Over the next few weeks, Snezana Lawrence, co-author of Mathematicians and their Gods, will be taking us into a Summer journey around the beauty of mathematics. In this first post, Snezana gives her personal and professional insight to the long time unanswered question: will we ever need maths after school?
What is the purpose of mathematics? Or, as many a pupil would ask the teacher on a daily basis: “When are we going to need this?” There is a considerably ruder version of the question posed by Billy Connolly on the internet, but let’s not go there.
When I was a teacher some years ago I tired from the question to such an extent that I bought myself a crystal ball to keep on my desk in the classroom in case someone would dare pose this question again. If that happened, I would put my hands on the ball, look at the ceiling, and very studiously wait for everyone to get quiet for a few moments, to exclaim some time and date in the future far enough for pupils to not be able to test it… It worked actually, but they kept asking just for the sake of the spectacle.
Nevertheless, this is a very serious question in fact. With the students who actually asked this type of question, not in order to avoid doing mathematics, but out of real curiosity, I spoke at length about it. Different societies, cultures, and people, have debated the very same question and given mathematics very different meanings. Plato for example, discussed at length how important mathematics is to teach the principles of thinking. His dialogue with Meno, leading the slave boy to ‘find’ the knowledge and understanding within himself is a case in point.
In the middle ages, questions such as “how many angels can dance on the head of a pin?” (or, as another version has it, how many can sit), was not only theological but also included considerations relating to mathematics in terms of space, dimensions, and extension. In this case, mathematics was given the role of rational explanation.
The 16th century scholar, mathematician, philosopher, magus, spy, and one of the most famous intellectuals of English Renaissance, gave a different role to mathematics. John Dee’s immortal fame is earnt by his Preface to the first English language edition of Euclid’s Elements in 1570, in which he boldly states that:
“Many other arts also there are which beautify the mind of man: but of all other none do more garnish and beautify it than those arts which are called Mathematical. Unto the knowledge of which no man can attain, without the perfect knowledge and instruction of the principles, grounds, and Elements of Geometry. But perfectly to be instructed in them, requires diligent study and reading of old ancient authors…”
In the same vein, some years later, in 1612, Piticus, who is credited with the invention of the term trigonometry, states that:
“Nothing makes men more gentle than the cultivation of that heavenly philosophy (mathematics). But, dear God, how rarely is this gentleness a quality of theologians! And how desirable it would be in this century if all theologians were mathematicians, that is, gentle and manageable men!”
Nevertheless, the more utilitarian view of mathematics remained and is recorded in various places. During the French Revolution, one of the most revolutionary of the mathematicians, the one who is given the title of the father of École Polytechnique, Gaspard Monge, saw mathematics as a way of training the minds of young people for the prestige of his nation:
“In order to raise the French nation from the position of dependence on foreign industry, in which it has continued to the present time, it is necessary in the first place to direct national education towards an acquaintance with matters which demand exactness, a study which hitherto has been totally neglected…”
A 18th century Italian mathematician, Milanese Maria Gaetana Agnesi, saw mathematics as a way of training the mind to concentrate. By sharpening it as a mental tool for learning, the mathematical mind also becomes an instrument through which spiritual enlightenment becomes possible.
So you see, mathematics can be given different roles and is assumed to beautify, free, and educate the mind. In these roles, mathematics is also considered to be dangerous; it can train people to think for themselves. Perhaps the most succinct expression I have ever come across in this respect is given by the Christian Orthodox Archibishop Gritorios V, who in 1819 issued a warning to all students and teachers of mathematics: “cubes and triangles, logarithms and symbolic calculus . . . bring apathy . . . jeopardizing our irreproachable faith…”.
So what is mathematics? It assumes different roles and meanings in different cultures, places, and times. The common factor to them all is that this is a universal tradition of abstract thinking which, with study and perhaps some adaptations, can be understood and contributed to universally. As such, it is the international language that, whilst still conditioned on locality, all of humanity is able to, if not necessarily speak, then understand. To study is to link, via mathematics, to that tradition of humanity.
Featured image credit: Apis florea nest closeup by Sean Hoyland. Public domain via Wikimedia Commons.
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