Defining Quote by Jacques Hadamard
“Can the existence of a mathematical entity be proved without defining it ?”
About This Quote
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.
![“[Mathematics is] purely intellectual, a pure theory of forms, which has for its objects not the combination of quantities or their images, the numbers, but things of thought to which there could correspond effective objects or relations, even though such a correspondence is not necessary.” quote by Hermann Hankel](https://sms4smile.com/quotes/img-quotes/9d5/hermann-hankel-65857_combination_mathematics-is-purely-intellectual-a-pur_2076406.jpg)
![“I never left my roots. You can identify me as someone that didn't become high and mighty. Humility is a defining [trait] all of us can forever learn, and I try to be as humble as anyone can be.” quote by Serena Williams](https://sms4smile.com/quotes/img-quotes/517/serena-williams-1589_defining_i-never-left-my-roots-you-can-identify-m_17115.jpg)
