The Maths/Art Nexus

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Until the end of 2010, expatriate New Zealander Peter James Smith was Professor of Mathematics and Art at RMIT in Victoria, Australia.

Smith has straddled two very different fields for three decades. He has written an influential statis
tics textbook, and exhibited his landscape oils covered with handwritten maths notation, as well as work in other media in regular solo exhibitions since the 1970s. He first mixed mathematics and art in an exhibition of paintings using the Fibonacci numbers in Auckland in 1977. “People en
courage trans-disciplinary work,” he says, “but it’s very difficult to assess. It’s important to do because the education system separates people from age 12 into one stream or the other. It’s a very
destructive split. Often teams of people collaborate across art and science disciplines, but they don’t understand what the other side has done - it’s not seamless.”

He concentrates on the language of maths in his paintings. “I don’t like beautiful symmetric diagrams; the formulae that produce symmetry are interesting but not the picture of symmetry. It’s wonderful to bring to non-mathematicians some of the simple delights of how group theory works - the 1+1= 0 argument - they’re so used to the language that they don’t know what a gift it is.”

The mathematical language in his paintings has included data sets, such as 1880s experiments on speed of light, and the orbital elements (position, location and appearance) of Halley’s Comet. “It illustrates how statistics is such a powerful thing – by gathering that data you get to know about the world. I used a lot of theorems and simple proofs, often from number theory, and my own research; I produced a new result on a painting before it was published in a journal. That’s when the nexus is working really well, having that moment of insight when you’re working on a canvas that mathematicians have at the blackboard.”

He was in New Zealand to give a lecture on Truth + Beauty, the title of his recent solo exhibitions and of a book he is writing. “It contextualises the mark making on my paintings over the last 30 years. It will have a lot of maths - understanding the nature of proof, deductive reasoning; all those things art people don’t know. The process of proofs and the failed alleyways that mathematicians go down to discover things are very precious.”

“Starting with axioms and definitions and constructing and proving theorems - just like Euclid built all geometry from five axioms - that’s the wonder and the magic.”

Smith was one of two Antarctic New Zealand Artist Fellows in early 2010. Their most mathematically interesting find was NASA’s website tracking of icebergs between 2000 and 2005, when they drifted north of Christchurch. “The traces they left bordered on chaos theory; it’s an interesting relationship between something mathematically chaotic and some scribbled mark.”

In 2010, Smith was applying linear regression to art and real estate markets. “It’s ironic that when you retire, your research suddenly starts looking hopeful! I was working with a database of realised secondary market (auction) prices for art, which is an example of left censoring. The information you have is not the actual realised price, but you know the price is less than the reserve because it was passed in at auction. The reserve therefore becomes a left censored data point. Real estate people would pay millions to type in an address and get a value for a property based on sales and properties passed in at auction.”

Like all teachers, Smith aimed to ‘future-proof ’ his statistics teaching. “You teach students what boxplots look like, so they can recognise the analytical thinking that goes into that object when it changes to a new generation, and they can question it and invent a better one.” However, he thinks there is a danger with “pressing a button on statistics software that works dynamically”, because at the end they still may not know what the animation represents.

“Variability is very difficult for students to understand. I think it takes more than slick software.”

Top: Ice Station, 2011, oil on linen, with a diagram of Antarctica’s annual mean sea ice extent that shows it is increasing.
Panel from Fading Light series, 2003, oil on linen, with research created on canvas before publication in the scientific literature.