Mathematics has been deeply involved in design since it was used to plan the pyramids of the Old Kingdom of Egypt. Chris Ormell FRSA charts changes in the relationship between the two disciplines and argues for a radical shift in maths teaching that recognises its critical role in design, innovation, science and technology.

Mathematics was used to design the tomb of Mausolos, the Lighthouse at Alexandria, the Corinth Canal, the ampitheatres in hundreds of Roman cities and much else.

The Greeks knew that monuments designed with mathematics had an aura, a panache that could only be achieved in this way. Getting an underlying geometrical structure with symmetry and optimisation had this effect. The geometry was, essentially, the next, natural step in abstraction after line drawing. But the great value of mathematics as a practical art stemmed from its extension of the designer’s *imagination*. The designer could experiment with the geometry of different designs and see, with precision, what the effect would be. It was a capital discipline for trying-out design ideas. So, mathematics, which had begun much earlier as a simple tool kit of marks needed by shepherds and merchants to keep tabs on their stocks, began to acquire a superior image. Gradually some of the mystique associated with the great monuments rubbed off onto the profession of mathematician.

Perhaps inevitably, this came with a downside. Mathematics began to be valued for its own sake. The priceless mathematics-imagination meld which had created the mystique of the subject was soon forgotten.

So, as the professionals began to believe in their new-found mystique, they tended to treat mathematics less and less as a design aid, and more as an end in itself. In this way clever, neat, pure mathematics turned into a kind of intellectual jewellery: elegant, precise, abstract, high-level, and immensely special. Any awareness that mathematics had made its ascent of Mt Parnassus via its use in design virtually disappeared. Much mathematics continued to be used as a design aid, but those who fielded it in this way were often treated as mere mechanics, far below the aesthetic and intellectual level of the pure masters.

Mathematics was worshipped for its timelessness, its elegance and the exceedingly high levels of logical ability needed to understand it.

The rest is history. The leaders of the mathematics community eventually became High Priests. By the 20^{th} century higher mathematics - the most abstract form of human knowledge - became a quasi religion; around 1900 this acquired the added burden of trying to provide the hyper-abstract concepts needed in physics. A dash for abstraction followed. Soon the subject had soared into the stratosphere where any connection with design (or indeed ordinary physical reality) was well and truly lost. (Incidentally few of the millions of hyper-abstract concepts created by mathematicians after 1945 ever helped in physics.)

In the 1960s the high priests of mathematics tried to impose their stratospheric view of pure mathematics onto the ordinary school curriculum. An amazing, revolutionary, idealistic bandwagon began to roll. At first it glowed brightly with the white heat of zeitgeist, modernity, involvement and acclaim. But this soon cooled. Pupils, teachers, parents, employers rumbled that it was all in aid of… *art for art’s sake*! By 1972 professional mathematicians in universities had also realised that many students coming up from schools lacked the solid grounding of yesteryear. They could talk some of the talk, but not mathematically walk the walk.

A counter-revolution in favour of so-called ‘practical maths for schools’ followed Shirley Williams’ Great Debate and the Cockcroft Report of 1982. This was welcomed with open arms after the excesses of hyper-abstraction. But it was too dull, too technical and too mundane to last for long in schools. Soon schools reverted to an uninspiring mish-mash of traditional, abstract modern and ‘practical’ maths: a mish-mash which remains the status quo today.

Going back to ‘practical maths’ was an understandable, if insensitive, over-reaction. In terms of values it was a forlorn attempt to revert to the mundane purposes of the shepherds and merchants of the pre-ancient world. What should have happened was a return to maths melded with imagination, a style of maths acclimatised to conceiving, planning and designing projects. Unfortunately hardly anyone realised that mathematics had originally evolved by this route.

There is still room for a revolution in school mathematics, which would switch the thrust of the subject *from* a mixture of art-for-art’s-sake and mundane practicality *to *the vital numerate/visual foresight aid needed in design, innovation, science and technology across the board. What is needed is a complete paradigm shift. But it will only come about when enough people realise that the quality of the current status quo is - as Eric Schmidt said in his McTaggart lecture (27 August 2011) - not good enough.

The author studied maths and philosophy at Oxford University and later ran a project called Mathematics Applicable at Reading University, which experimented successfully for ten years with teaching maths as a design and foresight aid to sixthformers. He is editor of Prospero.

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Well, people are saying the same things about physics, after all quantum chromodynamics is not something that you can easily explain to someone after you have explained to him how to play with moment of inertia in a rotating chair. We can cry how good it was in a idyllic past time when men learned about anatomy, arts, astronomy, mathematics, engineering, languages, law and even architecture in the same place, but unfortunately for some these times are no more, we live in the present and by now you can even spend an entire life studying the applications of epigentical epidemiology to agriculture (I actually know of someone doing this) without even resorting to geometry. I don't think this problem has a optimal solution for everyone after all.

Chris, I welcome some of the ideas you suggest but I think your love of mathematics has coloured your views.. or at least obscured them a little. All buildings are built with mathematics... engineering is essentially applied mathematics. What you touched on in the beginning ... the single reference to 'symmetry' is where you should have placed your emphasis. Its the absence of 'natural numbers' in our designs that makes them look cumbersome. The Greeks used the golden section, phi, as the basis for all proportions, especially in their temples, the use also of symmetry, of the number 6, the hexagram and other similar natural numbers and elements of nature is what gave them the aesthetic beauty we see.

It would also be appropriate to acknowledge that the emphasis in building design today is in its economics rather than its artistry... and this is the cause of design failures.