mathematical proof

Rigorous demonstration that a mathematical statement follows from its premises

Entitymathematical concept mathematical textformQ11538

Also known as proof · proof in mathematics · proof (mathematics)

Instance of: mathematical concept
, mathematical textform
Subclass of: mathematical reasoning
, argument

Overview

From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0

A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning that establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning that establish "reasonable expectation". Presenting many cases in which the statement holds is not enough for a proof, which must demonstrate that the statement is true in all possible cases. A proposition that has not been proved but is believed to be true is known as a conjecture, or a hypothesis if frequently used as an assumption for further mathematical work.

Overview

All data

38 statements · 11% with external sources · numbers in brackets are citations

Said to be the same as: formal proof
Uses: axiom
logic
theorem nature of statement: often
Has goal: theorem
Has characteristic: validity
proof
Studied by: proof theory
Different from: Q19814025
Follows: conjecture

On other databases

16 identifiers linking mathematical proof across the web's reference databases

Data quality

statements

11%

externally sourced

Source last edited October 13, 2026. AIDb refreshes this page daily.

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AIDb. (2026). mathematical proof (Q11538). Retrieved from https://aidb.si/e/mathematical-proof-Q11538