Sum of success

The wellbeing of our economy, and our society, depends in large measures on the competitiveness of UK industry. Increasing competitiveness depends on increasing the rate at which we innovate. And that depends on mathematics. It is true for all companies, in all sectors. And it has always been true.

As an electrical engineer one of my great heroes is Michael Faraday, one of the greatest experimental scientists ever, who, on 29 August 1831, discovered the means by which we now generate electricity continuously.

Without that discovery, I wouldn't have a profession. And without another that he made 14 years later, I wouldn't have a job and none of us would have radios, televisions or mobile phones. The discovery was particularly revealing about the role maths plays in innovation.

In 1845, Faraday performed a decisive experiment to show that electricity and magnetism are related to light. He suggested the nature of that relationship is that all forms of electromagnetic energy travel in waves. He described his idea in plain English — he had no choice as he was no mathematician. Indeed, he admitted he had only once performed a mathematical operation — when he turned the handle of Babbage's calculating machine.

Faraday knew that, ultimately, the further development of his idea about the relationship between electricity, magnetism and light would depend on being able to describe that relationship mathematically.

A few years later, James Clerk Maxwell did just that. In 56 pages of closely-written equations he confirmed that electricity, magnetism and light take the form of waves. He predicted that electromagnetic waves travel through space at the speed of light. Best of all, he set out his conclusions in language which, 150 years later, is just as understandable by scientists, engineers and mathematicians.

Mathematics is a language that transcends national boundaries, cultures, ages, scientific fields, industrial sectors — and time. If we were to design a language specifically to harness the innovative diversity in our society, it is unlikely we could improve on maths.

Faraday and Maxwell — the experimental scientist and the mathematician. Which of them should I and two and a half billion other people around the world thank for beginning the innovative trail that gave us our mobile phones? Both of them, in equal measure. They would have thought that right, because they knew it is hard to innovate alone.

When Faraday read Maxwell's work, he wrote: 'I was at first frightened to see such mathematical force made to bear upon the subject, and then wondered to see that the subject stood it so well.'

The tonality of an innovative partnership — collaboration not competition — is so important. And Faraday and Maxwell set the standard for us all. Rigour, communication and collaboration — all are accelerants of innovation. And all are aided by maths.

But there is a fourth accelerant, which is uniquely a property of maths. The ability for scientists, engineers and technologists — all of us — to work at higher levels of abstraction.

Engineers have always worked in the abstract, of course. How else could any of the pioneers of my profession, from Faraday onwards, have completed so many projects in one working lifetime? Today's engineers would never complete anything if they had to master every detail. To come to terms with the increasing richness of engineering, we must work at a level of abstraction.

The development of software engineering depended on recognising that truth. In 1975, Fred Brooks, a Fellow of the Royal Academy of Engineering, wrote: 'The programmer, like the poet, works only slightly removed from pure thought stuff. He builds his castles in the air, from air, creating by exertion of the imagination.'

That was more than a quarter of a century ago, when software engineers had workstations and hardware engineers had benches. But things have changed.

Now we all have workstations. And we are all building castles in the air, from air — with breathtaking speed. These 'castles' are mathematical models, of course. Then we use more maths to turn the models into tangible reality — into products — nearly as quickly.

Abstraction and cycle time are related. The higher is the level of abstraction, the shorter is the cycle time. And, since cycles present opportunities for us to learn, every cycle drives the level of abstraction a little higher and shortens the cycle time a little more.

If increasing abstraction and shortening cycle time are the keys to innovation, then mathematicians are the locksmiths. All of us depend on the competitiveness of UK industry. Competitiveness is a function of innovation. Innovation is a function of mathematics. QED.

Edited extracts of a speech given by

chairman Sir David Brown at a recent EPSRC-hosted event 'why maths matters'