Patenting mathematical methods

According to the section 3 (k) of the Indian Patent Act, mathematical and business methods, computer programmes per se or algorithms are categorized as non patentable subject matter.

Why are mathematical methods not patentable?

The Manual of Patent Office Practice and Procedure provides reason as to why mathematical or business methods are not considered patentable.

With reference to section 3 (k), the manual says, and I quote:

“Mathematical methods’ are considered to be acts of mental skill. A method of calculation, formulation of equations, finding square roots, cube roots and all other methods directly involving mathematical methods are therefore not patentable. With the development in computer technology, mathematical methods are used for writing algorithms and computer programs for different applications and the claimed invention is sometimes camouflaged as one relating to the technological development rather than the mathematical method itself. These methods, claimed in any form, are considered to be not patentable.”

The interpretation of this section has generated several debates and arguments over the years. This section can be analyzed in support of a case, which may provide a better interpretation of section 3 (k) and especially inventions dealing with mathematical methods.

Electronic Navigation Research Institute vs. Controller General of Patents

On July 5th, 2013, the Intellectual Property Appellate Board (IPAB) passed a decision denying a patent to Electronic Navigation Research Institute for their invention that relates to a method for calculating Chaos Theoretical Exponent value (CTEV).  The Deputy Controller in his decision had denied a patent to the applicant on the grounds of non patentable subject matter under Section 3 (k) of The Patent Act.

In light of this case, the controller and IPAB’s considerations, while deciding denial of patents for inventions that fall under section 3 (k), especially mathematical methods, are analyzed.

 The Deputy Controller held that the above invention was based on a mathematical method for solving mathematical equations and declined to accept the technical effect theory, as he was of the opinion that Indian Patent Act does not allow patents for mathematical methods, which have technical advancements. Hence the invention was rejected as non patentable under Section 3(k) of the Indian Patent Act.

The Appellant’s invention relates to a system for analyzing a time series signal by a method based on Chaos Theory and calculating a chaos theoretical exponent value (CTEV). The conventional chaos theoretical exponent value calculation systems presumed that it analyses a system of stable dynamic. Thus the temporarily changing dynamics cannot be calculated as a significant value. The inventors claim to have invented a system which makes it possible to calculate a CTEV that could not have been so far processed in a system of temporarily changing dynamics and to perform the process thereof at a high speed and on a real time basis, and to calculate a CTEV even from a time series signal which includes noises. The complete specifications also describes that the invention calculates the average CTEV in a shorter time of two decimal orders or more.

Controller’s Decision

The Patent Office issued the First Examination Report (FER) on 11th June 2007 with the objections that the claims fall within the scope of the clause (k) of Section 3 and Section 2(1) (j) of the Indian Patent Act, 1970 as it lacks novelty and inventive step. A response to the first examination report (FER) was filed by the applicant on 9th April 2008. A hearing was also requested by the applicants along with the submissions. After considering the submissions made by the Applicant, as well as descriptions and claims as on the records, the Deputy Controller was of the opinion that the alleged invention still falls under Section 3(k) of the Patents Act. Hence a grant of patent to the above application was rejected.

Appellant’s allegations against the controller’s decisions

The Appellant (who are the applicants) then filed an appeal against the Controller’s decision before the IPAB, and one of the grounds was that the Controller had wrongly negated the ‘technical effect” holding incorrectly that the Indian Patent Law does not follow the EPC.

IPAB’s decision to the above allegation

In response to the Appellant’s allegation, the IPAB referred to a previous case Yahoo vs. Rediff, which was raised on the same grounds. The IPAB cited that “inventive step must be a feature which lies with a patentable subject matter. Otherwise, the patentee by citing economic significance or technical advance in relation to any of the excluded subjects can insist upon grant of patent thereto. Therefore, this technical advance comparison should be done with the subject matter of invention and it should be found it is not related to any of the excluded subjects…….”

The IPAB here declined the allegation by the Appellants by stating that the Controller was of the opinion that the claimed invention, although it was a technical advancement, it still was nothing more than a mathematical method based on various algorithms for which the Indian patent law does not grant a patent. The identifiable technical contribution provided by the claimed invention itself came under the excluded subject matter and so the IPAB justified the controller’s decision that a patent cannot be granted for a mathematical method according to the patent law in India and the appeal was dismissed.


In light of the above discussion, one of the ways of analyzing patentability of inventions that involve mathematical methods is by adopting a “problem and solution” approach of analysis. One may try to define the technical problem the invention is trying to solve, and thereafter identify the technical solution that addresses that problem. Further, one can try to determine whether that technical solution itself is the “mathematical method” or is it beyond the “mathematical method”. Inventions that propose and claim a technical solution that is beyond a “mathematical method” have a higher probability of having a patent granted. 

We hope you found this article useful. You may be interested in reading our articles:

What can be patented and what cannot be patented    
Are software inventions patentable in India?     
Issues concerning patentability of discoveries in India    
Issues Concerning Patenting Inventions Relating to Plants, Animals and Microorganisms    

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