Mathematics a thing of beauty for Victoria University’s Dr Whittle
A PROFESSOR who recently brought Wellington to the mathematical world’s attention by solving a 40-year-old conjecture says he is drawn to the beauty and aesthetic appeal of maths.
After more than 15 years of work, Professor Geoff Whittle of Victoria University solved “Rota’s Conjecture” with two others, an unproven theory that there are only a finite number of things within a geometric shape.
He now faces multiple years and hundreds of pages to explain how they solved it – no easy feat when the researchers solved it in their own “secret language.”
As he heads off on a trip to Canada and South America, the Spanish-speaking philosopher-turned-mathematician looks forward to the time when he can sit down and practice his art – mathematics.
Dr Whittle believes mathematicians have suffered because their field is so useful, and because of this people are not able to see the beauty in it.
“If you were talking to a musician would you ask them about the practical application of the music?” he asked, “or would you ask a poet that?”
While some fields are judged on usefulness, as he regrets mathematics is, subjects such as art, literature, and opera are free of this expectation.
After starting out at the University of Tasmania studying philosophy, history and maths, and a masters in philosophy, he ended up in mathematics for his PhD – yet has never given up his Bachelor of Arts roots.
“I am only motivated by aesthetic reasons, I don’t care about usefulness.”
He tells his students this – including first year engineering students who are only in the class because of usefulness – because he believes learning improves when people understand something conceptually and can appreciate the beauty of it.
Saddened that many people never get to see the beauty of mathematics, he is passionate about sharing this world with students, some of whom have turned to maths because of him.
“It’s not something that many people ever get to see,” he said. “Unlike music, where you don’t have to be a musician to hear and even appreciate patterns in music, you need to be able to read and write mathematics to be able to appreciate it.
“We mathematicians have this wonderful world that is largely not known by the general public. It’s not because it’s all that difficult, it’s just that people largely don’t go there.”
While not interested in the practical implications of maths, Dr Whittle is still motivated by solving problems that are meaningful.
To find those that are worth giving time to, he says you have to understand that mathematics is more about what is unknown than what is known.
“You see that you’re only just standing on the shore of a huge new continent that is essentially all unexplored. You can go and explore whatever little bits you like but you have to feel you’re doing something genuinely significant, which is somehow different from usefulness.
“Its as if there is this mathematical universe. If someone works something out in mathematics, it’s there forever. If the Greeks did something we can look back and say they did it right.
“There’s this mysteriousness about what mathematics really is, which I really like. It’s this world that is my workplace.”
Unlike Plato, who believed a mathematical universe literally existed, Dr Whittle says to him it’s a mental state that he pokes his head into each day and imagines what things are like.
He finds to solve a problem you have to get close to obsessive about it, much to his wife’s annoyance.
“She’s become an expert at detecting if I’m smiling and saying ‘yes, dear’ but actually thinking about the problem.
Because of the relatively obsessive nature of it, he says there are a good proportion of mathematicians who are “pretty dysfunctional” socially.
“I would say to be a mathematician you don’t have to have Asperger’s syndrome, but it helps.”
He says this is because unlike many other careers, you can be a good mathematician without social skills.
“Actually to be honest, I’m not even sure that it’s true about a lot of mathematicians being on the spectrum, but you certainly go to a mathematics conference and you do get a sense that some of them are a bit special…”
At these conferences, he likes to surprise mathematicians by throwing in some philosophical questions, because he finds that a lot of mathematicians never ask bigger questions, they just like to solve problems.
He says that because mathematicians often have their own language, the next four years are going to be a challenge for him and his colleagues Jim and Bert from the Netherlands and Canada.
“We can know we’ve absolutely got something worked out, but because we speak to each other in a secret language it’s even difficult to explain it to other mathematicians.”
For example, the three researchers have a code name for a particular formula they have used over the years – a ‘pony ride’.
“A pony ride is code for something that’s an application of a version of a thing called Ramsey theory, which says basically if we make something really, really huge we’ll be able to find inside some smaller thing that’s got more structure.”
One time when they were stuck they felt like they only had one trick – so this technique became a one trick pony, and evolved to be called a pony ride.
“We can just say ‘pony ride’ to each other, but to actually write it down and convince our colleagues that it really all works takes a lot of work.
“We’ve spent so much time together, and when you spend enough time with each other you hardly need words. We’ve taken this journey, we’ve explored things and we know what we have mutually explored, so we can just hint at sometime and go ‘oh yes, that will go just like something we did three years ago’.”
Over the next four years Dr Whittle will be blocking out times to focus on writing, while balancing it with being deputy head of the Department of Mathematics at Victoria University, teaching, being on the appointments committee and helping graduate students on their own projects.
Living with your head in the mathematical universe is all a bit crazy, he says, and some day he would love to go back to his philosophical roots.
“We work with infinite things all the time. We live in a weird world.”