**Introduction**: Much of the research that is being funded nowadays is multidisciplinary. It is sometimes called interdisciplinary, but that is a misnomer. A multidisciplinary project is one that needs at least two different types of expertise, but it usually falls within a particular discipline. As an example, one might consider a collaboration between a geologist and a numerical analyst to study a problem in sedimentation. Another example would be a collaboration between a molecular biologist and an epidemiologist, to investigate the mechanism and population prevalence of a particular congenital defect.

Interdisciplinary work is one that does not fall in a domain of any well-defined discipline. For example, much philosophy nowadays is really interdisciplinary, encroaching on psychology, history, rhetoric and so on. If it is obvious who is the Principal Investigator on a grant, the project is not an interdisciplinary, but possibly a multidisciplinary one. We would like to discuss the advantages and disadvantages for mathematicians of getting involved in such projects.

**MG**: Let me first of all say that I myself have benefited from the funding of such projects, having been a postdoc at the University of Bath on a project that involved computer scientists and biologists. I understand the reasoning of research councils in funding multidisciplinary projects: it is largely a safe bet that something will come out of it, as to apply for such a grant, one more or less promises the results upfront. Such activity is characteristic of “normal” science in the sense of Kuhn. I cannot imagine a multidisciplinary project leading to a Nobel prize.

So let us consider such a project from a point of view of a mathematician. I am not doubting that her contribution to the project will be valuable: she will be able to analyse data, streamline other participants’ thinking via a model, get the numerics done, etc. She will also be able to learn something of their discipline.

The problem is that multidisciplinary work requires her to be an expert, not a researcher. It will not make her curious about mathematics, will not make her a better mathematician, will not make her learn new mathematics. In fact, it is even worse. She brings to the project, just like everybody else, her expertise in an area (mathematics). But since she does not know everything in her area, what she already knows defines what she brings to bear on the research problem. So questions of optimality of a particular mathematical approach cannot arise during the life-time of the project. So mathematics that gets done during such a project is by and large mediocre; good mathematics cannot be done to order or to a deadline.

This reliance on fixed expertise makes one stale as a mathematician. The toolkit one needs is a very limited one: ODEs, PDEs (and how much of that?), some usually out-of-the-box but never revolutionary (what for?) numerics, dimensional analysis, asymptotics, continuum mechanics, graph theory, linear algebra. More than that, much of what passes for mathematical modelling is not mathematical at all as no mathematical questions are being asked. Everyone can use mass action kinetics to set up differential equations and then have MATLAB take over (for that reason I see that the term “mathematical models” is being phased out in favour of “computational models”). Growing stale in mathematics, unlike in the experimental sciences, is, from my observations, irreversible.

My feeling is that one only learns new mathematics by working either alone or with other mathematicians on mathematical topics which can find their inspiration in the natural sciences; see below.

Also, multidisciplinarity means working outside of the department. So much of one’s intellectual activity is not directed inward, which is a move towards people in the department functioning as monads with no common interests. I cannot see how this can be good for social or intellectual cohesion of a department.

A final remark. I am not indicting applied mathematics as such. There is, for example, a vast difference between mathematics as done in multidisciplinary projects on biological problems and mathematics done by mathematicians inspired by biology. The latter can be exploratory, visionary and hard; the former can be useful for the project, but has negligible mathematical content. One could say that being useful for an important project is quite enough, but then I wonder why no-one ever encourages biologists to do work with negligible biological content, or who should be doing substantive mathematical work.

**NJM**: … a few comments in response to your points.

Firstly I should say that I have worked on projects which could be classed as unidisciplinary, multidisciplinary and interdisciplinary. It’s hard to judge between these projects in terms of their worth and the science that has derived from them but in purely personal terms I have enjoyed the interdisciplinary projects more than the others.

But back to your discussion of multidisciplinarity…

Much of what you say is true if your sole intention is to research and discover new mathematics. Obviously this is a perfectly fine intention but need it be the only intention of an academic?

Yes we are in a Department of Mathematics (and Statistics), but should that define our personal or group work so strictly? I’d prefer the older model of being a member of the academy who works towards new knowledge and happens to have started his training in one area (Mathematics) but has branched into other areas as well.

I know that external factors tend to force us into disciplines — in fact all of the external forces I can think of at the moment are financially driven — but should we let them restrict us?

Of course work in a pure discipline is fine… more than fine, it’s essential… but as someone who works in the fuzzy grey areas around mathematics and physics I hope that is not the only worthwhile endeavour.

I have never discovered new mathematics or even new physics but I have contributed to new understanding — through a mathematical description of a physical system we have been able to explain and predict.

Maybe this research isn’t going to win a prize but that doesn’t mean that it isn’t worthwhile. Thinking of an example off the top of my head… how about recent work trying to understand the fossil record (I listened to a very good radio program on the Cambrian explosion this morning). While paleontologists had a hard time understanding how the fauna of the Precambrian and Cambrian times had evolved into modern day species, it is through working with molecular biologists that they have now been able to fit these fossils into the modern framework.

A few specific responses to your points:

It will not make her curious about mathematics, will not make her a better mathematician, will not make her learn new mathematics.

I agree… and if those things are your only goals then you should probably not do inter/multidisciplinary work.

One only learns new mathematics by working either alone or with other mathematicians on mathematical topics which can find their inspiration in the natural sciences.

You’re probably correct there too.

Since she does not know everything in her area, what she already knows defines what she brings to bear on the research problem.

Also very true, but true of everyone in the “team”. Hopefully if some aspect of mathematics is needed which is outside your area then you might know of other people who may help. Just after moving to Strathclyde I started a project with HP which proved relatively successful. HP have since come to me with other interesting problems, but which I could not help with because I wasn’t an expert in the area. I passed the problems on to others and since then HP have been involved in three other projects in the Department; hopefully these have been or will be successes as well.

Much of what passes for mathematical modelling is not mathematical at all as no mathematical questions are being asked.

That depends on your definition of “mathematical”, I suppose. The models which emerge from the systems I look at are best expressed in terms of PDEs; the analysis of them often (always) needs some form of simplification; but even the grossest simplification needs some of the methods I have learnt over the years. I have never invented new methods but I have used existing methods to tackle problems which have never been understood and in using these methods we have gained insight.

Multidisciplinarity means working outside of the department. So much of one’s intellectual activity is not directed inward, which is a move towards people in the department functioning as monads.

Again very true… unless you define yourself as part of academe rather than the Department. However, during my 11 years at Strathclyde I have managed to publish with members of every one of the old Maths Dept research groups so it hasn’t turned me into a monad.

Of course, this whole debate is not particularly new but may have been coming to a head in recent years. I have a few basic questions that I think need asking before we understand the worth of multidisciplinary research…

1. Has the compartmentalisation of research/knowledge over the last 100–150 years overly constrained academia so that there are large gaps between disciplines?

2. Is research which needs understanding of many different disciplines now possible without a team of researchers?

3. Is bringing together people from different disciplines the best way to do it? Or is taking a single person who knows much about many different disciplines and who works alone a better approach?

4. Alternatively, should we be trying to educate students to have interests in a wide range of disciplines?

5. And the inevitable question… How should such research be judged and funded and how should we organise these researchers into groups to make administration possible?

On that last point, I like to be in a Department of Mathematics and Statistics because I believe conversations with my colleagues here are the most important ones I have. If I’m based in a physics or engineering department (I’ve been in both in my career) then I tend to break things and the experimentalists get annoyed, and if I was based in a special multidisciplinary department then I suspect I would spend a lot of time walking back to the Maths Department to talk to people… although my experience is that the coffee and biscuits are always better in a multidisciplinary department.

(MG/NJM)