When struggling with a mathematical problem, a student might ask “What’s the use of this stuff?” The question is often an expression of frustration: the student does not really want an answer. However, the question remains. What is the use of mathematics today? These days, we have smart calculators and sophisticated computers to do our calculations. Has mathematics passed its use-by date?
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On the contrary, mathematics has become increasingly important in the modern world. Each year, the Australian Mathematical Sciences Institute publishes a book entitled “Maths Ad(d)s”. This book contains advertisements for jobs that require understanding of mathematics at a high level. The fact that this book is published each year with new advertisements indicates the continued growth in demand for people with strong skills in mathematics.
New terms have evolved to describe areas in which mathematics is important; biostatistics, data analysis, operations research, bioinformatics, marketing research, epidemiology, computer science, predictive modelling, quantitative analysis, actuarial science, meteorology, econometrics, data science. And we have the classical areas for applications of mathematics in science and engineering.
The rise in computing power has made mathematics more applicable than it was in the past. Calculations that were too difficult twenty years ago can now be carried out with the click of a button. With the assistance of computers, theory can be put into practice more easily. Advanced mathematical ideas often find applications much more quickly than they did before.
In addition the rise in the availability of data especially through the internet has made many problems more accessible. In Australia, one only has to look at the data from the Australian Bureau of Statistics or the Australian Institute of Health and Welfare to appreciate the immense amount of data that we have at our fingertips. We now have a field of “big data analytics”.
However, history shows us that mathematical ideas are often developed without any thought of modern applications. Cartesian geometry is a case in point. René Descartes (1596-1650) was a French philosopher and mathematician who developed what we call Cartesian geometry. In Cartesian geometry, each point in space can be labelled by coordinates. Curves and surfaces are represented by equations. Descartes turned problems in geometry into problems in algebra.
Students who do not like algebra may not regard this as progress! However, it is hard to imagine how we could make robots without Cartesian geometry. Somehow you have to instruct the robot to pick up an object in one place and put it down in another. A system of coordinates would seem to be essential for this task. And we can be sure that Descartes would not have been thinking about robots when he developed his ideas more than 300 years ago. The lesson is that, what appears to be useless knowledge today, may be essential for the future.
On the other hand, what is important today may be unimportant tomorrow; the ability to use a slide rule is one example.
Advanced ideas in mathematics are built on the basics: arithmetic, algebra, and geometry. For Australia to make the best use of mathematics and its applications, we need teachers who are well trained in, and passionate about, mathematics.
Terry Mills is Emeritus Professor of Mathematics, La Trobe University and Honorary Statistician, Bendigo Health.
