A white Mobius Strip on an orange background

Finding R&D eligibility in pure mathematics

Share this article

Since its inception in 2000, the R&D tax relief scheme has excluded any R&D done in the area of pure mathematics, preventing companies from claiming the costs of these projects. However, this has now changed, and for claim periods starting on or after 1st April 2023 work seeking to make an advance in pure mathematics can be included. 

What is pure mathematics?

Pure mathematics is the study of mathematical concepts with no application outside of the world of mathematics, and tends to focus on more abstract theories not directly related to anything in the real world. Applied mathematics, on the other hand, is the application of mathematics to real world scenarios, often involving the use of mathematical models, for example in engineering or insurance. 

Why has HMRC made this change?

In reality, the distinction between pure and applied mathematics is fuzzy at best, and at worst is a philosophical point debated between mathematicians. Despite this, when the legislation and guidance for R&D tax relief was first drawn up, pure mathematics was excluded, with the guidance stating ‘…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.’

While this exclusion did not affect many companies, for those that were carrying out research into mathematics it caused major headaches. The difficulties centred around working out which projects could be seen as applied mathematics and be included in the claim, and those that HMRC would see as pure mathematics and exclude for the claim. Without strict definitions, this has led to extended enquiries and debates between HMRC and claimant companies, and has been seen as unnecessary and unfair by many people in the R&D tax relief sector. 

How will this affect my clients?

For the vast majority of claimant companies, this will make no difference to their claims – there aren’t many companies out there seeking to make advances in the area of mathematics, but for those that do this removes the need to exclude projects that HMRC would class as pure mathematics. The types of companies that will benefit from this are fairly wide-ranging, from software companies, especially those working in the areas of cybersecurity and crypto currencies, through to insurance companies and engineering firms. 

What do I need to look for in terms of eligibility?

The good news is that this change will make it easier for advisors to assess eligibility of clients carrying out mathematics research. For claims from 1st April 2023, all you will need to do is determine that they are seeking to make an advance in mathematics and that other eligibility criteria have been met, and you’ll be able to make a claim. No more having to take the extra step of trying to establish whether it is applied or pure maths—all is eligible!

How to write an R&D tax relief technical narrative

With HMRC’s new mandatory requirement for project descriptions on all submissions, we wanted to share our experiences to help others to write their best possible technical narratives.

Available to download here.

Related Articles