6.3.2 Mathematical methods

Purely abstract or intellectual methods are not patentable. The exclusion applies if a claim is directed to a purely abstract mathematical method and the claim does not require any technical means. If a claim is directed either to a method involving the use of technical means (e.g. a computer) or to a device, its subject-matter has a technical character as a whole and is thus not excluded from patentability under Art. 52(2) EPC and Art. 52 (3) EPC.

Merely specifying the technical nature of the data or parameters of the mathematical method may not be sufficient to define an invention in the sense of Art. 52(1) EPC, as the resulting method may still fall under the excluded category of methods for performing mental acts as such (Art. 52(2)(c) EPC and Art. 52 (3) EPC, see Guidelines G‑II, 3.3 and G‑II, 3.5.1 – March 2024 version).

Even if the idea underlying an invention may be considered to reside in a mathematical method a claim directed to a technical process in which the method is used does not seek protection for the mathematical method "as such" (T 208/84, OJ 1987, 14; G 2/88, OJ 1990, 93).

The case law of the boards of appeal has established that, if a method which is not per se "technical" e.g. a mathematical method, is used in a technical process, and this process is carried out on a physical entity by some technical means implementing the method and provides as its result a change in that entity, it contributes to the technical character of the invention as a whole (T 208/84, OJ 1987, 14; T 641/00; T 258/03; T 1814/07, OJ 2003, 352).

In T 1784/06 (point 3.1.1 of the Reasons) the board stated that the algorithm is a mathematical (inter alia Boolean) method and, as such, has technical character only if it served a technical purpose (see e.g. T 1227/05, point 3.1 of the Reasons, OJ 2007, 574; see also T 306/10). In T 1326/06 it was held that a method of encrypting/decrypting or signing electronic communications may be regarded as a technical method, even if it is essentially based on a mathematical method.

In T 208/84 (OJ 1987, 14) the board stated that a basic difference between a mathematical method and a technical process can be seen in the fact that a mathematical method or a mathematical algorithm is carried out on numbers (whatever these numbers may represent) and also provides a result also in numerical form, the mathematical method or algorithm being only an abstract concept prescribing how to operate on the numbers. No direct technical result is produced by the method as such. In contrast, if a mathematical method is used in a technical process, that process is carried out on a physical entity (which may be a material object but equally an image stored as an electric signal) by some technical means implementing the method and provides as its result a certain change in that entity. The technical means might include a computer comprising suitable hardware or an appropriately programmed general purpose computer. The board was, therefore, of the opinion that, even if the idea underlying an invention may be considered to reside in a mathematical method, a claim directed to a technical process in which the method is used does not seek protection for the mathematical method as such. In contrast, a "method for digitally filtering data" remains an abstract notion not distinguished from a mathematical method as long as it is not specified what physical entity was represented by the data and it forms the subject of a technical process, i.e. a process which is susceptible of industrial application (see also T 1161/04 and T 212/94).

In T 953/94 the board stated that an analysis of the cyclical behaviour of a curve was clearly a mathematical method excluded as such from patentability. The reference to a digital computer only had the effect of indicating that the claimed method was carried out with the aid of a computer, i.e. a programmable general-purpose computer, functioning under the control of a program excluded as such from patentability. The fact that the description disclosed examples in both non-technical and technical fields was confirmation that the problem solved by the claimed mathematical method was independent of any field of application and could thus lie, in the case at issue, only in the mathematical and not in a technical field.

In T 1326/06 the board took the view that processes for encoding/decoding or signing electronic communications by RSA had to be regarded as technical processes, even if they were based essentially on mathematical processes (see also T 953/04, point 3.3 of the Reasons and T 27/97, point 3 of the Reasons).

In T 556/14 the invention related to a method for masking a private key used in cryptographic operations on a security token such as a smartcard against power analysis attacks. The board held that due to the express reference to a smart card on which the key parts and also the new parts are stored, the claimed method of masking was not a mathematical method as such.