Successive Governments have emphasized the importance of innovation to economic growth. Conventional wisdom holds that Britain has excellent scientific research, but is poor at turning research output into commercial success stories. Only yesterday, the Prime Minster reiterated this familiar refrain in her speech at the CBI Annual Conference 1.

So how does the Government currently attempt to boost the UK’s investment in Research and Development? One key policy has been the availability since 2000 of R&D tax credits to UK companies, which help to reduce the cost of investing in research.

Unfortunately, the R&D tax credit system is no longer in step with the needs of the modern economy, in large part because of its inequitable treatment of mathematics.

To understand the problem, let’s go back to basics. The Government lays out the scope of the R&D tax credit as follows: 2

Your company can only claim for R&D tax relief if an R&D project seeks to achieve an advance in overall knowledge or capability in a field of science or technology through the resolution of scientific or technological uncertainty – and not simply an advance in its own state of knowledge or capability.

The keywords here are ‘advance’, ‘uncertainty’ and ‘science’, which are explained in an accompanying set of guidelines: 3

An advance in science or technology means an advance in an overall knowledge or capability in a field of science or technology (not a company’s own state of knowledge or capability alone).

Scientific or technological uncertainty exists when knowledge of whether something is scientifically possible or technologically feasible, or how to achieve it in practice, is not readily available or deducible by a competent professional working in the field.

Nothing too controversial there. The difficulty lies in how the policy interprets science:

Science is the systematic study of the nature and behaviour of the physical and material universe … Mathematical techniques are frequently used in science, but mathematical advances in and of themselves are not science unless they are advances in representing the nature and behaviour of the physical and material universe.

What was that? That’s right: “Mathematical advances …. are not science ….” Someone should tell all those world-leading academics who are labouring away in departments of Mathematical Science.

The current policy on R&D tax credits, with its emphasis on the ‘physical and material universe’ is fundamentally unsuited to the needs of a modern economy, in which the lines between services and products are being increasingly blurred by the world’s most successful companies.

As is so often the case, we can learn from the past. Newton’s work on the mathematics of gravity would have been eligible for a tax credit. James Clerk Maxwell’s work on the mathematics of electromagnetism would have been eligible for a tax credit. Paul Dirac’s formulation of the relativistic wave equation for spin-1/2 particles in quantum mechanics would have been eligible for a tax credit.

On the other hand, A.K.Erlang’s ground-breaking mathematical work on the operation of telephone exchanges, carried out in the years around 1920, would not have been eligible, because it was not concerned with the ‘physical and material universe’. Ironically, of the people I’ve mentioned above, Erlang is also the only one who was working in a commercial setting, for the Copenhagen Telephone Company. His work directly underpinned the growth of the telecommunications industry throughout most of the 20th century. A more recent example is the mathematics that was embedded in Google’s search algorithms in the late 1990s – this unleashed phenomenal economic value but would also not have been eligible for a tax credit.

Companies are being sent a message through the tax system that mathematics is not worthy of investment. Is it any wonder that for the most part they give no thought to collaborating with the mathematics departments in our leading universities? The signal should be in completely the opposite direction. In her CBI speech, Mrs May highlighted Britain’s strengths in robotics, artificial intelligence and quantum computing – all areas underpinned by mathematics, and all areas where mathematical research would not be supported by the current policy on tax credits.

Fortunately, the Prime Minister’s speech also displayed a willingness to consider change:

Since 2010 we have made the Research and Development Credit more generous and easier to use – and support has risen from £1 billion to almost £2.5 billion a year.

Now we want to go further, and look at how we can make our support even more effective – because my aim is not simply for the UK to have the lowest corporate tax rate in the G20, but also a tax system that is profoundly pro-innovation.

As I hope is now clear, there is one way in which the system could easily be changed to be more pro-innovation. Put an end to the philosophical contortions over what is science and what is not. Put an end to inequitable treatment of some research areas over others. Recognise that companies choose to carry out R&D in whatever area because they see its commercial potential. It would be a simple matter to remove the current restrictions on mathematics, and in doing so to send a positive signal to business that harnessing mathematics is crucial to the success of the Government’s economic ambitions.