me once. He has worked with oceanographers on the movement of deep, slow streams in the abyssal ocean – currents that affect climate change. He has helped linguists estimate the age of ancient languages, and geneticists to trace the ancestry of HIV.

He has jokingly called himself a “problemacist”: someone who helps others understand what is – and, importantly, what is not – lurking in their data.

God knows where he got it from. Perhaps the grandmother who whipped his 10-year-old ass at chess while making scones. This is more impressive than it sounds, because at the time, he was fresh from vanquishing two academic chess nerds (two games, two against one). Does chess have anything to do with maths ability? As a boy, maths wasn’t Geoff’s best subject. Determination was. “Chases the ball relentlessly,” wrote a PE teacher on his report card when he was 11, a comment repeated many times, in various forms, on his reports over the years.

I envy him the extra language he has worked so hard to earn, although I grant him a few extra brain cells. I am nervous around numbers, and I say this without a shred of dignity. To brag about innumeracy today is, as Geoff points out, “hard currency for young New Zealanders, especially women”.

It drives Geoff mad to hear me say, “I can’t do maths.” He has a point. Can you imagine declaring that you are semi-literate?

“If you can stir a spoon around a cup of coffee,” he told me, “you can do maths.”

Just chase the goddamn ball.

Mike Ellicock of the British “numeracy charity” National Numeracy agrees. “Throwaway remarks about being ‘no good at maths’ are often inaccurate and always insidious. They confuse maths and numeracy and, above all, perpetuate the view that some people are simply not ‘mathematical’ and that this does not matter. The expression of such views, whether by figures in public life, including the media, by parents, carers or even – very occasionally – by teachers, always needs challenging.”

Dr Rhys Jones, a teaching fellow in the Department of Statistics at the University of Auckland, made the same point recently in his heartfelt piece for Newsroom, Being bad at maths is not a badge of honour: “Why is it not okay to admit if you can’t read or write, but socially acceptable to say you can’t do maths?”

I am not bad at maths, then – just, all right, I admit it – a blend of anxious and lazy. As privileged as any other white New Zealand farmer’s daughter, I can’t even blame my teachers.

Not even hothouse remedial lessons from my kind, clever cousin Noel Bridgeman* could propel me into my maths happy space. Noel was, at this time, head of my high school’s maths department. Determined to launch me into the world with a mighty School C maths grade, he scoffed at my maths teacher’s prediction that I would get “something like 66%”. This intel, relayed back to me by Noel, was supposed to ignite a steely and ambitious flame to hit B+ at least.

Just chase the goddamn ball.

When my maths results came in, I had got – I am not joking – 66%.

Geoff likes to tell me he preferred English to arithmetic – but he loved applied maths. What’s the difference?

Arithmetic, it seems to me, is to maths as spelling and grammar are to writing. Confidence with numbers, or numeracy, protects us from stuff like the product insurance that costs two-thirds the price of the item, claims of “100%” cures, or even the sense that if we just gamble long enough at a casino, we will eventually win.

I’m not a gambler, at least: maybe I can thank Noel and my 66% score for knowing the house always wins. And my lack of any higher maths cred doesn’t mean I don’t enjoy watching other people do it, even at its most rarefied.

A new book, The Universe Speaks in Numbers, by an English adjunct professor of physics, Graham Farmelo (Allen & Unwin, $45) is a beautifully written argument, not just for sensible everyday numeracy or even for the applied mathematics my brother uses, but for the potency of abstract mathematics – the promise of figuring out the universe and everything in it with nothing but a pencil and paper.

“It’s strange how things theoretical physicists find interesting often turn out to be interesting to mathematicians,” an American mathematician, Lauren Williams, tells Farmelo.

The book does a good job of describing what abstract maths is doing for theoretical physics, and what theoretical physics is doing for abstract maths. If this sounds dull, it isn’t – because Farmelo is so good at bringing the central characters to life.

Who would not be gripped by the tale of the 26-year-old Italian physicist who, sitting in an Israeli cafe in 1968, scribbled a formula in his notebook that ended up transforming physics? His equation was so mind-blowingly simple and ingenious, says Farmelo – so “beautiful” – that “for years theoreticians would remember their first encounter with it”.

The formula was the first inkling of string theory, a now well-subscribed explanation of space and time developed by mathematicians who, after years of physicist avoidance, finally began to compare notes in the late 70s. (You may know string theory, a contender for a “Theory of Everything,” from TV’s The Big Bang Theory; Sheldon and Leonard support string theory, while Dr Leslie Winkle does not.)

Although thinkers like Williams find the connection between nature and numbers intriguing, even spine-tingling, others complain that mathematicians are leading physicists down magical rabbit holes of pointless abstractions that can never be tested.

It’s “fairy-tale physics” and “not even wrong”, they say.

Farmelo argues they are wrong. “This view is misguided and pessimistic... I argue that today’s theoretical physicists are taking a path that is entirely reasonable and extremely promising.” He explains how the interface of maths and physics today is based on a bedrock of observation-based physics that began with Isaac Newton.

For those of us on the mathematical sidelines, the theories Farmelo describes are not in the least bit easy to understand, although there are (almost) no equations in the book.

But... follow the ball. This is an intellectual adventure filled with drama, controversy and discovery, and there is nothing hard about those.

The book offers insight into the catfights and characters of the mathematical and physics academic stratosphere. It also shows, without really meaning to, the dominance of the US and English university behemoths within contemporary theory, and how many obstacles are still faced by women and researchers of colour. Even so, Farmelo’s index is a striking snapshot of the sheer internationalism of science.

As historian and essayist Simon Schama has written: “If this world is a city, like all the best ones, it is diverse.”

Nearly everyone at science’s highest table is either a migrant, like my brother, or the child of migrants. Farmelo’s index makes an incidental mockery of Donald Trump’s obtuse brand of xenophobia.

In the index’s first two pages we find Nima Arkani-Hamed, an American-Canadian physicist of Iranian descent; Michael Atiyah, the late British-

Lebanese mathematician; theoretical physicist Freddy Cachazo, born in Venezuela; Indian-American astrophysicist Subrahmanyan Chandra-sekhar; and the mathematician Shiing-Shen Chern, a Chinese-American.

Two New Zealanders make an appearance on this back-of-the-book red carpet: physicist Stephen Parke and mathematician Sir Vaughan Jones. And both of them were born in Gisborne.

What are the odds of that?

Leo might know...

I was looking forward to hearing Noel Bridgeman’s rich chuckle over this column, but it was not to be – he died in July, as I was writing it.

Find Jenny Nicholls on Twitter￼ @jmnicholls

This article was first published in the March 2019 issue of North & South.

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