Patenting mathematics-based inventions: Navigating sufficiency and the inventive step squeeze

Mathematical methods play a central role in many modern technologies, from machine learning models used in artificial intelligence systems to cryptographic security in blockchain technologies and physics engines in modern gaming.

We have previously explored the general question of whether mathematics can be patented in Europe and the UK (see “Can you patent mathematics?”). In this article, we focus on the drafting pitfalls that often arise in practice, particularly sufficiency and inventive step.

While mathematical methods as such are excluded from patentability under both the European Patent Convention (EPC) and UK law, patents are routinely granted where mathematical steps contribute to a technical solution to a technical problem. Historically, this has resulted in European patents being granted in fields such as cryptography and signal processing, among many others. 

In practice, however, mathematics-based inventions frequently encounter difficulty not only with patentability itself, but also with sufficiency of disclosure.

Sufficiency and the skilled person #

The “sufficiency of disclosure” requirement under Article 83 EPC means that an invention must be disclosed so clearly and completely that the skilled person can carry it out without undue burden, a standard established by case law. For inventions with a significant mathematical component, the key question becomes: what level of mathematical knowledge should the skilled person be expected to have?

The “skilled person” is a practitioner with the common general knowledge of the relevant technical field. For multidisciplinary inventions that combine expertise from more than one area of technology, the skilled person may be viewed as a team of specialists. Crucially, this team is not assumed to have any inventive skill. It is simply a combination of standard practitioners from different technical fields, not a group of experts with extraordinary abilities.

A sufficiency problem often arises when an application describes what a mathematical method achieves but not how to implement it, assuming the skilled person can work out the details. This can be a problem, especially where the derivation of a mathematical model or technique has multiple steps which require, for instance, a selection of functions or parameters and the reason for the selection is not provided. Problems may also occur where there are particular assumptions about the behaviour of a variable which are not clearly stated.  

This failure to provide a complete disclosure can be fatal under Article 83 EPC.

The inventive step squeeze #

This creates a dilemma known as the “inventive step squeeze”, where the arguments for sufficiency and inventive step pull in opposite directions and can result in problems either way.

On the one hand, if the skilled person is assumed to have a high level of mathematical knowledge, the patent application can be less detailed, as it can be assumed the skilled person can fill in missing details from their common general knowledge. However, this assumption can also make the invention appear obvious, since such a skilled person would be expected to readily apply the relevant mathematical principles without inventive skill.

On the other hand, if the skilled person is assumed to be a technical practitioner with only a standard level of mathematical knowledge, which may require explanation of the underpinnings of a mathematical method, the invention is more likely to be regarded as inventive. The consequence is that the patent application must then provide a much more detailed explanation of the mathematical method, as failure to enable this non-specialist to carry out the invention will likely lead to a refusal for lack of sufficiency.

In other words, this squeeze can mean, depending on the level of detail provided in a patent, that an invention is either insufficient or obvious, and both can be fatal for the validity of a patent. 

Practical recommendations when patenting mathematical-based inventions #

The key to navigating this dilemma is a careful and thorough drafting strategy. It is strongly advisable to:

• Assume a standard level of mathematical knowledge. This helps support inventive step, while ensuring that the application contains enough detail to meet the requirement for sufficiency.
• Provide at least one concrete, step-by-step example. This is often the most effective way to demonstrate sufficiency. For broader claims, however, multiple examples may be required to show the invention is enabled across its full scope.
• Clearly explain the purpose of key equations and parameters, including what each variable controls and how it contributes to the final technical outcome.
• Explicitly connect each key mathematical feature to the specific technical advantage it provides, explaining how it contributes to solving the overall technical problem.

Adopting this strategy from the outset helps to navigate the inventive step squeeze, supporting a robust case for sufficiency while also strengthening the argument for inventive step.

Concluding remarks #

Securing a patent for a mathematics-based invention requires careful balance. In particular, it is important to avoid the inventive step squeeze by defining the skilled person appropriately from the outset. 

Thoughtful consideration of the skilled person’s assumed knowledge is not merely a drafting formality but is central to demonstrating both sufficiency and inventive step, and ultimately to obtaining a patent that is both valuable and enforceable.

Murgitroyd’s mathematics team of patent attorneys has extensive experience helping companies tackle complex drafting challenges, including those discussed in this article. If your invention involves mathematical methods, we can guide you through the drafting process. Get in touch today to speak with a member of the Murgitroyd team.

Thank you to IP Stars for originally publishing this article.