### On the design of Buildings in which to do Mathematics

As the School of Mathematics at Manchester moves in to our new purpose designed Alan Turing Building, I am moved to reflect on the requirements of a building in which to do mathematics.

I am reminded of a letter written by Charles Dodgson (a.k.a. Lewis Carroll), his tongue firmly in his cheek, enumerating the requirements for buildings for the school of mathematics. Dodgson starts with a basic observation

*it has occurred to me to suggest for your consideration how desirable roofed buildings are for*

carrying on mathematical calculations: in fact, the variable character of the weather in Oxford renders it highly inexpedient to attempt much occupation, of a sedentary nature, in the open air.

carrying on mathematical calculations: in fact, the variable character of the weather in Oxford renders it highly inexpedient to attempt much occupation, of a sedentary nature, in the open air.

how much more true this seems in Manchester (well that opinion might be revised given the recent floods in Oxford). He also anticipates the modern trend towards open-plan offices

*it is often impossible for students to carry on accurate mathematical calculations in close contiguity to one another, owing to their mutual conversation; consequently these processes require different rooms in which irrepressible conversationalists, who are found to occur in every branch of Society, might be carefully and permanently fixed.*

While this is true to some extent about calculations, our own experience is that mathematics is often a social activity performed in groups of two or three around a blackboard, or in, its absence, the back of an envelope or even a table napkin or beer mat.

He continues with many more comical suggestions. My favourites are

*A piece of open ground for keeping Roots and practising their extraction: it would be advisable to keep Square Roots by themselves, as their corners are apt to damage others.*and

*A narrow strip of ground, railed off and carefully levelled, for investigating the properties of Asymptotes, and testing practically whether Parallel Lines meet or not: for this purpose it should reach, to use the expressive language of Euclid, "ever so far"*.

When we were asked about three years ago to express our own ideas about the design of a new building for the School of Mathematics, formed recently by the merger of the Mathematics Departments at UMIST and the (Victoria) University of Manchester, we were considerably less flippant. We had clear ideas about what worked and what did not. During the 60s and seventies many universities build high rise buildings to save on the costs of land. Experimental sciences were often not accommodated in high rise buildings due to practical considerations. For example heavy machinery or protection from vibration. Mathematics departments had no such reason and were often put in to the high rise buildings. There is anecdotal evidence that to some extent we, as a community colluded with this. High rise buildings were very fashionable and the promise of a new building is very tempting and perhaps its failings hard to anticipate. I wonder if to some extent we act like parent: in a determination not to repeat theworst aspects of the way we were parented we create a different set of problems ourselves.

So what is wrong with high-rise buildings as places in which to do mathematics? Well it is not the height per-se. One has to understand to some degree the social nature of mathematical collaboration. Of course Dodgson is right that there is a necessity for quiet solitude. Mathematical work is often characterised by long periods of intense concentration during which interuptions are unwelcome. However often progress is made by a chance encounter with a colleague who gives one a lead from the benefit of their own expertise. Of course it is often the case in the 21st century that what we are working on is so specialised that the only conceivable collaborators are on the other side of the planet, and progress is made by emails and scribbled notes faxed to each other. But there is something about a chance encounter in the corridor that allows one to ask an expert a stupid question. Even if you have been worrying about it for months, not knowing quite how to put the question, one can at least pretend the question has just occurred to you. Some how committing a statement of your ignorance to paper or email is braver: physical evidence that you did not understand something perhaps you should have. So it seems to me, and to many of my colleagues that an important aspect of the design of buildings in which to do mathematics is that the public spaces, corridors, stair ways and halls, are pleasant enough places to linger a while and have a discussion. Preferably with black boards close at hand (the topic of mathematicians and their blackboards discussed in Sasha Borovik's blog, although mainly in the context of teaching. I am able to disclose that Sasha has a white board in his new office!). Those of us who had the privilege to work or study at the old Mathematics Institute at Warwick, will understand exactly what I mean. The Isaac Newton Instute and the wider cluster of buildings constituting the Centre for Mathematical Sciences at Cambridge is a great example of building with these principles in mind. Jonathan Glancey's article in the Guardian explains.

So our own building new building, the Alan Turing Building, takes account of some at least of these design criteria. Only three floors are devoted to mathematics, and the lower of these has a large public area in an atrium and teaching rooms not all exclusively for mathematics.

The second and third floors contain offices for academic staff, post docs, visitors and postgraduate students, as well as research seminar rooms and a large common room spanning a bridge across the atrium. The corridors are glass walled walkways facing the atrium. Hopefully one can not only encounter colleagues by chance (and the layout is designed to increase the chance) but one can also spot a colleague on another level on the other side of the building. While there are lifts most of the time it will be quicker to take the stairs. Interestingly the fourth floor, accommodating the Astronomy and Astrophysics group which is part of a different School, is designed quite differently. Their corridors are between offices and do not have a view over the atrium.

There were of course many things that were frustrating for the academics who had to deal with the Estates Department and architects (Sheppard and Robson). Misunderstandings and going back on what had been agreed. I think in time it would be really helpful if those involved wrote a helpful guide to other academics involved in the planning of a new building. However to a large extent the mathematicians moving in to the new building are optimistic, and only time will tell if we have swapped one set of problems from the high rise phase of architectural error to new ones in the age of the steel frame and atrium.

- Collingwood, Stuart Dodgson, 1870-1937, The Life and Letters of Lewis Carroll (Rev. C. L. Dodgson), Project Gutenberg (specific section on-line)
- Glancey, Jonathan, "form + function = faculty squared", The Guardian, Monday July 14, 2003 Guardian Unlimited.
- Picadilly Partnership, Description of main features of architecture and design including energy conservation measures. Accessed July 2007
- School of Mathematics web site

Labels: Alan Turing Building, Architecture, mathematics