And here it is to be noted that a prince ought to take care never to make an alliance with one more powerful than himself for the purpose of attacking others, unless necessity compels him, as is said above; because if he conquers you are at his discretion, and princes ought to avoid as much as possible being at the discretion of any one.
— Machiavelli, The Prince, XXI
I suspect I’m a member of what Simon Jenkins calls the “maths lobby”. I’ve sat on altogether too many committees, helped draft rather too many documents, organised or supported umpteen engagement or maths-enrichment events, and even attended the launch a few years ago of the Deloitte report on the economic benefits of the mathematical sciences. (I was the one in the corner tilting a glass of lukewarm apple juice and muttering about why that claim about 16% of GDP didn’t seem plausible to me.) It’s not surprising in the circumstances that I don’t have much sympathy for Jenkins’s conspiracy theories about the threat the maths lobby poses to society. I find myself more worried, these days, about the threat we might pose to ourselves.
Mathematicians aren’t, in fact, terribly good at being a lobby. Compared with physics or chemistry — distinctly smaller subjects in terms of student numbers in either secondary or higher education — we’re poor, fragmented, and hopeless at putting forward a coherent, media-friendly message. (About the time of the Deloitte report, the IoP put out its own bid for attention with the promise of cures for cancer and for terrorism, plus the inevitable smartphones.) In practice, what the maths lobby tends to do is to hitch its calls for more or better support for maths onto a larger narrative, and this is where my worries start — because Machiavelli was neither the first nor the last to note the dangers of allying with somebody bigger and nastier than oneself.
Perhaps the most prominent train into which we hitch our little maths wagon is the dominant political narrative of economic prosperity and growth. Prof. Alan Champneys recently made this argument with great clarity in his response to Jenkins, and it was a Twitter exchange with him that prompted this post. It’s an honourable enough case: the world needs goods and services, and plenty of the people who provide those goods and services need more than a minimal level of maths to do their jobs. The trouble is that in our political culture the discourse around economic prosperity is one of numbers, and not the sort of numbers that I like.
These numbers, starting with that 16% of GDP, tend to look good for mathematics. The result is that our argument ends up being built of them, and they’re precisely the sort of numbers that a mathematical education should teach one to mistrust. To arrive at them requires a complicated and ad hoc process of data gathering and processing, at every step of which decisions must be made that might be perfectly reasonable but which lack the objectivity that the numerical result implies. As a tool for understanding how mathematics might be entwined with the UK economy, the Deloitte report is perhaps useful; as a quantification of anything in particular the headline figure is useless, and it gains potency in public debate only if the public are mathematically naïve enough to believe the numbers they are fed. (In fact, I suspect that the public tend to lean the other way, and are so saturated with tendentious economic statistics that they react to any such claim more sceptically even than they ought.)
To attach ourselves to the economic-prosperity narrative, then, mathematicians need to forego our usual prerogative — arguably our usual duty — of interrogating any number, any quantitative argument that’s put in front of us. We must hope that if we blink at the numerical misdemeanours of those who pronounce on the ways of wealth, they will return the favour by employing us to blink at more misdemeanours. Possibly they will, but I doubt that at the end of the day we will still be mathematicians.
The same argument applies to another narrative, the technocratic one of Big Data and an algorithm-driven elysium in which we have data-mined and nudged and smartened our society so completely that there is no more need for those flawed, subjective, biased human judgements. I don’t know whether this narrative is pure fantasy or whether the technologies involved really could deliver the kind of control their proponents claim; I am sure that if they do work, most of our fellow citizens will be even less well placed than I am to appraise them or to resist the power that they will place in the hands of those who pay the algorithmists. It seems a lousy kind of defence for the social utility of mathematics in either case.
A narrative of a different kind is provided by the politicians who in recent years have been struck with PISA envy — and this is the one point in Jenkins’s article where we should admit he has a point. Let’s leave aside the Yellow Peril undertones of this ongoing moral panic, and let’s also admit that there might — perhaps, and with appropriate awareness of surrounding cultures — be something to be learned from Shanghai or Singapore. The fact remains that the PISA rankings are a single output from a single instrument, that any assessment instrument, however good, is readily gamed, and that throwing money at the task of rising up the PISA rankings out of sheer patriotic fervour makes about as much sense as throwing money at the Olympics. It’s tempting to use British or Scottish underperformance in PISA as a lever to direct more much-needed resources into school-level maths, but we’re starting to see in England the danger that these resources will be devoted to that ancient art of teaching to the test. Our PISA scores will rise proudly; our underlying mathematical literacy might, I fear, remain rather flaccid.
A final and less malign set of allies are the other “STEM” subjects. Evidently there are problems here given that much of the lobbying done on behalf of STEM is the same as that done on behalf of M alone (albeit with better PR and shinier images), and suffers from all the flaws noted above. Even without these, and without talking down what maths has to gain from its interactions with science or engineering, we need to ask ourself whether the commonalities with these subjects are concealing our commonalities with others. In education, certainly, teaching methods in a lab science and in mathematics are worlds apart; in our way of doing research, too, we often have more in common with parts of the humanities than with our big-grant, big-team Big Science cousins. Ranked alongside S, T, and E, we are clearly a poor, grubby and rather ineffective science which exists mainly to help students of other disciplines to get their graphs right. Joining forces with the other arts, if we asked nicely, perhaps we could be seen as another of those subjects whose social purpose is to help human beings become more thoroughly human, and — not incidentally — also better citizens.
Because that’s where I’d argue the real social utility of maths education is to be found: not in producing obedient rule-followers, but in producing informed critics of arguments that masquerade as mathematical. Somebody who knows the methods of history is unlikely to be taken in by Holocaust denial. Somebody who knows the methods of rhetoric is equipped to spot the techniques of deceit and persuasion in the mass media. Somebody who knows the methods of mathematics should be capable of resisting those who would rule us and confuse us with numbers — not the “maths lobby”, but the lobby of financial and political numerologists and quantocrats, the praetorian guard of those who understand numbers just fine and do not wish to share that understanding.
Perhaps I shouldn’t be downcast that mathematicians are such ineffective lobbyists, when the most effective ways that we could lobby for our discipline would involve a compromise with these powers. It might just be that by being too incompetent to gain the world we will accidentally preserve our souls.