The Research Excellence Framework recognises the uncertainties of translation difficulties in measuring the impact of research on economic and social well-being, and is permitting a window of 15 years for reporting. Mathematics is particularly difficult in this respect. It is not possible in law to patent mathematics and many mathematical contributions go simply unacknowledged. Much work is curiosity driven. For example, it took many decades for the importance of discoveries in early nummber theory to be recognised as absolutely essential to modern cryptography, granting security in financial and other communications. In many cases, in this process the language of the original mathematics can be lost in its appropriation through other academic disciplines. Equally, mathematics has the potential for rapid transferral; this is illustrated by the take-up of the Itô calculus for stochastic systems. Equally, the deep long-term impact of incremental changes should not be underestimated.

… it typically takes any technology some 20 years to emerge from the lab and be commercialised — and even then it can succeed only with sustained effort from researchers, industry and funding agencies

How much longer, then, from mathematician’s notebook to commercialisation?

Second, with the way that impact is measured by the REF, it seems to me that there is no reasonable way to predict in advance who and what research will have impact (at least in mathematics). Moreover, it is not transferable with the researcher. So how are universities supposed to change their behavior to achieve more impact? Moreover, the time scale is so large that most people that make the decisions will not see the result of their decisions before they retire, so why bother? In addition, who can know how research is going to be evaluated in 10-15 years from now?

Third, I think one of the main points that are missed about impact of mathematics, is that much of it is indirect. Namely, people who finish their undergraduate or graduate degree in mathematics move to another area of research or technology but carry mathematical values, approached and knowledge into the new area. This is clearly not measured. What values will be carried by people that are educated by mathematicians that are focused on funding research rather than doing research?

Fourth, I think also that unfortunately the REF’s impact is going to have impact. It is going to add lots of noise to the system. The impact measured is focused on very few individuals and is so arbitrary that it is likely that its variance is going to be quite broad and as I said quite arbitrary (a department might be lucky to have someone with high impact or might not be lucky). On the other hand, the variance of papers and research environment is not going to be so large. Thus, we will suddenly have two similar departments that will be ranked very differently due to the impact.

My final point is that we can still do something about it. I believe that if the LMS and other professional organizations in other science areas would have recommended to their members not to take part in REF committees unless the impact is canceled, then this would have changed things. Politicians wouldn’t like to be seen as fighting with the experts. I honestly doubt if they really care about the impact. They just want to be seen doing the “right” thing.

Of the examples you give– all that research can be found in many, many textbooks for very little money. Much cheaper than employing an expensive mathematician! About the only argument I can make is that someone had to teach this to, say, Brin and Page so they could invent the Google Page-Rank algorithm. Unfortunately, that’s an argument for having maths teachers, not researchers (or, at least, not for paying people on the basis of their research).

I do genuinely come around to the view expounded by comedian David Mitchell: http://www.guardian.co.uk/commentisfree/2009/sep/27/david-mitchell-pointless-studies-survey If an idea has obvious economic impact, then business should be paying for it (and, frankly, business _will_ pay for it, because it will pay them back). The whole point of government funding is to pay for research which wouldn’t be funded otherwise. I do think there’s a strong argument for doing academic research for the hell of it– it’s a mark of civilisation that we allow our curiosity to lead us.

Yep, in the short term, we have to play by the HEFCE rules. But I do think that, some of the time, we do need to continue to suggest that the very idea the rules are based upon is wrong.