The world of research has gone berserk
Too much paperwork
sang Bob Dylan in 2006.
Part of the recent increase in paperwork which British researchers are forced to do concerns impact. Both the Research Councils and the Higher Education Funding Council now insist that the “impact” of a piece of research will be taken into account in the decision to fund it.
At face value, this is an unarguable proposition. Nobody would deny that the proof of Fermat’s last theorem, establishing a very strong correspondence between two quite different mathematical worlds (elliptic curves and modular functions), has vastly more impact on mathematics than yet another study of, say, nonassociative ultradistributions, and is more worthy of funding. The councils are spending taxpayers’ money, and have a duty to insist that taxpayers are getting the best possible value; this value can be equitably judged by mathematical referees.
Unfortunately, this is exactly what is not meant by the term “impact”. The definitions adopted by the two bodies are not the same, but both explicitly forbid counting impact on the discipline. The research councils are slightly more liberal; things like the impact on the career of the postdoc employed as a research assistant can be counted. However, the funding council proposes that only “economic and social impact” should count (together with “quality of life”, in the unlikely event that they discover a way to measure this before they actually have to make such an assessment). Moreover, this impact must occur within twenty years of the research. In other words, you must have something which will become a successful commercial product within this rather short time.
Ari Laptev, president of the European Mathematical Society, wrote on this topic in the Society’s Newsletter this September. He gave an impressive list of areas where mathematics has had real impact. He wrote:
- Integral geometry, dealing with so-called inverse problems, has provided a methodology used in medical imaging for identifying tumours, weather radars, the search for oil fields, astronomy, etc.
- The creation of modern fibre optic cabes would not be possible wthout the discovery of special solutions of non-linear equations called solitons.
- The arrival of the Internet made people fear that the world would be drowned in vast amounts of information. This problem has been successfully resolved by Google, which invariably delivers, instantly, the information sought. It seems like magic but the searching algorithm of Google was in fact provided by mathematicians.
- The theory of wavelets has been enormously important in telecommunications. It allows us to transmit information in a most compct way and ultimately gives us the possiblity of all sorts of wireless connections.
- Credit card security is only possible thanks to cryptology, which uses a branch of number theory.
- Mathematicians are involved in improving the understanding of fundamental problems in genomics research, cell signalling, systems physiology, infection and immunity, developmental biology, the spreading of disease, and eclogy.
- Together with theoretical physicists, mathematicians are working on the unified physical theory that involves the latest developments in algebraic geometry.
The last two items on this list refer to ongoing work in applied mathematics of various sorts. In all the other cases, the mathematics preceded the application. In the case of wavelets, I don’t know the history; it may be that the developers of the theory had the applications in mind. But in most other cases, the mathematics was done for its own sake, and often preceded the application by a very long period of time. The mathematics behind Google’s page rank algorithm is linear algebra, developed in the mid-nineteenth century.
Let us test the proposition another way by looking at the great mathematical breakthroughs of the last twenty years. I would single out three: the proofs of Fermat’s Last Theorem and the Poincaré conjecture, and the (somewhat belated) Classification of Finite Simple Groups. (The last of these was announced in 1980, but took another 25 years to complete.)
It is hard to see any positive economic or social impact of any of these. Perelman did not show up to collect the Fields Medal awarded to him, and has announced that he will not accept the Clay Foundation Prize either. (Clearly he will not be asking the Research Council for a grant!) When CFSG was announced by Gorenstein in 1980, some of the army of group theorists who had worked on it decided to leave research and went into University administration instead. Would applications from Wiles and Taylor, Aschbacher and Smith be turned down because of lack of economic and social impact?
Looking further back, the seeds of CFSG were sown in the nineteenth and early twentieth centuries, when Jordan, Dickson, and others discovered various families of finite simple groups, and (I think) especially when Mathieu discovered five “sporadic” groups which didn’t fit into any family. Nobody can bear to leave a situation like that unexplained; and when, in the 1960s and 1970s, the five grew to twenty-six, we had to find out for certain whether there were any more.
Now Mathieu’s discovery had another spin-off. In the hands of Skolem, Witt, and Golay, it was realised that Mathieu’s groups were intimately connected with various discrete configurations, leading to the Golay code which was used for error-correction in the Voyager missions to the outer solar system. If these missions had found unequivocal evidence of life on the moons of Jupiter or Saturn, the social impact would have been enormous; we would have known for sure that we are not alone in the universe!
My view is that our contract with our funders (and indirectly with the taxpayer) is that in return for financial support we do the best mathematics we can; posterity will find the fields where it will have impact. Bean counters have no method of judging this. (In fact, one of the objections that has been raised against the funding council’s statement is that there is currently no objective measure of social and economic impacct, and there are no “experts” who could be paid to sit on these panels. It is simply a way of undermining any research which is not close to the market.
In any case, if we are forced to work on things that do not capture our imagination, we will not do what we are capable of doing.
If you feel that something is not quite right here, I encourage you to look at Leslie Goldberg’s web page. I found a statement there which seems to me to sum it up well:
As Don Braben so aptly put it, funding the technology but not the basic research on which it depends is “living off the seedcorn”.
Here is a draft of a document I produced to advise my colleagues on producing impact statements for grant applications. This does not address the more severe criterion proposed by the funding council.
All EPSRC applications now require an “Impact Statement” of up to two pages, in addition to the usual case for support. This statement should describe the impact of the research outside the academic research community (that is, public sector, commercial private sector, or the wider public); impact may be economic, or on health, quality of life, development of public policy, etc. The impact statement should describe who will benefit and how, and what steps you propose to take in order to bring about these benefits. (And of course you are allowed to claim for money to support such steps.)
Needless to say, very little pure mathematics research is likely to have such an impact, so this seems like another way of making research funding for pure mathematics harder to get. (Your proposal will be in competition with others which can demonstrate impact, and panels will take this into consideration.) My advice is, if there is little to say, then say little, don’t pad it out with unjustifiable statements. (No lower limit on the length of the statement is prescribed.)
However, there are a couple of things that can be said.
The first two are generic. First, pure mathematics has demonstrable effects on the economy, which cannot be foreseen. Examples include the use of linear algebra in the Google page rank algorithm, and the use of number theory in cryptography. The problem is that EPSRC expect impact within fifty years, which may be too short for most pure maths research.
Second, contributing to a thriving research community in pure mathematics will attract overseas researchers and students to the UK, to conferences, as longer-term academic visitors, or as postgraduate students or postdoctoral researchers, and these have a direct positive effect on the economy.
On to more specific items. In these cases, there is expertise within the School; consult your colleagues or the Research Directors on how to ensure that your research reaches potential beneficiaries.
If your research has the potential to generate algorithms which could be incorporated into computer algebra systems such as GAP and MAGMA, say so. These programs are used outside the academic world.
Some pure mathematics research is relevant to statistics (e.g. design of experiments) or to information and communication theory. Mention this if it applies to you.
If you are already collaborating with users of your research, then ask them what would be helpful to them, and claim for the time and person power to implement your suggestions.
In time we hope to build up a stock of examples of impact statements from successful proposals.