R&D relief for pure maths

UK R&D reliefs are government funding designed to promote the generation of new knowledge amongst competent professionals that is gained by undertaking innovative projects associated with science and technology. However, this technological and scientific focus has meant that projects seeking advancements in theoretical fields, such as pure mathematics, were not historically eligible R&D activities.

However, since 1 April 2023, R&D tax relief has been reformed to include pure maths as an eligible activity.

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Pure or applied maths?

Advancements related to applied maths could already qualify for an R&D tax relief claim, but where the project strayed into pure maths there was uncertainty and disputes over claims. Pure maths was not defined within tax legislation, but it is generally acknowledged to be the study of mathematical concepts that do not have any application outside of mathematics, effectively differentiating it from applied maths.

This lack of clarity over how ‘pure maths’ is defined and interpreted by HMRC led to increased risks when claiming R&D tax relief on projects and sub-projects whose innovation was largely mathematical, even where the intended output would have an industrial application, such as those related to finance, shipping, and automotive insurance.

Guidance has been published by HMRC, see here, which explicitly states that from April 2023 mathematical advances in themselves are treated as science for the purposes of R&D, whether or not they are advances in representing the nature and behaviour of the physical and material universe.

Finance – Algorithmic trading and financial engineering

With algorithmic trading systems being used more and more widely when trading equity and alternative assets, it comes as no surprise that companies are investing large amounts of money to further improve the performance of their algorithmic systems.

The current R&D rules focus on activities that seek some form of a physical advancement (i.e. reduced computational energy consumed to carry out the calculation). If the new rules also enable financial KPIs to be deemed a metric of an eligible advancement (such as alphas generated, trading signal accuracy, maintaining accuracy even when reducing the number of data variable inputs, etc.), we expect to see an increase in claims from hedge funds, investment banks and pension funds.

Shipping Insurance

As insurance costs are one of the largest operational expenses in shipping, great efforts have been made to find better ways to underwrite, spread and pool the respective risk for insurers. However, such research activities require complex risk management and risk modelling exercises which, previously could not be included in an R&D tax relief claim. This was because such activities were considered to be an advance in social science, not necessarily contributing to the generation of new scientific or technological knowledge. 

The inclusion of pure maths as an eligible activity has led to the re-classification of seeking actuarial science advances as eligible activity, resulting in an increase in R&D tax relief claims from shipping insurance companies.

Automotive insurance

Automotive insurance companies use telematic data from black box systems to better understand and capture how specific driving characteristics and trends correlate to driving accidents and, by extension, repair and damage costs. This is achieved by leveraging complex data models and statistical inference techniques, which are in turn utilised to better estimate the insurance cost and thereby insurance premiums.

These innovations have historically been based on data modelling and statistics, and did not warrant the development of new hardware software systems, so the cost of such activities were not claimed in an R&D tax relief claim. 

The definition of pure maths within the new legislation permits improved modelling accuracy as a form of advancement in its own right, even without the need to appreciably enhance the technology itself (for example, the python libraries carrying out these analytics). This has resulted in an increase in R&D claims from the automotive insurance industry.