# Geoffrey Goodhill: how maths helps us understand the brain

If you fire an arrow into a forest, how far will it travel? For most of us, this problem sounds like something out of that age-old, recurring nightmare where you have to take an exam you haven’t studied for. Where are our familiar friends: numbers, equations, key terms? Panic turns to frustration. How can we possibly be expected to interpret such a vague, open-ended question, let alone answer it?

For distinguished computational neuroscientist Professor Geoffrey Goodhill, grappling with problems like this – sans parameters and rulebook – was both part of his undergraduate degree and what modern science has to do if we are to understand the vast complexities of the human brain.

Based at the Queensland Brain Institute at The University of Queensland since 2005, Goodhill studies brain function and the information-processing properties of the structures that make up the nervous system. More specifically, he uses experimental, mathematical and computational techniques to understand the brain as a computational device. “At the heart of the mathematical approach is the idea that if we can’t program an algorithm to mimic brain functions then we haven’t understood what’s really going on,” he says.

## Neuroscience path not initially planned

It’s a field Goodhill didn’t initially see for himself. Enrolling in a Bachelor of Science in Mathematics and Physics at Bristol University in the 1980s, he admits that he wasn’t particularly interested in biology: “I saw this big mess of terminology without any sense that there were some unifying principles. I saw myself becoming a mathematical physicist.”

However, whilst working on a project as part of his Master’s degree in Artificial Intelligence at Edinburgh University, he was presented with a clearly defined biological problem where there was “the germ of a mathematical approach” and a realisation that mathematical modelling was a key to understanding how the brain works at its most fundamental level.

This then led to a PhD in Cognitive Science at Sussex University and a move to the USA in 1994, where he did further postdoctoral study in Computational Neuroscience. Today Goodhill describes it as a field that is “data rich but theory poor”. He cites understanding how growing nerve fibres – axons – navigate through the developing nervous system as an example of this.

“Many cognitive disorders have been linked to the initial wiring of the brain during development so it is crucial to gain an understanding [of] the basic rules by which nerves find their targets if we want to prevent these disorders in the future,” he says. With an estimated quadrillion nerve connections in the brain, this is a problem surely only a mathematician could love.

## Full potential of maths in neuroscience not yet fully realised

Goodhill sees computational neuroscience as a field which is wide open for applications and new ideas: “The full potential of mathematics in neuroscience has not been fully realised yet. There’s a very rapid pace of technological development and that is producing lots of new data which is often very challenging to understand and interpret, and so it needs more people from a mathematical background to make sense of that.”

For him though, it’s the basic research and uncovering the deep principles of things that are most appealing. “I think my interest and the thing I’m best at is taking a problem which is not yet defined and figuring out the kind of tools that could make progress on that problem. What I enjoy is that sense of ‘Well, here’s a problem, let’s try and think about what kind of equations we could use to describe it.’”

And this is something Goodhill’s colleagues acknowledge is his great strength. Laboratory alumna Dr Irina Vetter says, “He is a brilliant scientist who has managed to fuse two (seemingly) polar opposites – computational mathematics and neuroscience” – an opinion shared by former Editor-in-chief of the *Network: Computation in Neural Systems* journal, Professor David Willshaw, who agrees that Goodhill has “impressive pedigree in several different fields of computational neuroscience”.

Interestingly, this “impressive pedigree” extends beyond Goodhill’s scientific career to his passion for playing jazz saxophone. Since the mid-1970s when he took up first the clarinet and then the saxophone whilst a schoolboy, music has been a serious part of his life. From chamber music to rockabilly, Afro rock, jazz, swing and the blues, the seriously talented Goodhill certainly seems to have played it all – and played it in some impressive places including the Royal Albert Hall, Scottish television and some of the major jazz establishments in Washington DC. And yes, he can even be found on YouTube.

From his base on the fourth floor of QBI, however, Goodhill is more serious-minded scientist than cool blues hound. Clearly a passionate scientist, he says his favourite part of his job today is making new discoveries about the brain: “What drives me is that thrill of discovering something or realising I’ve been looking at something the wrong way.”

Ultimately, for Goodhill, how far the proverbial arrow in the forest goes is not the problem; it’s the chain of mathematical reasoning that leads us from assumption and uncertainty to understanding phenomenon such as the functions of the human brain.