Welcome to the new version of the Patents Manual. Please note there are changes to the numbering and sequence of the chapters and pages in the manual. You are encouraged to take the time to explore and familiarise yourself with this new structure. Mathematical Algorithms

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A mathematical algorithm is a procedure for solving a given mathematical problem, commonly applied in the field of computer software related inventions.

Case law

In Grant v Commissioner of Patents (2006) FCAFC 120, the Full Court stated:

“It has long been accepted that 'intellectual information', a mathematical algorithm, mere working directions and a scheme without effect are not patentable.”

However, while a mathematical algorithm per se may not be a manner of manufacture, the presence of such an algorithm within the steps in an otherwise patentable method does not exclude a claim from patentability. For example, in the matter International Business Machines Corporation v Commissioner of Patents (1991) FCA 625 the Court, in considering a method for producing an improved (that is, smoother) visual representation of a curve, found (at paragraph 16) that:

“In the present case, it seems to me that the use of the algorithm is not different conceptually from the use of the compounds involved in National Research and Development Council. Just as those compounds were previously known, so here, it is not suggested there is anything new about the mathematics of the invention. What is new is the application of the selected mathematical methods to computers, and in particular, to the production of the desired curve by computer. This is said to involve steps which are foreign to the normal use of computers ....”

The distinction to be drawn is between a claim to an algorithm (or scientific principle or natural phenomenon) in the abstract sense and the application of the formula to a process such that it produces “some advantage which is material, in the sense that the process belongs to a useful art as distinct from a fine art”.


Examples of inventions involving mathematical algorithms that would be patentable are:

  • any otherwise patentable process which uses a specific algorithm or mathematical formula, for example, a claim to a method of annealing a tungsten alloy, where the heating time (seconds) = 6.78 mass of ingot/temperature (C); and
  • a method that generates a more accurate measurement/calculation of an amount of oil in an underground deposit using a mathematical algorithm to process measured input data. Here, the invention can be classified as technical or practical.

Examples of inventions involving a mathematical algorithm that would not be patentable are:

  • a method that uses an algorithm to calculate data indicative of success of aspects of commerce such as investments. Here, the invention is akin to business innovation as opposed to technical innovation, being in an abstract art of organising or analysing human activity; and
  • a pure mathematical formula (unapplied), for example, a claim to a method of calculating a value c, where c = ex sin (t).

Note that c, x, and t are pure variables with no defined significance to the real world.

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Amended Reasons

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