démonstration

Démonstration is a term used to refer to the act of showing something to be true or evident. The word derives from Latin demonstratio, from demonstrare “to point out, show.” In French, démonstration covers several related senses, and English usage sometimes borrows the term with similar nuance while distinguishing its specific meanings.

In mathematics and logic, a démonstration (demonstration) is a formal proof: a rigorous, step-by-step argument deriving a conclusion from axioms and previously established results. A good démonstration is deductive, complete, and verifiable by others. Classical examples include Euclid’s proofs, which establish the truth of theorems through logical necessity.

In education and science, a demonstration is an act of showing how a process or device works, often through a live experiment or a demonstration model intended to teach or illustrate a concept. Such demonstrations emphasize clarity, reproducibility, and practical understanding.

In rhetoric and everyday language, demonstration can mean an argument or presentation intended to persuade by reasoning and evidence. It involves assembling supporting facts, premises, and logical connections to establish a claim.

In social and political contexts, a demonstration is a public gathering to express opinion or demand action, such as a protest or rally. These events are organized around messaging, routes or venues, and legal or safety considerations, and they may vary widely in scale and form.

In French usage, démonstration is commonly used for mathematical proof, while demonstration (without accent) can refer to displays, protests, or demonstrations of methods. Context typically clarifies which sense is intended.