Best things Quote by Saharon Shelah
“Given a conjecture, the best thing is to prove it. The second best thing is to disprove it. The third best thing is to prove that it is not possible to disprove it, since it will tell you not to waste your time trying to disprove it. That's what Gödel did for the Continuum Hypothesis.”
About This Quote
Source Quote: Personal commentary, Saharon Shelah, 1990
In mathematics, proving a conjecture is best; disproving is second; showing it cannot be disproved is third, highlighting limits of proof.
In simple terms: Prove, then disprove, then show impossibility of disproof.
Key Takeaway
Recognize limits of proof and focus on feasible approaches.
Themes
logic
mathematics
philosophy of science
limits
Mood
analytical
skeptical
Type
theoretical
philosophical
When to use this quote
- research planning
- academic debate
- problem solving
- theoretical work
Key Concepts
Gödel
continuum hypothesis
proof strategies
Questions to Reflect On
- When should you stop trying to prove or disprove a problem?
- How do you decide a problem is worth pursuing?
A Different Perspective
Not all problems are resolvable; chasing impossibility may waste resources.
![“purposely ignored by him. [16] Tu Mu's conjecture seems to be based” quote by Sun Tzu](https://sms4smile.com/quotes/img-quotes/e9c/sun-tzu-283_conjecture_purposely-ignored-by-him-16-tu-mu-s-conj_350543.jpg)
![“Physiognomy is not a guide that has been given us by which to judge of the character of men: it may only serve us for conjecture. [Fr., La physionomie n'est pas une regle qui nous soit donnee pour juger des hommes; elle nous peut servir de conjecture.]” quote by Jean de la Bruyere](https://sms4smile.com/quotes/img-quotes/3cd/jean-de-la-bruyere-575_character_physiognomy-is-not-a-guide-that-has-been_207056.jpg)
