a statement or idea that can be proven by a series of logical steps based on assumptions, a mathematical proposition that can be proved from other propositions that have already been proved or are assumed to be true

Bayes' theorem, Euclid's theorem, Pappus's theorem

Formal and Informal Expressions of theorem

In different contexts, you can replace 'theorem' with suitable alternatives. In a more formal setting, 'proposition, formula' is apt. In informal speech or writing, 'rule, law' is a commonplace synonym.

theorem: Explore its Definition & Usage

theorem Definition

1a statement or idea that can be proven by a series of logical steps based on assumptions
2a mathematical proposition that can be proved from other propositions that have already been proved or are assumed to be true

Using theorem: Examples

Take a moment to familiarize yourself with how "theorem" can be used in various situations through the following examples!

Example
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Example
Fermat's Last Theorem was finally proven after centuries of attempts.
Example
The theorem of calculus is a fundamental concept in mathematics.

theorem Synonyms and Antonyms

Synonyms for theorem

Phrases with theorem

Bayes' theorem
a mathematical formula used to calculate conditional probabilities
Example
Bayes' theorem is used in many fields, including statistics and artificial intelligence.
Euclid's theorem
a geometric theorem attributed to the ancient Greek mathematician Euclid, stating that there are infinitely many prime numbers
Example
Euclid's theorem is one of the oldest and most famous results in number theory.
Pappus's theorem
a theorem in projective geometry that relates the areas of two triangles that share a common cevian
Example
Pappus's theorem has many applications in architecture and engineering.

Origins of theorem

from Greek 'theorema', meaning 'a sight, speculation, theory'

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Summary: theorem in Brief

A 'theorem' [ˈθiːərəm] is a statement or idea that can be proven through logical steps based on assumptions. It is often used in mathematics, such as the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Other examples include Bayes' theorem, Euclid's theorem, and Pappus's theorem.