Dr Natashia Boland, operations researcher

Dr Natashia Boland was awarded a PhD by the University of Western Australia for her work on operations research using continuous optimisation techniques in 1992. She was a postdoctoral research fellow at the University of Waterloo, Canada, in the Department of Combinatorics and Optimisation. This was followed by a postdoctoral research fellowship at the School of Industrial and Systems Engineering at Georgia Institute of Technology, USA.

She is a senior lecturer in the Department of Mathematics and Statistics at the University of Melbourne and is actively involved in a number of research projects in both theoretical and applied operations research, including the optimisation of processes such as cancer treatment plans and aircraft paths. She regularly provides consulting services to industry on a wide variety of topics.

Teachers' notes to accompany this transcript.
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Interviewed by Ms Marian Heard in 2001.

Contents


Fun and inspiration in childhood mathematics

Natashia, your interest in maths began almost as soon as you were born! When was that?

I was born in 1967, in Perth, Western Australia. When I was at pre-school, I think even as early as two, I really loved blocks and trains and trucks. My Mum and Dad bought me lots of Lego and Meccano sets and things like that, which I would play with for hours. I was always building in sandpits and taking the sand in Lego trains into the house, and trying to build bigger and better systems. Then when I was about 12, we found my grandfather's Meccano set at his house. It was the old metal type, and as I'd only had the plastic type it was a really big thrill. Even as a teenager I spent hours playing with that, just building things.

Did your school teachers encourage you in maths?

Yes. My second-grade teacher, Mrs Martini, was very important. I looked up to her and she really encouraged me. During that year we had a lot of maths books and basically we just worked through each one doing exercises. But I got sick (with chickenpox, I think) and had to take two weeks off school. Not being sick enough to stay in bed, during that time I worked through all the maths books we had for the year, and then my teacher had to do something about that. Luckily for me, she had a split class and so she could enable me to go up to grade 3 early, without being away from my friends or encountering any big stigma. She helped me catch up with the English and so on to do that, and really encouraged me. That felt good – it's always nice to be able to do what you want to do and go at your own pace.

Probably the single most important person in getting me where I am today, however, was Janet Hunt, the maths teacher I had for four of my five years at Churchlands High School, Perth. She was very inspirational and took a lot of care of me, giving me extension materials and encouraging my interest. We never really talked about my personal life or anything, but she set a great example by her focus on her teaching.

I often wondered why that teacher never had any trouble in her class. We were a very naughty year and we didn't always behave well, but nobody ever misbehaved in her class. She wasn't a dragon, she didn't yell at everybody or anything: she held our attention by her total focus on the maths, her dedication to it and her interest in it. I don't know how she kept it going through so many years. Her interest and just her professional attitude really held me. And she also made it possible for me to go to a maths camp, the National Mathematics Summer School, in Canberra – a great experience – at the end of year 11.

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The terrific interplay of maths and computer science

You did your science degree at the University of Western Australia, choosing a double major in maths and computer science. Why this combination?

There are several answers, I guess. I chose maths mostly because I loved it and enjoyed it. I chose the computer science initially out of practicality, wanting to make sure I did something that would be very employable at the end of my degree. Now I realise that probably maths is enough on its own to make you employable, but at the time I felt that computer science was important.

I have to confess I didn't like computer science at first. I found it very hard going for the first couple of years, but I was stubborn and persevered with it. By the third year I started to realise that maths and computer science are incredibly intertwined and they really belong together because of the type of thinking you have to do and also because an awful lot of mathematics, in order to be useful in the world, has to be embodied in the form of a computer program. Often you can't even try out your ideas in mathematics without a computer program to test what happens. Suppose you write down equations for the Mandelbrot set. They don't look very exciting. But if you implement a program that converts those equation to colours and pictures, you can have beautiful pictures of fractal sets – you can bring something into the real world.

So maths and computer science was a great combination in the end, better than I realised when I started.

How can a robot best use its arm? Beginning to apply the maths

What work did you do for your Honours degree?

My Honours supervisor was Dr Robyn Owens, who again really encouraged me. The project was on robotics, which was her area of research.

She was one of the main people working on a sheep-shearing robot at the University of Western Australia. Its stated aim was to shear sheep, but really it was more of a testbed for all sorts of different ideas in robotics. A problem had been encountered, however, with certain positions of the robot arm. You might have seen that a robot in a factory has an arm that picks up things and moves them, or that inserts rivets, say. It is very much like a human arm but of course made of metal, and often with more joints. My specific project was to study how to control a robot, looking at the equations that govern its motion at extreme positions – for example, stretched straight out or folded completely back on itself – which cause problems.

One of the things that I contributed, when I thought about this problem, was that these two extreme positions are really quite different. The second type of position – the arm folded back on itself – is useful. When the arm is tucked back, I can change the angle of the hand. So this position is actually useful and not necessarily to be avoided as people had thought.

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How can airline crews' work best be scheduled?

After a successful Honours year, you completed your PhD – towards the end of which you had a couple of transformational experiences.

I should mention that a lot of my PhD experiences which really helped were thanks to my supervisors, Professor Alistair Mees and Dr C J Goh. They both took good care of me and made sure that I could have these types of experiences.

One such experience was the Mathematics-in-Industry Study Group. It is a great event, initiated by the CSIRO, and hosted every year by different places in Australia. On the first day, representatives from about eight to 10 companies get up and they each talk about a problem of interest to them which they think mathematics can be applicable to. They might even have brought along some samples – if, say, they want wear and tear in train wheels looked at, they might bring some train wheels along. Each company rep then goes to a different room. The mathematicians that have come along (often upward of 100 from around Australia, and PhD students like I was at that time) just go to the room for whatever problem they like the sound of and think they can contribute to. And for the whole week everybody workshops ideas on those problems.

The problem that really influenced me was one in airline crew scheduling. A given crew, for example, might start working in Melbourne on a certain day and take a flight to Sydney and then perhaps a flight to Canberra. If that's the end of their working day, they might stay the night in Canberra and maybe do a couple more flights next day, et cetera. There are zillions of such tours of duty or combinations for a crew. What you want to do is combine them in the most efficient way so that every flight gets a crew and every crew's work is reasonable. That problem really caught my interest, and I've been involved in problems of that sort ever since.

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The buzz of overseas experience and contacts

How did the trip you made to the United States at the end of your PhD influence you?

I was lucky enough to get some funding – again through the help of my supervisors – to spend about eight weeks in the United States, where I did a combination of things. I went to a conference; I visited a university where people were working on specifically what I was working on; and I also had a one-month 'vacation studentship' working at Bellcore, which is one of the research institutes that came out of the AT&T group when it broke apart. Bell Labs, now called Lucent, was one group and Bellcore was the other, and although they were separate they did actually work together and I visited Bell Labs as well (the place where they invented the transistor). It was a big thrill to get to go to these places.

That trip was fantastic because it put me in contact with a lot of people working in my area. Working in specialised areas of maths can be quite isolating at times. There aren't necessarily a large number of people in Australia working on your particular area. Of course you've got people around you working in related areas, but to be at a conference where hundreds of people speak my language and know what I'm talking about, and the nitty-gritty detail, was a very pleasant and exciting experience. I think the whole time I was there I was just buzzing with interest and excitement about everything that was happening.

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Postdoctoral affirmation and impetus

You had two postdoctoral fellowships. The first, at the University of Waterloo, in Canada, was an opportunity for you to see how Australians working in your field shaped up with the best in the world. How did they compare?

It was a real confidence-building experience, because I found that Australians were right at the top of the field and no different from anyone else there – Canadians, Americans, people from all over the world. There were three of us Australians in Waterloo at the time, and I think we were all thriving and found that we fitted in, we belonged. A senior professor in that department was from Melbourne originally, and besides me there was another student from Perth (I actually didn't know him until we met there) who has gone on to finish his PhD and actually get a position in that same department. That is a real coup, because it's a top department. It seems Australians often ask themselves, 'How do we compare?' and everybody is very excited when sports people make it big. But I've found that we just naturally are at home. I think our education system has been absolutely great; we certainly are not at all disadvantaged, compared with our North American counterparts, by the quality of education here. It's really fantastic and we do very well when we get the chance to go somewhere else.

Tell us about the postdoctoral fellowship you moved on to after the year in Canada.

That was a really wonderful experience. I had met Professor George Nemhauser for the first time at a conference in Singapore, when I was still a PhD student or just finishing, and he inspired me to change my career direction a bit from my PhD research into a line which was much more practical – still within the same general field, but focusing on problems like the air crew scheduling problem that I mentioned. He's a big expert in air crew scheduling, and he gave a half-day workshop at that conference that triggered my interest and gave me extra impetus to change to that field. And through meeting up with him I got offered a postdoc to work with him at the Georgia Institute of Technology's School of Industrial and Systems Engineering. So after Canada I took up that position for a year, and it was a really inspiring one.

That department does a lot of work on theoretical maths but also has a tremendous amount of involvement with different companies: it seemed like every other week there was a company bringing a problem to be worked on by students and staff. So you got to see a huge variety of different industries and to actually see how the solutions played out. Professor Nemhauser has mentored a lot of careers, and he was a really great mentor to me. He spent a lot of time with me. When a person with his experience and his background is able to devote time to you, that is invaluable. He told me all the things I needed to think about and to do in order to have a good career and to pursue an academic career as I wanted to. He made that happen, and helped make me passionate about what I do.

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How can radiation best be used against cancer?

You returned to Australia to take up your current job at the University of Melbourne, where you are working on a number of projects. Would you tell us about the one involving cancer radiation treatment?

This project was brought to me by some researchers in Germany who I've been working with for the past year. (That started when I spent a month last year working with them in Germany.) In the treatment of cancer using radiation, you have a beam source which moves in a semicircular arc around the patient. The beam head will move and stop in a given position, and then fire off radiation at the tumour. The idea is to maintain focus on the tumour but keep changing the angle from which you fire the radiation at it. So the tumour gets hit a lot of times with the radiation but the healthy tissue around it only gets struck from one angle, and the radiation builds up in the tumour without accumulating too much in healthy tissue.

We've been trying to optimise the treatment planning process. There are a lot of decisions to be made when you plan radiation treatment, such as the angles at which you are going to stop and release radiation at the tumour, the sort of pattern of radiation you are going to release when you do that, and how you can get the machinery to deliver that pattern in the most efficient way. There are lots of different combinations of angles you can stop at and ways you can do all these things, so we use mathematics to help us find the best. And by 'best' we usually mean the tumour will get a lot of radiation and the healthy tissue will get as little as possible, and the patient will not have to spend too long in treatment – you want to keep their treatment time as low as possible. Those are the goals, and with mathematics we are able to make some quite substantial advances towards achieving them.

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What is the best aircraft path?

Another, quite different, project you are working on involves some work that has been taken up by researchers working with the United States Air Force.

This project highlights the broad spectrum of problems you can use mathematics for. In military contexts you might want, for example, an aircraft to fly from point A to point B through some hostile terrain without being detected. Your intelligence forces might have found out where there are, say, radar detection devices, and so you hope you know where those are positioned. What you do is look at every possible point that the aircraft might travel through to get from point A to point B, and try to assess the risk at each point of detection. You would then plan a path from point A to point B to minimise the risk of detection by all these devices, but at the same time you have to satisfy some constraints such as not having the aircraft flying a huge distance or runing out of fuel. There could also be a whole lot of other constraints – perhaps restrictions on height – depending on the type of aircraft. Addressing those problems is something that mathematics is very good at.

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Mathematics in the real world: challenge, creativity and variety

Natashia, you're very enthusiastic about mathematics. What would you tell a young person considering taking up a career in maths were the most rewarding aspects?

There really is a mental challenge, it's fun. Sometimes it's almost like you get to play a game every day, because you're pitting your wits against a problem and it's exciting and fun to see what you can come up with and what you can create. So I would point to that problem-solving aspect, the fun of having new problems to tackle and the challenge of tackling them and using your wits.

There's a surprising amount of creativity in mathematics. People think about careers in the arts or that type of thing as being creative, but you're constantly thinking of new ways to use mathematical ideas to help. That's a really nice part of it.

And then another part is the variety. Maths comes up in almost every aspect of life. When you are a very young child and watch something like Sesame Street, you'll see two elephants walking past, then two zebras walk past, and then two balls roll past, and eventually you realise, 'Oh, the concept here is two.' Two is an abstract concept, a mathematical concept, but it embodies all those different things – elephants, zebras and balls – that live in the real world. That carries throughout mathematics: common mathematical structures come up and appear and are embodied in almost every aspect of the real world. And discovering the common structure, getting that light bulb to switch on, 'Oh, that's the number 2,' but having it happen in ever more complex and interesting ways, is another really nice part of it.

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Skills for an exciting career

What skills do you think are needed for a career in maths or science today?

It's not enough any more to focus on just one skill, you really have to develop quite a variety of different skills. Logical and critical thinking is obviously needed: developing your ability to, for example, look at someone's argument and see where the holes in it are. Be suspicious, don't just accept what anybody tells you – examine it. That type of critical thinking is crucial, because with mathematical ideas we're often modelling real systems, and we must check, 'Does this mathematics properly model it? Does it model it in every respect that we need it to?' So we're constantly putting up ideas but then really hammering at them to see whether they hold up under scrutiny. You don't want to move forward with decisions based on mathematics unless it's been properly scrutinised. That's not only an important life skill but it really plays out in a big way in mathematics. Logical and critical thinking are important faculties to develop.

Computer skills are also needed. I mentioned at the beginning that computers and mathematics are interrelated. You get a huge amount of excitement from seeing mathematics come out in the real world, and very often that happens via computers. In my area, to get back to the crew scheduling example, the way that the mathematics plays out – when it helps us sort through all those different combinations and find the best one – is that it sits behind a scheduler's computer system. The scheduler sits there and tries to come up with the best schedule, using a computer and graphics and everything to show their plans for the schedule. But then there'll be a button there which helps them optimise that. When they press that button, there's mathematics running in the background. Mathematics has been embodied in that computer code. So the more you can enhance your computer skills, the closer you can make the link between the mathematics and getting it to come out in the real world and be useful to people.

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Enduring interests

You have a range of interests besides mathematics.

I love music. It has always been something I've wanted to do, right from being a small child. My parents, both being very unmusical, were a bit puzzled by this but they encouraged me. It was actually my father who had me sit the test for the musical scholarship which enabled me to go to Churchlands High School, where the scholarship gave me classes in the violin. So I played the violin, and we had a school orchestra and I used to sing in the choir; it was our school that would do the Anzac Day parades and things like that. It was great fun, and to this day I still love classical music and listen to a lot of it.

Also, since I was 20 or so I've liked running and that type of thing, so I've done quite a few fun runs – the longest was a half-marathon. I'm certainly no professional athlete; I'm just happy if I make it to the end. Recently I've got quite keen on triathlon – again nothing long, just the really short ones, but doing them and doing all the different types of training is great fun. So again I like the variety.

And apart from triathlons, I really love hiking. I love getting out in the bush, and having some fresh air and seeing beautiful scenery and watching animals and things like that.

Your husband shares those interests, I believe.

Yes, sometimes slightly reluctantly. He doesn't appreciate the triathlon wake-up call at 6am, but I think he figured if he was going to get out there he might as well do it. He's done the last couple of triathlons with me, and having him along at training is good fun and helps to make it more enjoyable. And he definitely comes on the hikes.

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Towards using the potential of mathematics more effectively

You've achieved a lot already in your career. Where do you see yourself in 10 years' time?

I guess I have two main goals for the next 10 years. I would like to have a family, some children. That's a very important goal for me. But on the career side of things, I would like to move more into enabling mathematics to play out in the real world. In my actual research I have been fortunate enough to have applications used, based on what I have been working on, and as well I still do quite a lot of theoretical work, which is great fun and really exciting in its own way. But I would like to move more towards actually making it happen, enabling the mathematics that exists to be used more, because I believe the state of the art in mathematics is beyond what is being used: there is a real gap between what we know we can do and what is actually being done. I would very much like to try to narrow that gap a bit and to do a bit of 'technology transfer' – to use a buzzword. That's where I'd like to move the emphasis of what I do.

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