Mathematical algorithms may contribute to the technical character of an invention only in so far as they serve a technical purpose (see e.g. T 1784/06, point 3.1.1 of the Reasons; T 1358/09, T 306/10, T 566/11, T 2035/11 and T 2249/13). In T 1784/06 the board stated that as the algorithm is a mathematical (inter alia Boolean) method and mathematical methods as such are deemed to be non-inventions (Art. 52(2) and Art. 52(3) EPC), a technical character of the algorithm could be recognised only if it served a technical purpose (see e.g. T 1227/05, OJ 2007, 574).

At issue in T 625/11, was a method to establish at least one threshold value of a parameter for operating a nuclear reactor with a view to making better use of the reactor's capacity. The board found that establishing a threshold value for the first operating parameter lent the claim a technical dimension going beyond the mere interaction of the numerical-simulation algorithm and the computer system, the established parameter having a purpose closely linked to operating a nuclear reactor, regardless of whether or not it was actually used for that. The board thus acknowledged that the approach taken in T 1227/05 (OJ 2007, 574) was appropriate.

In T 1358/09 claim 1 defined a method for classifying text documents essentially in terms of an abstract mathematical algorithm. The board noted that a mathematical algorithm contributes to the technical character of a computer-implemented method only in so far as it serves a technical purpose (see T 1784/06). In the case in point, the algorithm served the general purpose of classifying text documents. The classification of text documents was certainly useful, as it could help to locate text documents with a relevant cognitive content, but in the board's view it did not qualify as a technical purpose. Whether two text documents in respect of their textual content belong to the same "class" of documents was not a technical issue. The board noted that the same position was taken in decision T 1316/09, which held that methods of text classification per se did not produce a relevant technical effect or provide a technical solution to any technical problem. The board pointed out that not all efficiency aspects of an algorithm are by definition without relevance for the question of whether the algorithm provides a technical contribution. However, such technical considerations must go beyond merely finding a computer algorithm to carry out some procedure (see G 3/08 date: 2010-05-12, OJ 2011, 10; see also T 2418/12, T 22/12).

In T 2418/12 the board's stated, among other things, that the consideration that an intermediate result produced by an earlier algorithmic step may be re-used in a later step is an algorithmic rather than a technical consideration, as it does not require considerations about the internal functioning of a computer. This was in line with the case law of the boards of appeal, which generally holds that algorithmic efficiency is not a technical effect (cf. T 1784/06, T 42/10, T 1370/11).

In T 2035/11 the application mainly related to navigation systems that could be tailored to a user's particular wishes. The focus of the application was on the route-planning functionality of a navigation system. The board held that the subject-matter of claim 1 lacked an inventive step within the meaning of Art. 52(1) and Art. 56 EPC. Optimisation algorithms are mathematical methods, excluded "as such" from patentability under Art. 52(2) and (3) EPC. It noted that mathematical algorithms may contribute to the technical character of an invention only in so far as they serve a technical purpose (see e.g. decision T 1784/06). The purpose of the algorithm was the mere display of an optimal path to the user for cognitive processing. The user could act on the information, but did not need to. As stated in decision T 1670/07, a technical effect may arise from either the provision of data about a technical process, regardless of the presence of the user or its subsequent use, or from the provision of data (including data that on its own is excluded, e.g. produced by means of an algorithm) that is applied directly in a technical process. In the case at issue, the data was produced by means of an algorithm and was not applied directly in a technical process, so that neither possibility applied. The board's reasoning did not rely on a particular suggestion in the prior art, but on the finding that the proposed algorithmic change had no technical motivation and that its implementation was, uncontestedly, trivial. In so far as it was the appellant's view that technicality was irrelevant for the assessment of inventive step, this view was contrary to the established case law. The board noted that the German Federal Supreme Court had come to a similar conclusion in respect of a navigation system offering the user the possibility to exclude road segments based on a user-selectable property such as the road segment being a toll road (see BGH, 18 December 2012, X ZR 3/12, GRUR 2013, 275 – Routenplanung).

Methods of text classification per se did not produce a relevant technical effect or provide a technical solution to any technical problem (T 233/09, T 1316/09, and T 1358/09).