Mathematics has its own intrinsic beauty and aesthetic appeal, but its cultural role is determined mainly by its perceived educational qualities. The achievements and structures of mathematics are recognized as being among the greatest intellectual attainments of the human species and, therefore, are seen as being worthy of study in their own right, while the heavy reliance of mathematics on logical reasoning is seen to have educational merit in a world where rational thought and behaviour are highly valued. Furthermore the potential for sharpening the wit and problem-solving abilities fostered by study of mathematics is also seen as contributing significantly to the general objectives of acquiring wisdom and intellectual capabilities. These cultural aspects affect all Canadians to some degree through our formal educational processes, reflecting the degree to which Canadian society is committed to "liberal" or "humanist" education. In particular, it is a point of view adopted by many professional mathematicians in their teaching and research activities.
The "functional" aspect of mathematics stems from its importance as the language of science, engineering and technology, and its role in their development. This involvement is as old as mathematics itself and it can be argued that, without mathematics, there can be neither science nor engineering. In modern times, adoption of mathematical methods in the social, medical and physical sciences has expanded rapidly, confirming mathematics as an indispensable part of all school curricula and creating great demand for university-level mathematical training. Much of the demand stems directly from the need for mathematical and statistical modelling of phenomena. Such modelling is basic to all engineering, plays a vital role in all physical sciences and contributes significantly to the biological sciences, medicine, psychology, economics and commerce.
Rapid Development of Computing Power
The rapid development of computing power has created its own demand for mathematical techniques and has permitted the implementation of large-scale mathematical models that would have been impractical before. Indeed, development of computer science itself owes much to the contributions of mathematicians, and its continuing explosive growth draws on, and contributes to, mathematical science. For example, the analysis of algorithms, the structure of formal languages, robotics, logical design, and large-scale scientific computation may be seen as important components of computer science which require, and stimulate, mathematical analysis in their development.
The pervasive and ever-increasing use of mathematical methods in science, commerce and government implies that a well-informed public must be mathematically literate to some degree. In practical terms this means that, in the mainstream of primary and secondary education, there must be effective mathematical education, bringing students to a point where they can readily calculate and think in quantitative terms, where information presented graphically or in statistical terms is easily comprehended, and where the logic and precision demanded in communication with computers is appreciated. There is an ever-increasing need for people who are well trained in mathematics and are confident with the mathematization of problems in the world around us.
Place of Mathematics in Society
In any country, the place of mathematics in society depends on the nature of the society and its ambitions. Canadian society has inherited the European traditions of cultural and scientific freedoms, and it is reasonable to assume that these will be maintained. Also, from a prosperity based on the extraction of primary resources, Canada aspires to a leading role on the international scene as an industrialized nation and as a producer of consumer goods and high technology products. These aspirations are strongly influenced by the proximity of the US and, in particular, by Canadian economic dependence on that country. The role of mathematics in Canada, and of all the basic sciences, depends partly on the degree of economic independence chosen by Canadians now and for the future.
This discussion sets the context in which the past and present role of mathematics in Canada must be assessed and suggests a context for the future. It implies, first, that building on existing programs a relatively high level of mathematical literacy should be an objective of the primary and secondary school systems. This is necessary if the layperson is to cope with the computer and information revolution and with the ever-increasing use of quantitative methods in governmental decision making. It is also a necessary foundation for the appreciation of modern scientific activities and the history of sciences, as well as for those wishing to participate in more advanced technical, scientific or mathematical subjects. At the post-secondary level, Canada should maintain a strong tradition for mathematics education in all its forms if it is to maintain a viable position in the world's scientific and technological enterprise. It must continue to maintain an active community of mathematicians engaged in research.
Diversity and Value of Modern Mathematical Developments
The extent to which such a commitment to mathematics is explicity accepted by society and the Canadian public is questionable. For the great majority, exposure to mathematics is limited to something less than a current grade 12 high-school curriculum. Hence, the corresponding view of mathematics is narrow, extending little further than arithmetic, with a smattering of algebra, geometry, trigonometry and, possibly, formal calculus. Such exposure cannot extend in any substantive way beyond the state of mathematical knowledge achieved in the 17th century. With this limited view, it is practically impossible to conceive of the extraordinary volume, diversity and value of modern mathematical developments. Consequently, there are widely held misconceptions about the significance and usefulness of mathematics that leave the subject vulnerable to periodic and shortsighted popular demand for functional education. There is also evidence that a negative attitude, or a feeling of anxiety towards mathematics is common in Canadian society and is even shared by many teachers of mathematics, especially at the primary level. Such considerations put responsibility on the mathematics community to recommend improvements in methods and curricula, and on governments and local authorities to ensure that high standards and, especially, proper hiring practices are maintained.
It is necessary to recognize difficulties (like those mentioned in the preceding paragraph) with the development of skills in mathematics and of awareness of the importance of mathematics in Canadian society. Nevertheless, mathematics has a respected place in the Canadian cultural and educational spectrum. The necessary educational and organizational infrastructures exist, and the subject is alive and well in Canada in both its cultural and functional forms.