In recent years I’ve felt quite glad I never read G.H. Hardy’s massively influential book *A Mathematician’s Apology* (1940). I’d heard of this by the time I arrived at university but never got around to borrowing the copy I saw in the Hall library. Recently I decided to take a look and found much to dislike.

First, there’s his view of public communication of mathematics. Sometimes it seems all advice on public engagement starts with a quote from the *Apology*; as though a mathematician must acknowledge, like Hardy in his introduction, the improper nature of their endeavour.

I remember being told by an established communicator of mathematics about the importance of maintaining a strong research record to quell critics who might accuse him of undertaking public engagement work only because he has ‘lost his touch’ for research. In the introduction to the *Apology*, Hardy says that writing about mathematics,

is a confession of weakness, for which I may rightly be scorned or pitied by younger and more vigorous mathematicians. I write about mathematics because… I have no longer the freshness of mind, the energy, or the patience to carry on effectively with my proper job.

You may be aware that this blog takes its name from the *Apology*‘s opening paragraph. Hardy regards communication of mathematics as work for ‘Second-Rate Minds‘. We quote Hardy with irony, because we do not agree with him.

I believe there is great importance in communicating mathematics as widely as possible. I think it is important that children are encouraged to enjoy mathematics so that they might take further interest in the subject. Equally important is the view of mathematics held by the general public. Despite Hardy’s disdain for applications, mathematics nevertheless pervades the modern world and benefits from society valuing its role.

I feel sorry that a passionate and able communicator may not be valued by mathematicians, and that such abilities might be tempered by concerns about the scorn of one’s fellows. I happily accept that outreach is not for everyone; indeed society will benefit more from most mathematicians getting on with their research. Still, I don’t think we should look on those with a passion for communicating their subject as having failed.

I’ve chosen to pick on Hardy for his views on public communication of mathematics, though there’s much else I find fault with in his *Apology*. He expresses several opinions which are these days widely held and which I dislike.

Hardy is a proponent of the unfortunate cult of youth, writing, “if a man of mature age loses interest in and abandons mathematics, the loss is not likely to be very serious either for mathematics or himself”. Hardy hates teaching, although loves lecturing to “extremely able classes”.

Perhaps most famously, there’s his view on the “utility” of mathematics. It is easy to pick on a number theorist writing in strong terms against mathematics that can be applied to the real world, particularly to the business of war, at a time when modern cryptography was being nurtured at Bletchley Park. I have seen people take this argument to an extreme, somewhat unfairly since Hardy also writes against the “misconception” that “pure mathematicians glory in the uselessness of their work, and make it a boast that it has no practical applications”.

Having criticised these views, there is much in the *Apology* that is thought provoking and it is certainly worth a read. I like some of what Hardy says about the nature of mathematics and there is an interesting and frank account of what led him to the subject as a boy. Still, I am not sad that I missed reading the book in a more formative state of my development.

**Afterword**: Although I didn’t realise it at the time I sent the first draft of this text to Samuel for editing the morning after Sarah Shepherd died. A few days later when I received Samuel’s comments I had heard the news. I haven’t changed the substance of the piece since then, just tidied up a couple of useful points Samuel made about the flow and grammar of what I had written, yet the topic is curiously close to my involvement with Sarah’s work. I think Sarah would have agreed about the importance of promoting mathematics and the place of applied mathematics. She wrote passionately about the value of mathematics applied to the real world and the importance of communicating this to children and the general public. Through her * iSquared Magazine* she encouraged many young researchers to take their first steps in public engagement by writing about their research area for a popular audience. Consequently I dedicate this essay to Sarah Shepherd.

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