Experience has shown, and a true philosophy will always show, that a vast, perhaps the larger portion of the truth arises from the seemingly irrelevant.
Edgar Allan Poe
The Mystery Of Marie Rogêt
In my last post, about the history of mathematics, I mentioned briefly the mathematician GH Hardy, who was based in Cambridge in the early twentieth century and who was the mentor of Srinivasa Ramanujan, the subject of Hollywood’s latest foray into the world of mathematical genius. Hardy wrote a wonderful book called A Mathematician’s Apology, in which he discusses the beauty of mathematics and expounds the importance of mathematics for its own sake, rather than for its applications. Hardy was vociferous in his belief that the most beautiful mathematics was pure mathematics, that which had no applications. It wasn’t that Hardy was against applying mathematics per se, more that true elegance existed in a discipline that was pursued chiefly as a matter of intellectual curiosity, or in the act of creating or discovering something truly new, without the ulterior motive of improving the material lot of humankind.
Hardy’s own field of expertise was number theory. He boasted of his efforts, “Nothing I have ever done is of the slightest practical use” as if this made his life’s work all the more satisfying. Perhaps the greatest irony of Hardy’s pronouncements is that it is specifically his field which has formed the basis of much of the modern world. Turing and the Bletchley Park scientists cracked the Enigma code using number theory. Public-key cryptography, on which the web relies, is number theory. But the fact that the work of Hardy and numerous other pure mathematicians who do “maths for maths sake” often turns out to be eminently useful in no way nullifies the ideas Hardy espoused.
Hardy’s ideas are hugely important when considering education, what we teach and why we teach, not just in mathematics but in every subject. In striving to make our curriculum “relevant” or “applicable” we create a state whereby those whose experience is naturally limited are confined indefinitely to their current borders. They are unintentionally taught that what is important is what you already know and experience. In so doing, one of the greatest capacities of the human mind is dulled: intellectual curiosity and the desire to understand and explain. Hardy knew that although the proof of the irrationality of the square root of two was irrelevant to most people, there was a whole universe of numbers and mathematics out there whose mere existence meant it had to be discovered, and that the utmost satisfaction was to be gained in the pursuit of this knowledge. What we know, with the benefit of history and reflection, is that intellectual curiosity always leads to relevance in some form or another, although not always immediately, therefore it is silly to make relevance our aim.
Instead of searching for relevance we need to expose children to the vast expanses of human history, discovery and creativity: the literature that has shaped our language, the history that has produced our collective identity, the geography that explains how we live, the art that brings us delight, the mathematics that provides absolutes, the science that explains how it all works, and everything else inbetween. In doing this we allow them to take the next steps, create something truly new or, at the very least, understand where they have come from and where they might go explore next. In not pursuing relevance we give everything importance.