My father, an Edinburgh university prize-winning mathematician and life-long teacher of the subject, tried very hard to explain mathematics to me – its beauty, importance, as well as its utility, but I was a poor student and the subject has always been a complete black hole for me - impenetrable, obscure, complicated and unintelligible. Of course basic addition and subtraction of use every day is needed, an ability to read and understand a balance sheet is essential for business, and of course too necessary for building and engineering. But pure mathematics, no thanks, I had better things to do. And so an unspoken but definite gulf of non-understanding on this subject, so close to his heart and mind, settled between us. Now however that has changed.
Seventy-eight years ago G.H. Hardy, mathematician, Fellow of the Royal Society, and Fellow of Trinity College Cambridge, published a slim volume entitled A Mathematician’s Apology. He used the apology in the classic sense of a defence or justification, not to say sorry for his view, but in fact what he wrote is a beautiful love letter explaining why he loved mathematics, specifically pure mathematics. Although dated in some respects of language and style, and wrong in several predictions, the essence of what Hardy had to say is as fresh and as compelling today as it was when it was first published in 1940.
The essence of Hardy’s point is that pure mathematics is as beautiful as great art or great poetry. To that we might add not only other great science, but also a great political achievement or business success – because they too, no less than mathematics, art and poetry, in their purest forms demand great precision and finesse if serious success is to be achieved. Hardy contends that pure mathematics has, or should have, no practical application as its intended aim. That it is a joy in and of itself, but the fact is by successfully pursuing pure mathematics positive and useful outcomes do occur, and indeed are vital to human advancement. Many great endeavours are undertaken because they are there to be done, rather than to achieve a specific purpose. Scott raced to the pole because it was a race to be won. The scientific and photographic legacies were a by-product – and no less valuable for being so.
A Mathematician’s Apology is a product of its time and place and this has to be taken in to account, but should be no barrier to its essential truth. That mathematics is an art as well as a science, it is beautiful and precise, its discovery and evolution is fundamental to nearly all other forms on learning.
There are some, small parts, that I do not understand and probably never will. I have come to it late – but better than never! It does not matter. This is a beautiful and clearly written book, which can be easily understood and appreciated by all. It should be compulsory reading for all children, as early as possible, and certainly before they are compelled to start studying seriously for their GCSEs. I certainly wish I had.