What Makes Mathematical Formulae-Based Inventions Patentable?

Kiran S Bettadapur

Parinita Ravi

October 9, 2026

Diamond v. Diehr, 450 U.S. 175 (1981) was a milestone decision of the United States Supreme Court, which dealt with the patentability of computer-implemented inventions.

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The judgment established the clear distinction between an unpatentable mathematical formula and a patentable industrial process that incorporates such a formula.

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Case Backdrop

The applicants, John Diehr and Theodore Lutton, filed a patent application for an invented synthetic rubber curing process. The conventional method of curing rubber involved placing uncured rubber in a mold and heating it for a specified period. Determining the precise curing time was a problem, because factors such as temperature and the composition of the rubber affected the curing process.

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Diehr's invention addressed this problem by continuously measuring the temperature inside the rubber mold and repeatedly calculating the appropriate cure time using the Arrhenius equation, a well-known mathematical formula. Diehr’s invention relied on a computer to monitor whether the rubber had reached the requisite curing state and to open the press at the right time automatically.

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The US Patent and Trademark Office rejected the patent application on the ground that the claims effectively sought to patent the underlying mathematical equation. The Court of Customs and Patent Appeals reversed that decision.

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Consequently, the matter ultimately reached the US Supreme Court.

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The Verdict

In a 5–4 split decision, the court upheld the patentability of the claimed process. The Court emphasized that 35 U.S.C. §101 broadly permits patents for any new and useful process, machine, manufacture, or composition of matter, subject to the statutory exceptions and the requirements of novelty, non-obviousness, and disclosure.

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The Court acknowledged that laws of nature, natural phenomena, and abstract ideas—including mathematical formulas—are not patentable.

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Yet, it rejected the proposition that the presence of a mathematical equation automatically renders an entire process unpatentable.

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Supreme Court’s Reasoning

To examine the patentability of the invention, the Court first defined ‘process’ as follows:

A ‘process’ is ‘an act, or a series of acts, performed upon the subject-matter to be transformed and reduced to a different state or thing. If new and useful, it is just as patentable as is a piece of machinery…the machinery pointed out as suitable to perform the process may or may not be new or patentable.

It further held that the invention was patent-eligible, because considered as a whole, the entire industrial process rather than the mathematical formula itself was claimed. The Court therefore held that the applicants were not attempting to pre-empt the use of the Arrhenius equation itself. Rather, they claimed a particular application of the equation in a rubber-curing process. The fact that a computer was used to perform the calculations did not change the patentability analysis.

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The court observed as under:

“…When a claim containing a mathematical formula implements or applies the formula in a structure or process, which, when considered as a whole, is performing a function which the patent laws were designed to protect (e.g., transforming or reducing an article to a different state or thing), then the claim satisfies §101’s requirements....”

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In Diehr, the mathematical equation was used as part of a practical industrial process for transforming raw materials into a different state. The claimed invention included several physical steps, such as, placing the rubber in a mold, measuring the temperature, calculating the cure time, and opening the press automatically when the calculated time had elapsed.

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Importantly, the Court rejected the approach of dissecting claims into old and new elements and then concluding that the mathematical formula constituted the only novel element. For ascertaining patentability, the claimed invention must be analysed as an integrated whole.

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Concluding Remarks

Diamond v. Diehr became a foundational authority for software and computer-implemented inventions. Its cardinal principle was that although an algorithm or abstract mathematical formula cannot itself be patented, a practical technological process that incorporates such a concept may nevertheless be patentable when, viewed as a whole, it applies that formula in a practical technological process.

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The decision became extremely vital in the development of US patentability jurisprudence, and led to other precedents, including Mayo Collaborative Services v. Prometheus Laboratories[1] and Alice Corp. v. CLS Bank International.[2]

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At BLAZE VENTURES, we have elaborate processes and qualified professionals to strategically advise parties on the patentability of ideas, inventions and innovations and to help protect IP effectively.

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[1] 566 U.S. 66 (2012)

[2] 573 U.S. 208 (2014)

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