Legal Definitions - mathematical-algorithm exception

The mathematical-algorithm exception refers to a principle in patent law that limits what can be patented. Specifically, it states that abstract ideas, laws of nature, and natural phenomena cannot be patented. Pure mathematical algorithms, when presented as abstract concepts or formulas without a practical, concrete application, fall under this exception.

While inventions that *utilize* mathematical algorithms in a practical way to achieve a new and useful result can be patentable, the algorithm itself, as a fundamental mathematical principle or abstract method, is not. This is because such basic mathematical tools are considered building blocks of scientific and technological progress, rather than specific inventions.

Here are some examples to illustrate this concept:

• Example 1: A New Prime Number Formula

  Imagine a brilliant mathematician discovers a groundbreaking new mathematical formula that can generate prime numbers with unprecedented speed and efficiency. This formula is a purely theoretical construct, expressed through mathematical symbols and logic, describing a fundamental property of numbers.

  How it illustrates the term: This new formula, despite its intellectual brilliance and potential utility in various fields, would fall under the mathematical-algorithm exception. It is an abstract mathematical concept, a discovery of a natural law or property of numbers, rather than a practical application or a specific machine or process that *uses* the formula to achieve a new, tangible result. Therefore, the formula itself cannot be patented.

• Example 2: An Abstract Data Sorting Method

  A computer scientist develops a novel algorithm for sorting large datasets that is theoretically more efficient than any existing method. The algorithm is described purely in pseudocode and mathematical notation, outlining the logical steps to reorder data, but it does not specify how it would be implemented in a particular software program, integrated into a specific hardware device, or applied to a unique industrial process.

  How it illustrates the term: In its abstract form, this sorting algorithm is a mathematical procedure for organizing information. Because it is presented as a pure concept or a set of instructions without a concrete, practical application tied to a specific technological process or machine, it falls under the mathematical-algorithm exception. It is considered an abstract idea for processing information, not a patentable invention in itself.

• Example 3: A Theoretical Resource Optimization Algorithm

  An operations research specialist invents a new mathematical algorithm designed to theoretically optimize the allocation of resources within a complex system, such as a city's traffic flow or a hospital's patient scheduling. The algorithm provides a mathematical framework for achieving optimal efficiency but does not specify how it would be integrated into a computer system, control specific traffic lights, or manage a particular hospital's operations.

  How it illustrates the term: This algorithm, as a theoretical method for optimization, is considered an abstract mathematical concept. It outlines a way to solve a problem using mathematical logic. Without a concrete application that transforms this abstract idea into a practical, inventive process or system (e.g., a specific software program controlling specific traffic signals to improve flow, or a unique patient management system), it is not patentable due to the mathematical-algorithm exception.