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.


About Peter Cameron

I count all the things that need to be counted.
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11 Responses to Impact

  1. What appears to be missing from the increasingly intensive discussion is that the REF proposal provides not just justification for suppressing independent academic research, it offers a mechanism for its implementation, too. The latter is described in a few innocuous lines about the aims of the exercise:

    “We will be able to use the REF to encourage desirable behaviours at three levels:

    [ , page 8]

    The emphasis on inducing change in the behaviour of “individual researchers” is the result of a slow evolution of the RAE/REF. In 1996 and in 2001, the RAE went to great lengths to ensure that individual researchers could not be identified in the panels’ responses. This changed in 2008, when the percentages of the submission with each number of stars were published. So it was possible, in the case of a small unit, to work out exactly how many papers were internationally excellent, etc., and make a fairly good guess which papers they were.

    The passage in the REF proposal concerned with “individual researchers” is much more worrying, especially since this time “the overall excellence profile will combine three sub-profiles – one for each of output quality, impact and environment – which will also be published.”

    If “behaviour” just meant “doing good/bad/no research”, it would not be so terrible, but since extraneous things like “impact” now loom large, HoDs will be able to use this to warn staff off doing their preferred research and onto more “impactful” projects. There is a danger that, at department level, the REF might be translated into unheard of levels of bullying and harassment.

    • I’m grateful to Sasha for pointing this out to me.
      In the new world we face, it may no longer be possible for pure mathematicians to say, “I don’t need a research grant to do my work; I can afford pencil and paper”, for many reasons. This will add another one: pressure from our bosses to work on “impactful” research.
      At the London Mathematical Society AGM this Friday, Ken Brown will give us his thoughts about the REF. I will report on anything that strikes me from his discussion.

    • The Problem Corner of the European Mathematical Society newsletter reprinted from the Mathematical Intelligencer a statement by Sir Michael Atiyah about how he chooses what problems to work on:

      “I just move around in the mathematical waters, thinking about things, being curious, interested, talking to people, stirring up ideas; things emerge and I follow them up. Or I see something which connects up with someting else I know aboout, and I try to put them together and things develop. I have practically never started off with any idea of what I’m going to be doing or where it’s going to go.”

      How fortunate for Sir Michael that he never had to write an impact statement! Yet I surely don’t need to demonstrate the enormous impact his work has had, from the Index Theorem to the work on instantons.

  2. At the LMS AGM, Ken Brown spoke about the HEFCE consultation document on the REF, and the response to it being produced by the Council for the Mathematical Sciences. I will simply report his comments on impact here.

    The situation is worse than I thought. It will work like this. Impact can be claimed on work done in the unit of assessment (that is, the department) concerned within the last 15 years. It is not clear to me whether the person who did the work is required to be still in the department (or even living). But it can only be claimed if the “commercialisationn” which led to the social or economic impact was also done within the department. So, if a member of your department invented a data compression algorithm which was developed by the engineering department at your university, then sorry, you have had no impact.

    I am reminded of the comment of Paul Erdős about the difficulty of finding the Ramsey numbers R(5) and R(6) (see an account here). He said that, if aliens landed on Earth and threatened to destroy the planet if we didn’t tell them the value of R(5), then we should put all the mathematicians and computers on the planet to work on it, and we might succeed. But if they asked us for R(6), our only hope would be to kill them before they kill us; we have no hope of answering their question.

    Similarly, I think that if we put a lot of time and effort in it, we can probably work with the RCUK definition of impact; but with HEFCE, the only hope is to kill them before they kill off mathematics research.

  3. I just Googled “nonassociative ultradistributions” – it seems that this might actually be a real subject; I hope my comments haven’t insulted anybody! The phrase stuck in my mind from an article (advice to young mathematicians about publishing) by Bernhard Neumann in the 1960s or 1970s. He clearly used it in the sense I intended to, that is, a plausible-sounding but nonexistent subject. I still stand by what I wrote.

  4. I have received a comment of the report on Impact by the group Educators for Reform. I have put it on the web here. Please take a look.
    Also, time is running out to sign the UCU petition. Please sign this if you haven’t done so already.

  5. Peter Cameron says:

    Nik Ruskuc told me yesterday that the fifty-page HEFCE consultation document contains the word “impact” no less than 234 times (averaging nearly five occurrences per page).
    You can draw a number of conclusions from this, none of them flattering.

  6. Pingback: You choose … « Peter Cameron's Blog

  7. Pingback: A year’s work (lessons learnt) « Yet another blogging mathematician…

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