“As a mathematician, I’m often challenged to come up with compelling reasons to study mathematics. If the questioner is serious, I reply that there are three reasons or, more accurately, three broad classes of reasons to study mathematics. Only the first and most basic class is practical. It pertains to job skills and the needs of science and technology. The second concerns the understandings that are essential to an informed and effective citizenry. The last class of reasons involves considerations of curiosity, beauty, playfulness, perhaps even transcendence and wisdom.”
The second and third answers are reflected in the words inscribed on the door of Plato’s Academy: “Let no one ignorant of geometry enter” (Ἀγεωμέτρητος μηδεὶς εἰσίτω):
The first answer relates to the critical importance of mathematics in several fields of human endeavour, including science, engineering, medicine, and finance. For example:
A stressed ribbon bridge is strong if its shape is that of the mathematical curve called a catenary.
The spread of an infectious disease can be predicted by a set of three differential equations, relating three variables: S, I, and R (left). Real-world disease outbreaks show a similar pattern (right).
Many people list this as the only reason for studying mathematics, but it only applies to a minority of students – those keeping open the option of entering those fields. The second answer relates to the importance of mathematics in decision-making by ordinary citizens, and this applies to everybody. Some of those decisions by citizens require quantitative thinking. For example, which groceries are the best value for money? If two studies on 20 people report that a certain vegetable causes cancer, and one study on 1,000 people report that it doesn’t, is the vegetable safe? More subtly, training in mathematics helps in thinking clearly even about non-quantitative issues. Plato seemed to think that mathematics was essential training, and I would agree. Bertrand Russell put it this way: “One of the chief ends served by mathematics, when rightly taught, is to awaken the learner’s belief in reason, his confidence in the truth of what has been demonstrated, and in the value of demonstration.”
What is the best value for money – the melons at $5 each, the grapes at $4 per kg, or the blueberries at $3 per punnet?
This classic book has applications to more than mathematics.
The third answer relates to a famous remark of Debussy – “La musique est une mathématique mystérieuse dont les éléments participent de l’infini” (“Music is a mysterious mathematics whose elements partake of the Infinite”). It works the other way around too. Mathematics is a mysterious and beautiful music that puts one in touch with the Infinite. As Plato would have said, mathematics reminds us that more things exist than just the finite and physical. This particularly applies to those parts of mathematics which relate to infinity, such as the number π, or the Mandelbrot set:
Rudy Rucker’s little book The Fourth Dimension and How to Get There is also a great mind-stretcher. And, of course, having one’s mind stretched like that is a lot of fun.