# Your request: what is a mathematical theorem?

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A mathematical theorem is a statement that has been proven to be true using mathematical logic and reasoning.

## Detailed response to your request

A mathematical theorem is a statement that has been proven to be true using mathematical logic and reasoning. The proof of a theorem is a series of logical deductions from a set of axioms and previously proven theorems.

According to the famous mathematician Paul Erdős, “A mathematician is a machine for turning coffee into theorems.” Mathematical theorems are central to the field of mathematics, as they provide the foundations for further work and discoveries.

• Some of the most well-known theorems include Euclid’s theorem on the infinitude of primes, Pythagoras’ theorem on the relationship between the sides of a right triangle, and Fermat’s Last Theorem.
• The proof of Fermat’s Last Theorem, which states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than 2, was famously elusive for over 350 years.
• The first known use of the word “theorem” was by the ancient Greek mathematician Pythagoras.
• A theorem may have multiple proofs, and some theorems even have hundreds of different proofs.
• In some cases, a statement may be widely believed to be true but not be classified as a theorem until it has been rigorously proven using mathematical logic and reasoning.

Here is a table showing some famous mathematical theorems and their discoverers:

Theorem Discoverer
Pythagorean theorem Pythagoras
Euclid’s theorem on the infinitude of primes Euclid
Fermat’s Last Theorem Pierre de Fermat (proved by Andrew Wiles)
Fundamental theorem of calculus Isaac Newton and Gottfried Wilhelm Leibniz
Brouncker’s theorem William Brouncker

In this video, the importance of proofs in mathematics is explained. Euclid of Alexandria is introduced as the father of geometry who formalized mathematics with axioms. Proofs provide a solid foundation for mathematicians, logicians, and statisticians to build and test their theories on, ensuring the validity of a theorem. The usefulness of proofs extends beyond mathematics and into architecture, art, computer programming, and internet security. The video ends with fun reasons to learn and appreciate proofs in mathematics.

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## Here are some other responses to your query

A theorem is a statement or formula in mathematics or logic that has been or is to be proved by accepted operations and arguments. A theorem is part of a larger theory and may embody a general principle. A theorem can also be a rule or law expressed by an equation or formula.

theorem noun [ C ] mathematics specialized uk / ˈθɪə.rəm / us / ˈθiː.rəm / (especially in mathematics) a formal statement that can be shown to be true by logic: a mathematical theorem

theorem noun the·​o·​rem ˈthē-ə-rəm ˈthi (-ə)r-əm 1 : a formula, proposition, or statement in mathematics or logic that has been or is to be proved from other formulas or propositions

A theorem is a statement that can be demonstrated to be true by accepted mathematical operations and arguments. In general, a theorem is an embodiment of some general principle that makes it part of a larger theory. The process of showing a theorem to be correct is called a proof.

theorem, in mathematics and logic, a proposition or statement that is demonstrated. In geometry, a proposition is commonly considered as a problem (a construction to be effected) or a theorem (a statement to be proved). The statement “If two lines intersect, each pair of vertical angles is equal,” for example, is a

See synonyms for theorem on Thesaurus.com noun Mathematics. a theoretical proposition, statement, or formula embodying something to be proved from other propositions or formulas. a rule or law, especially one expressed by an equation or formula.

## You will be interested

Did you know: The concept of a theorem was first used by the ancient Greeks. To derive new theorems, Greek mathematicians used logical deduction from premises they believed to be self-evident truths. Since theorems were a direct result of deductive reasoning, which yields unquestionably true conclusions, they believed their theorems were undoubtedly true.
Interesting: According to the Nobel Prize-winning physicist Richard Feynman (1985), any theorem, no matter how difficult to prove in the first place, is viewed as trivial by mathematicians once it has been proven. Therefore, there are exactly two types of mathematical objects: trivial ones, and those which have not yet been proven. R.
Interesting fact: Some mathematicians have stated that proving the theorem using trigonometry is impossible without circular reasoning, because trigonometry relies so much on the theorem itself. Two New Orleans high school students say they’ve proven the theorem using trigonometry without relying on circular reasoning.

What is an example of a mathematical theorem?
As an answer to this: What is an example of a theorem? The Pythagorean theorem is an example for theorem. It states that the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the sides of the triangle.
What is the mathematical theorem?
In reply to that: Mathematical theorems can be defined as statements which are accepted as true through previously accepted statements, mathematical operations or arguments. For any maths theorem, there is an established proof which justifies the truthfulness of the theorem statement.
What are the 3 types of theorem?
Answer: Linear Pair Theorem If two angles form a linear pair, then they are supplementary. supplements theorem If two angles are supplements of the same angle, then they are congruent. Congruent complements theorem If two angles are complements of the same angle, then they are congruent.
What is a theorem in simple terms?
Response to this: : a formula, proposition, or statement in mathematics or logic deduced or to be deduced from other formulas or propositions. : an idea accepted or proposed as a demonstrable truth often as a part of a general theory : proposition.
How do you prove a theorem?
As a response to this: In order for a theorem be proved, it must be in principle expressible as a precise, formal statement. However, theorems are usually expressed in natural language rather than in a completely symbolic form—with the presumption that a formal statement can be derived from the informal one.
What is the definition of a theorem?
Response will be: A Theorem is a major result, a minor result is called a Lemma.
What are some examples of theorems?
Response: In geometry, a proposition is commonly considered as a problem (a construction to be effected) or a theorem (a statement to be proved). The statement “If two lines intersect, each pair of vertical angles is equal,” for example, is a theorem.
What is the importance of a theorem?
Put simply, a theorem is a math rule that has a proof that goes along with it. In other words, it’s a statement that has become a rule because it’s been proven to be true. This definition will make more sense as we look over two popular theorems in mathematics.
How do you prove a theorem?
Response will be: In order for a theorem be proved, it must be in principle expressible as a precise, formal statement. However, theorems are usually expressed in natural language rather than in a completely symbolic form—with the presumption that a formal statement can be derived from the informal one.
What is the definition of a theorem?
Answer: A Theorem is a major result, a minor result is called a Lemma.
What are some examples of theorems?
In geometry, a proposition is commonly considered as a problem (a construction to be effected) or a theorem (a statement to be proved). The statement “If two lines intersect, each pair of vertical angles is equal,” for example, is a theorem.
What is the importance of a theorem?
Put simply, a theorem is a math rule that has a proof that goes along with it. In other words, it’s a statement that has become a rule because it’s been proven to be true. This definition will make more sense as we look over two popular theorems in mathematics.

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