How to Copyright a Mathematical Formula: Process and Considerations

Securing intellectual property rights is crucial for creators seeking recognition and protection for their innovative works.

While copyright protection extends to various forms of creative expression, the realm of mathematical formulas presents unique challenges.

This article aims to provide guidance on how to copyright a mathematical formula.

Although copyright generally does not cover mathematical formulas themselves, we will explore alternative avenues for protecting these valuable creations.

Can Mathematical Formulas Be Copyrighted?

No, in general, mathematical formulas cannot be copyrighted.

Copyright law protects original works of authorship, and mathematical formulas are typically considered abstract ideas or laws of nature rather than creative expressions.

A mathematical formula represents a relationship between variables and is seen as a statement of a mathematical concept rather than an original work deserving of copyright protection.

While copyright may not apply to the formula itself, creative elements within a written explanation or accompanying text could be eligible for copyright protection. 

Copyright Protection for Expressions of Mathematical Formulas

While mathematical formulas themselves cannot be copyrighted, the specific implementations or expressions of those formulas can be eligible for copyright protection.

For example, you can obtain copyright protection for the way you express a mathematical formula, such as in a book that explains its concepts and applications.

The book, as a creative work, would be protected by copyright, including the specific expressions and explanations of the formula within it.

Similarly, software that incorporates a mathematical formula can also be protected by copyright.

The code and implementation of the software, including the integration of the formula, would be subject to copyright protection.

It’s important to note that copyright protection extends to the creative elements and expressions surrounding the formula, rather than the formula itself, which is considered a factual or functional element.

Why Mathematical Equations is Non-Copyrightable?

The copyrightability of mathematical equations is a subject that remains unclear due to the idea-expression dichotomy and the doctrine of merger.

Granting copyright to mathematical equations would create a monopoly, restricting their use by others, which goes against the principle of promoting progress and widespread access.

Mathematical equations, being the laws of nature, are not subject to copyright protection.

Just as the law itself cannot be copyrighted, mathematical equations are considered factual and available for everyone to use.

Copyright law aims to protect original expressions of ideas in literary, musical, artistic, or other creative forms, but mathematical equations do not fall under this category.

Allowing copyright on mathematical equations would impede the free flow of information and limit their use to only the copyright holder or authorised licensees, hindering scientific progress and innovation.

Therefore, mathematical equations are not eligible for copyright protection, ensuring their availability for all without the fear of infringement.

Copyright and Mathematical Equations: Understanding the Limitations

In the case of Chancellor Masters and Scholars of The University of Oxford v. Narendra Publishing House & Ors, Justice Bhat clarified that mathematical equations are expressions of laws of nature and the discovery of such laws cannot confer a monopoly on those who describe them.

The reason is that language is a limited medium that allows for the description of these laws in only a few ways.

For instance, the mathematical equation x+y=z, being a well-established law of nature, does not receive copyright protection.

This is where the doctrine of merger comes into play.

However, a book containing a collection of equations along with examples, questions, and other creative elements can be subject to copyright protection.

For example, authors like Mrs. Shakuntala Devi and M.L. Aggrawal hold copyright in their respective mathematics books, which present the general concepts of mathematics with different arrangements, examples, and questions.

In a legal context, the content of a math book, including diagrams, word problems, and illustrations, can be copyrighted.

However, the mathematical formulas, problems, proofs, and theorems themselves cannot be copyrighted.

Facts that are established and natural, such as 2*2=4, cannot be copyrighted.

Therefore, copyright protection extends to the book as an original work of authorship, but it is limited to the copying of the overall publication rather than the underlying math formulas.

Doctrine of Merger

The doctrine of merger is a legal principle that applies when an idea or expression is inseparable from a particular form of expression, thereby merging the idea and the expression into a single concept.

According to this doctrine, if there is only one or a limited number of ways to express an idea effectively, copyright protection does not extend to that expression because it would essentially grant a monopoly over the idea itself.

The doctrine of merger is relevant in copyright law to ensure a balance between the protection of creative expression and the free flow of ideas.

It prevents copyright from being used to monopolise common or essential elements that are inherent to a particular subject matter or concept.

When the idea and expression merge, copyright protection is not available, and the underlying idea becomes part of the public domain.

Conclusion

Copyright protection for mathematical formulas is a complex and nuanced area.

While the formulas themselves are generally not eligible for copyright, the literary expressions, creative explanations, and unique presentations of mathematical formulas may be subject to copyright protection.

The tangible form in which the formulas are expressed, such as in a book, article, or other literary works, serves as the basis for copyright protection.

By embodying the formulas in a tangible form and adding creative elements, the expression becomes an identifiable work of authorship.

However, it is important to note that copyright does not cover the underlying mathematical calculations or the concept of mathematics itself.

By recognising the distinction between the formulas and their creative expressions, individuals can navigate the complexities of copyright and ensure proper protection for their original works related to mathematical formulas.

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