--- title: "Meaning & Key Takeaway of: Can the existence of a mathematical…" description: "\"Can the existence of a mathematical entity be proved without defining it ?\" — Jacques Hadamard" image: "https://sms4smile.com/quotes/i/37b/jacques-hadamard-51080_defining_can-the-existence-of-a-mathematical-enti_2995388.png" --- # Can the existence of a mathematical entity be proved… ![“Can the existence of a mathematical entity be proved without defining it ?” quote by Jacques Hadamard](https://sms4smile.com/quotes/i/37b/jacques-hadamard-51080_defining_can-the-existence-of-a-mathematical-enti_2995388.png) [Download](https://sms4smile.com/quotes/i/37b/jacques-hadamard-51080_defining_can-the-existence-of-a-mathematical-enti_2995388.png) [Open image](https://sms4smile.com/quotes/i/37b/jacques-hadamard-51080_defining_can-the-existence-of-a-mathematical-enti_2995388.png) > “Can the existence of a mathematical entity be proved without defining it ?” [Jacques Hadamard](https://sms4smile.com/quotes/author/jacques-hadamard/) ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. Mathematical existence proofs may require definitions to be precise. **In simple terms:** Existence needs definition. Key Takeaway Define before proving. Themes mathematics logic definition Mood analytical curious Type philosophical academic When to use this quote - research - teaching - theoretical work Key Concepts philosophy of math foundations Questions to Reflect On - Can we accept undefined objects? - What role do definitions play in proof? A Different Perspective Some entities can be inferred indirectly. ★ ★ ★ ★ ★ No ratings yet [Existence](https://sms4smile.com/quotes/about/existence/) [Life](https://sms4smile.com/quotes/about/life/) ## Related quotes > [I put a lot of effort in creating something fictional, yet very personal, because Shook is a defining part of me and my music:…](https://sms4smile.com/quotes/shook/i-put-a-lot-of-effort-in-creating-something-fictional-yet-very/) [Shook](https://sms4smile.com/quotes/author/shook/) > [Autonomy means women defining themselves and the values by which they will live, and beginning to think of institutional arrangements which will order their…](https://sms4smile.com/quotes/gerda-lerner/autonomy-means-women-defining-themselves-and-the-values-by-which-they/) [Gerda Lerner](https://sms4smile.com/quotes/author/gerda-lerner/) > [Using less of the Earth’s resources more efficiently and productively in a circular economy and making the transition from carbon-based fuels to renewable energies…](https://sms4smile.com/quotes/jeremy-rifkin/using-less-of-the-earth-s-resources-more-efficiently-and-productively/) [Jeremy Rifkin](https://sms4smile.com/quotes/author/jeremy-rifkin/) > [I met people on college campuses who were defining themselves as genderqueer to express revolutionary feelings, or to communicate their individuality; they were gender…](https://sms4smile.com/quotes/andrew-solomon/i-met-people-on-college-campuses-who-were-defining-themselves-as/) [Andrew Solomon](https://sms4smile.com/quotes/author/andrew-solomon/) > [Modern societies accepted the treasures and the power offered them by science. 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