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Professor Reinout Quispel – Differential equations

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Ernest Raetz:

Welcome to a La Trobe University podcast. I'm your host Ernest Raetz and we'll begin with a question. Does maths really matter? Does it make a difference in the real world or only on the blackboard?  Most of the things we take for granted, our modern lifestyle, health and knowledge, would not exist without continuous advances in mathematics.  Professor Reinout Quispel, an ARC Australia Research Council Professorial Fellow in Mathematics, heads La Trobe University's Maths Research Group in Dynamical Systems and Scientific Computation.  One of his main areas of expertise is solving maths problems using differential equations for computer research. Maths is making a considerable impact in this field and modern computing in turn, is making amazing advances possible in maths.

Reinout Quispel:

Computers have gotten a lot faster over the last twenty years but of course with computers, there's two sides – there's hardware and there's software. The hardware has gotten better but our job is to try and make the software better, in particular the mathematical software. So the combination of those, that's what's made the computer revolution, if you like.

Ernest Raetz:

With maths and computing, we hear a lot about algorithms. So what are the differential equations that you are working on, just in layman's terms, tell us that, and also why are they important.

Reinout Quispel:

Well, in layman's terms, you might think of where you were in primary school. If you had to go a distance of, let's say, 200 kilometres, your speed was 100km an hour, then if you had to calculate how long it would take you to get there, it's two hours, right? But now the question is, what happens if the speed is not constant. Then it becomes more difficult and that's the kind of things that we use computers for, to calculate, and in particular things like spacecraft, where the speed can vary all the time, you start slowly, and you go faster, and then it becomes very important to have very precise calculations on where the spacecraft will be tomorrow or the day after. That's done using differential equations. Virtually everything that changes in time is described by differential equations. So, examples are water waves, or any kind of waves, sound waves, the motion of the planets, if you throw some sugar in your coffee, if you stir it, what happens then?  If you moved … all those things are described by differential equations.  And of course for your coffee it's not so important to calculate exactly what happens, but if you have a big factory where they're mixing paints and things like that, you do want to know exactly how to do that in such a way that you get the best mix of your paints and in the fastest possible way.

Ernest Raetz:

So how do you get this mathematical equation? I see a whole lot of symbols on your whiteboard behind you. How do you translate that into the point where you can actually use it in, say a paint factory, or a computer or a medical application? How do you actually physically go about your work?

Reinout Quispel:

That kind of thing is a team effort, right? So it's not one person that first thinks up the equations and then writes the computer program and solves it and then sort of works out what to do with the paint. I'm not an expert on paint. Paint is just some random example. But let's say the planets. I'm not particularly an expert on that, but I am on expert on how you could solve those equations. Those equations, we know what they are, more or less. My expertise is in a sense to come up with the ideas, what we call the algorithms, that really means the recipe for the computer program, then there are other people in our research group here who actually write the computer program, and then we collaborate with people who use that program for certain astronomical applications. For instance, to calculate how the planets in the solar system move in a very precise way.

Ernest Raetz:

So is this a very close collaboration? I mean, do you almost sit with them, and meet them on a daily basis, or is this more remotely done through the dissemination of papers?

Reinout Quispel:

Some of the collaborations are close, so for instance, we have a collaboration with Mark Sofroniou who works at the Wolfram Company which produces mathematical software. We interact on a daily basis. Other collaborations are, as you say, we publish a paper, other people use that for the applications that they work on, for instance in celestial mechanics or particle accelerators. All these areas are specialist areas.

Ernest Raetz:

So mathematicians actually contrary to what some people may think, do get out of their offices, and actually do interact and you will actually see this sometimes implemented in all sorts of areas.

Reinout Quispel:

That is true and I was just thinking of that this morning. So I have written more than a hundred research publications but only a handful I've written on my own. 95% or more I've written together with other people, and that can be other people in our group here at La Trobe but often there are also people involved from other universities in Australia, or in New Zealand. There's a lot of collaboration going on. The good thing is it's sort of competitive in a friendly way but it's not competitive in a way that people will steal your ideas. It's much more collaboration, different people have different expertises, so working together you actually both get a better result than if you work on your own. That's very much the way it works.

Ernest Raetz:

You're currently working on something to do with chemistry.

Reinout Quispel:

These computer programs are specifically used to calculate the motion of particles in a gas, because if you have a gas, you have an enormous number of particles in there. These are atoms, let's say. The number is a one, with 23 zeros behind it, so it is impossible to calculate how all these trillions, quadrillions of particles, move, so special methods have been developed for that, and that's one of the areas where our research comes in. You cannot calculate the motion of each atom individually, but you can calculate it very accurately, the statistical averages of how a gas moves. And this is so accurate that in a sense it's just as good as if you could calculate how each particle moves.

Ernest Raetz:

Why do we need to know this.

Reinout Quispel:

Well, this is one area, is the behaviour of gases. Now gas, of course, there are very many different kinds of gas. There's natural gas that you use in your car sometimes. It's of course very important in industrial applications, but other examples of this kind of motion is the motion of big molecules, such as DNA, how their shape comes about. Now that is very important to know because of biology. If you want to know how a medicine is going to work, then you have to know how these big molecules, how they fit together and how the different atoms are positioned in space, because otherwise your medicine may not be able to get to the place where it has to go.

Ernest Raetz:

OK, so this is for drug design.

Reinout Quispel:

That's certainly an area where computational mathematics is used a lot. And this is specifically an area where huge computers are used and a lot of work is done on that in the United States.

Ernest Raetz:

What's your view on the future of the discipline? Are young people taking up the field?

Reinout Quispel:

In any discipline, you always want more people to take up that field. The truth is that I'm actually optimistic about the future. I think there are a lot of very bright students coming to this area. It's true we probably could use slightly more. For instance, the best PhD student I ever had just graduated this year, so it's certainly not as if the students are any weaker than they used to be, in the good old days, it's just they're different. They have a different set of skills. Say when I finished high school, I had never touched a computer in my life. Now when kids come out of high school, they probably know more about the day to day use of a computer than I do. But that may mean that they know slightly less of other things. Know a little less mathematics, but they have other skills.; And in a sense, this is a golden age of mathematics. Major discoveries have been done in the last ten, twenty years – problems have been solved that nobody knew how to solve for hundreds of years, literally. No, it's a good time for mathematics.

Reinout Quispel

The job prospects are excellent. The problem is that there are so many good and interesting jobs out there that there are not enough people to teach maths in high school, because all our graduates go and do something else. What the solution to that is I don't know, but somehow I guess the profession of mathematics teacher needs to be made more attractive, and how that is done I leave to the politicians. That is clearly an important area.

Ernest Raetz

And the maths of course underpins so much of the science that you say is so important to the development of modern economies as well. Because there's this shortage then, what you're almost saying, of mathematicians, they tend to be sort of sidetracked more into financial type analysis and that rather than perhaps science.

Reinout Quispel

That has happened quite a bit over the last few years. A lot of our graduates have gone into the financial area. I guess the salaries there have been quite good and probably better than you'd get if you were a high school teacher. Now not everybody wants to go into finance, but there are also other opportunities for the maths graduates. It would be good if somehow we could attract more students into maths education – that really would be really important.

Ernest Raetz

Well, from what you're saying, it sounds like an exciting field, one that seems to be thriving.

Reinout Quispel

At the moment, there are four post-doctoral researchers, so they're funded by research grants. And then there is myself and there is Dr McLaren, who is now Emeritus, but who has worked here in the Department for twenty years. And so that's basically at the moment the size of my research group. From time to time there are also of course PhD students. For me, that's one of the joys is to work with these very bright and enthusiastic young researchers, because I may have some good ideas but they may come up with something that I never would have thought of. That's really the beauty of the work.

Ernest Raetz:

Professor Reinout Quispel there from the School of Engineering and Mathematical Sciences at La Trobe University.  That's all the time we have for the La Trobe University podcast today. If you have any questions, comments or feedback from this podcast, or any other,  then send us an email at podcast@latrobe.edu.au.