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Law ○꠹｜Definition｜1st｜20260426232300-00-⌔

Law (mathematics) - Wikipedia

Law (mathematics)

In mathematics, a law is a formula that is always true within a given context.¹ Laws describe a relationship, between two or more expressions or terms (which may contain variables), usually using equality or inequality,² or between formulas themselves, for instance, in mathematical logic. For example, the formula $a^2\ge 0$ is true for all real numbers a, and is therefore a law. Laws over an equality are called identities.³ For example, $(a+b{)}^2=a^2+2ab+b^2$ and ${\cos }^2\theta +{\sin }^2\theta =1$ are identities.⁴ Mathematical laws are distinguished from scientific laws which are based on observations, and try to describe or predict a range of natural phenomena.⁵ The more significant laws are often called theorems.

Printed 2026-06-28.

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Footnotes

1. Weisstein, Eric W. “Law”. mathworld.wolfram.com. Retrieved 2024-08-19. ↩

2. Pratt, Vaughan, “Algebra”, The Stanford Encyclopedia of Philosophy (Winter 2022 Edition), Edward N. Zalta & Uri Nodelman (eds.), URL: https://plato.stanford.edu/entries/algebra/#Laws ↩

3. Equation. Springer Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Equation&oldid=32613 ↩

4. “Mathwords: Identity”. www.mathwords.com. Retrieved 2019-12-01. ↩

5. “law of nature”. Oxford English Dictionary (online ed.). Oxford University Press. (Subscription or participating institution membership required.) ↩

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