--- title: "Meaning & Key Takeaway of: The goal of a definition is to introduce…" description: "\"The goal of a definition is to introduce a mathematical object. The goal of a theorem is to state some of its properties, or interrelations between var..." image: "https://sms4smile.com/quotes/i/70d/iu-i-manin-51977_argument_the-goal-of-a-definition-is-to-introduce_1600652.jpg" --- # The goal of a definition is to introduce a mathematical… ![“The goal of a definition is to introduce a mathematical object. The goal of a theorem is to state some of its properties, or interrelations between various objects. The goal of a proof is to make such a statement convincing by presenting a reasoning subdivided into small steps each of which is…” quote by IU?. I. Manin](https://sms4smile.com/quotes/i/70d/iu-i-manin-51977_argument_the-goal-of-a-definition-is-to-introduce_1600652.jpg) [Download](https://sms4smile.com/quotes/i/70d/iu-i-manin-51977_argument_the-goal-of-a-definition-is-to-introduce_1600652.jpg) [Open image](https://sms4smile.com/quotes/i/70d/iu-i-manin-51977_argument_the-goal-of-a-definition-is-to-introduce_1600652.jpg) > “The goal of a definition is to introduce a mathematical object. The goal of a theorem is to state some of its properties, or interrelations between various objects. The goal of a proof is to make such a statement convincing by presenting a reasoning subdivided into small steps each of which is justified as an "elementary" convincing argument.” [IU?. I. Manin](https://sms4smile.com/quotes/author/iu-i-manin/) ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. Definitions introduce objects, theorems describe properties, proofs justify statements through stepwise reasoning. **In simple terms:** Definitions create objects; theorems describe them; proofs justify. Key Takeaway Use clear steps to build convincing arguments. Themes mathematics logic structure Mood analytical inquisitive Type academic educational When to use this quote - teaching - research - writing proofs Key Concepts definition theorem proof reasoning Questions to Reflect On - How do you ensure each step is truly elementary? - What hidden assumptions might affect validity? A Different Perspective Complex proofs may still hide hidden assumptions. ★ ★ ★ ★ ★ No ratings yet [Argument](https://sms4smile.com/quotes/about/argument/) [Convincing](https://sms4smile.com/quotes/about/convincing/) [Definitions](https://sms4smile.com/quotes/about/definitions/) [Goal](https://sms4smile.com/quotes/about/goal/) [Goal Definition](https://sms4smile.com/quotes/about/goal-definition-6086133/) [Goal Proof](https://sms4smile.com/quotes/about/goal-proof-6086134/) [Goal Theorem](https://sms4smile.com/quotes/about/goal-theorem-6086132/) [Goals](https://sms4smile.com/quotes/about/goals/) [Introducing](https://sms4smile.com/quotes/about/introducing/) [Justified](https://sms4smile.com/quotes/about/justified/) [Mathematical](https://sms4smile.com/quotes/about/mathematical/) [Mathematics](https://sms4smile.com/quotes/about/mathematics/) [Objects](https://sms4smile.com/quotes/about/objects/) [Objects Goal](https://sms4smile.com/quotes/about/objects-goal-6086135/) [Presenting](https://sms4smile.com/quotes/about/presenting/) [Proof](https://sms4smile.com/quotes/about/proof/) [Property](https://sms4smile.com/quotes/about/property/) [Reasoning](https://sms4smile.com/quotes/about/reasoning/) [Small steps](https://sms4smile.com/quotes/about/small-steps/) [Statements](https://sms4smile.com/quotes/about/statements/) [States](https://sms4smile.com/quotes/about/states/) [Steps](https://sms4smile.com/quotes/about/steps/) [Theorems](https://sms4smile.com/quotes/about/theorems/) [Various](https://sms4smile.com/quotes/about/various/) ## Related quotes > [Theorems often tell us complex truths about the simple things, but only rarely tell us simple truths about the complex ones. 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Manin](https://sms4smile.com/quotes/author/iu-i-manin/) > [A proof only becomes a proof after the social act of "accepting it as a proof".](https://sms4smile.com/quotes/iu-i-manin/a-proof-only-becomes-a-proof-after-the-social-act-of-accepting-it-as/) [IU?. I. Manin](https://sms4smile.com/quotes/author/iu-i-manin/) > [A good proof is one that makes us wiser.](https://sms4smile.com/quotes/iu-i-manin/a-good-proof-is-one-that-makes-us-wiser/) [IU?. I. Manin](https://sms4smile.com/quotes/author/iu-i-manin/) [Explore all 7 IU?. I. Manin quotes ](https://sms4smile.com/quotes/author/iu-i-manin/) ## More Argument quotes > [A flourishing, morally credible media is a vital component in the maintenance of genuinely public talk, argument about common good.](https://sms4smile.com/quotes/rowan-williams/a-flourishing-morally-credible-media-is-a-vital-component-in-the/) [Rowan Williams](https://sms4smile.com/quotes/author/rowan-williams/) > [Preaching to the choir actually arms the choir with arguments and elevates the choir's discourse. 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