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

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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.

Interesting facts about mathematical theorems:

- 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 |

**This video contains the answer to your query**

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.

## 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.

## People also ask

**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.

**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.

**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.