What are examples of mathematical concepts that are considered abstract ideas?

This page is an FAQ based on guidance from the Manual of Patent Examining Procedure. It is provided as guidance, with links to the ground truth sources. This is information only: it is not legal advice.

Examples of mathematical concepts considered abstract ideas include:

• Mathematical relationships
• Mathematical formulas or equations
• Mathematical calculations

Specific examples cited in MPEP 2106.04(a)(2) include:

• A procedure for converting binary-coded decimal numerals into pure binary form (Gottschalk v. Benson)
• A mathematical formula for calculating an alarm limit (Parker v. Flook)
• The Arrhenius equation (Diamond v. Diehr)
• A mathematical formula for hedging (Bilski v. Kappos)

The MPEP states: “The Court’s rationale for identifying these ‘mathematical concepts’ as judicial exceptions is that a ‘mathematical formula as such is not accorded the protection of our patent laws,’ … and thus ‘the discovery of [a mathematical formula] cannot support a patent unless there is some other inventive concept in its application.’”