It is time we taught our students to speak mathematics - industry is in desperate need of such skills.
A near-solitary point of agreement in higher education policy is that universities should all engage in the education of future professionals and scholars. Most of us would happily add "and do so to acceptable international standards". But what if the students we enrol lack the basic academic preparation that makes this possible?
The crisis in UK mathematics education has reached the point where this is exactly the situation we face. During the 1990s, as staying-on rates at 16 soared, maths A level barely held on to its percentage share of A-level entries. With declining cohort sizes, the absolute numbers of maths A-level passes (and so of undergraduates with a maths A level) fell sharply compared with the 1980s. The AS reforms have, so far, not only failed to increase A level take-up in mathematics, but have had the opposite effect. High failure rates in 2001 maths AS led to a dive in A-level entries last summer. Not surprisingly in this environment, while total graduate numbers move ever upwards, the flow of maths graduates has barely increased.
Yet if there was ever a subject where we clearly need more qualified people, it is in mathematics. Labour market signals are clear. Recent graduates in quantitative disciplines enjoy far higher average wages than those in arts and social sciences; and this isn't just because these subjects attract the greedy - their relative advantage has widened sharply of late, and encompasses the engineers who, not long ago, the UK labour market was so widely criticised for undervaluing. Among people born in the late 1950s, those with a maths A level earn, on average, about 10 per cent more than those who in every other respect have the same qualifications and backgrounds. This advantage cuts in not when people first enter their jobs, but as they advance in their careers. In other words, it isn't just that employers think having an A-level in maths means you are clever: it is using these skills at work that brings in higher wages.
As you might guess, recruitment of sufficient maths teachers has been near-impossible for years (a point made to the government repeatedly, and increasingly desperately, by the school and teacher training communities).
So fewer pupils are offered good maths teaching. In turn, choosing to study maths A level becomes an ever-riskier choice for all but the strongest pupils. Yet, at exactly the same time, the importance of mathematics in a wide range of university subjects has increased, is increasing, and is set to increase further.
How can we teach economics to first-year students who cannot understand the textbooks, or maintain the quality of the chemistry graduates for our pharmaceuticals industry if large numbers of them gave up maths post-GCSE.
How can we teach the new evolutionary biology to which this country has made such huge contributions? Mathematics is a global language of the scientific, financial and technical community - and most of our students are unable to speak it.
University departments have been grappling for years with the consequences of undergraduates' lack of mathematics. Many departments that used to require maths A level for entry have been forced to abandon this requirement; with fewer qualified students to go round, it is that, or close. Others ought to be asking for sixth-form mathematics as their subject changes, and can't. Instead they face teaching a first-year group some of whom have good maths, and some of whom have very little.
The Gatsby Foundation has, for many years, been concerned about this worsening maths crisis. Its research has documented not only the threat to standards but also the incoherent, ad hoc way in which university departments try to plug the gaps, with a combination of some add-on classes, paid for somehow, and an optimistic reliance on self-teaching with worksheets and a bit of software. Since teaching oneself mathematics is diabolically hard, it is probably just as well that no one much is monitoring the outcome.
Belatedly, but thankfully, the government has recognised that secondary school mathematics teaching cannot go on as before. Adrian Smith, principal of Queen Mary, University of London, is chairing a mathematics inquiry whose job is to make recommendations "to ensure that the UK has a strong supply of mathematical knowledge and skills". Inquiries such as this do matter: this could be a once-in-a-generation chance to reverse a threatening downward spiral. If higher education ignores it, universities as well as students will be major losers.
Alison Wolf is professor of education at the Institute of Education, London.