--- title: "Meaning & Key Takeaway of: Given a conjecture, the best thing is to…" description: "\"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..." image: "https://sms4smile.com/quotes/i/ff8/saharon-shelah-67459_best-things_given-a-conjecture-the-best-thing-is-to_1331678.jpg" --- # Given a conjecture, the best thing is to prove it. The… ![“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.” quote by Saharon Shelah](https://sms4smile.com/quotes/i/ff8/saharon-shelah-67459_best-things_given-a-conjecture-the-best-thing-is-to_1331678.jpg) [Download](https://sms4smile.com/quotes/i/ff8/saharon-shelah-67459_best-things_given-a-conjecture-the-best-thing-is-to_1331678.jpg) [Open image](https://sms4smile.com/quotes/i/ff8/saharon-shelah-67459_best-things_given-a-conjecture-the-best-thing-is-to_1331678.jpg) > “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.” [Saharon Shelah](https://sms4smile.com/quotes/author/saharon-shelah/) ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. 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. ★ ★ ★ ★ ★ No ratings yet [Best things](https://sms4smile.com/quotes/about/best-things/) [Conjecture](https://sms4smile.com/quotes/about/conjecture/) [Conjecture Best](https://sms4smile.com/quotes/about/conjecture-best-4470639/) [Continuum](https://sms4smile.com/quotes/about/continuum/) [Disprove Best](https://sms4smile.com/quotes/about/disprove-best-4470641/) [Disprove Gödel](https://sms4smile.com/quotes/about/disprove-g-del-4470640/) [Given](https://sms4smile.com/quotes/about/given/) [Hypothesis](https://sms4smile.com/quotes/about/hypothesis/) [Mathematics](https://sms4smile.com/quotes/about/mathematics/) [Prove](https://sms4smile.com/quotes/about/prove/) [Prove it](https://sms4smile.com/quotes/about/prove-it/) [Science](https://sms4smile.com/quotes/about/science/) [Second best](https://sms4smile.com/quotes/about/second-best/) [Thing Disprove](https://sms4smile.com/quotes/about/thing-disprove-4470642/) [Thirds](https://sms4smile.com/quotes/about/thirds/) [Time](https://sms4smile.com/quotes/about/time/) [Trying](https://sms4smile.com/quotes/about/trying/) [Waste](https://sms4smile.com/quotes/about/waste/) ## Related quotes > [But there are times when men have serious thoughts, and it is at such times, when they begin to think, that they begin to…](https://sms4smile.com/quotes/thomas-paine/but-there-are-times-when-men-have-serious-thoughts-and-it-is-at-such/) [Thomas Paine](https://sms4smile.com/quotes/author/thomas-paine/) > [ “purposely ignored by him. \[16\] Tu Mu's conjecture seems to be based” ](https://sms4smile.com/quotes/sun-tzu/purposely-ignored-by-him-16-tu-mu-s-conjecture-seems-to-be-based/) [Sun Tzu](https://sms4smile.com/quotes/author/sun-tzu/) > [Do not walk in the path of human reason, and resist the pressures that would project you into conjectures about the future. Live one…](https://sms4smile.com/quotes/frances-j-roberts/do-not-walk-in-the-path-of-human-reason-and-resist-the-pressures-that/) [Frances J Roberts](https://sms4smile.com/quotes/author/frances-j-roberts/) > [“In science's pecking order, evolutionary biology lurks somewhere near the bottom, far closer to phrenology than to physics. For evolutionary biology is a historical…](https://sms4smile.com/quotes/jerry-a-coyne/in-science-s-pecking-order-evolutionary-biology-lurks-somewhere-near/) [Jerry A. Coyne](https://sms4smile.com/quotes/author/jerry-a-coyne/) > [“Fundamental values (such as equality and human rights) should not be held hostage to some factual conjecture about blank slates that might be refuted…](https://sms4smile.com/quotes/stephen-pinker/fundamental-values-such-as-equality-and-human-rights-should-not-be/) [Stephen Pinker](https://sms4smile.com/quotes/author/stephen-pinker/) > [We have to learn again that science without contact with experiments is an enterprise which is likely to go completely astray into imaginary conjecture.](https://sms4smile.com/quotes/hannes-alfven/we-have-to-learn-again-that-science-without-contact-with-experiments/) [Hannes Alfven](https://sms4smile.com/quotes/author/hannes-alfven/) > [“Now Aristotle says that the judgment which follows knowledge is in truth faith. Accordingly, faith is something superior to knowledge, and is its criterion.…](https://sms4smile.com/quotes/clement-of-alexandria/now-aristotle-says-that-the-judgment-which-follows-knowledge-is-in/) [Clement of Alexandria](https://sms4smile.com/quotes/author/clement-of-alexandria/) > [Physiognomy is not a guide that has been given us by which to judge of the character of men: it may only serve us…](https://sms4smile.com/quotes/jean-de-la-bruyere/physiognomy-is-not-a-guide-that-has-been-given-us-by-which-to-judge/) [Jean de la Bruyere](https://sms4smile.com/quotes/author/jean-de-la-bruyere/) > [I shall not mingle conjectures with certainties.](https://sms4smile.com/quotes/isaac-newton/i-shall-not-mingle-conjectures-with-certainties/) [Isaac Newton](https://sms4smile.com/quotes/author/isaac-newton/) > [I think everybody handles things very differently and you can conjecture, but until you're put in that situation, you really don't know.](https://sms4smile.com/quotes/laura-linney/i-think-everybody-handles-things-very-differently-and-you-can/) [Laura Linney](https://sms4smile.com/quotes/author/laura-linney/) > [The artist may be well advised to keep his work to himself till it is completed, because no one can readily help him or…](https://sms4smile.com/quotes/johann-wolfgang-von-goethe/the-artist-may-be-well-advised-to-keep-his-work-to-himself-till-it-is/) [Johann Wolfgang von Goethe](https://sms4smile.com/quotes/author/johann-wolfgang-von-goethe/) > [Rumour is a pipe Blown by surmises, jealousies, conjectures And of so easy and so plain a stop That the blunt monster with uncounted…](https://sms4smile.com/quotes/william-shakespeare/rumour-is-a-pipe-blown-by-surmises-jealousies-conjectures-and-of-so/) [William Shakespeare](https://sms4smile.com/quotes/author/william-shakespeare/) > [From the almost total absence of fossil evidence relative to the origin of the phyla, it follows that any explanation of the mechanism in…](https://sms4smile.com/quotes/pierre-paul-grasse/from-the-almost-total-absence-of-fossil-evidence-relative-to-the/) [Pierre-Paul Grasse](https://sms4smile.com/quotes/author/pierre-paul-grasse/) > [ The classes of problems which are respectively known and not known to have good algorithms are of great theoretical interest. \[...\] I conjecture that… ](https://sms4smile.com/quotes/jack-edmonds/the-classes-of-problems-which-are-respectively-known-and-not-known-to/) [Jack Edmonds](https://sms4smile.com/quotes/author/jack-edmonds/) > [A few of the sublimest geniuses of Rome and Athens had some faint discoveries of the spiritual nature of the human soul, and formed…](https://sms4smile.com/quotes/david-brainerd/a-few-of-the-sublimest-geniuses-of-rome-and-athens-had-some-faint/) [David Brainerd](https://sms4smile.com/quotes/author/david-brainerd/) ## More by Saharon Shelah > [There is an old maxim that says that two empires that are too large will collapse. The analog in set theory is that two…](https://sms4smile.com/quotes/saharon-shelah/there-is-an-old-maxim-that-says-that-two-empires-that-are-too-large/) [Saharon Shelah](https://sms4smile.com/quotes/author/saharon-shelah/) > [Number theorists say that number theory is too complicated, so let's pretend that there is only one prime number, and then let's combine all…](https://sms4smile.com/quotes/saharon-shelah/number-theorists-say-that-number-theory-is-too-complicated-so-let-s/) [Saharon Shelah](https://sms4smile.com/quotes/author/saharon-shelah/) > [Cardinal Arithmetics is much older than Number Theory. People used to exchange things way before there were numbers. Expressing numbers like 762 is already…](https://sms4smile.com/quotes/saharon-shelah/cardinal-arithmetics-is-much-older-than-number-theory-people-used-to/) [Saharon Shelah](https://sms4smile.com/quotes/author/saharon-shelah/) [Explore all 4 Saharon Shelah quotes ](https://sms4smile.com/quotes/author/saharon-shelah/) ## More Best things quotes > [I need the best things in life, that's women, thats cars. Cigars in Venice, bottle on ice, thats priceless.](https://sms4smile.com/quotes/nas/i-need-the-best-things-in-life-that-s-women-thats-cars-cigars-in/) [Nas](https://sms4smile.com/quotes/author/nas/) > [It hurt, of course, but more often than not the best things do, I've found.](https://sms4smile.com/quotes/stephen-king/it-hurt-of-course-but-more-often-than-not-the-best-things-do-i-ve/) [Stephen King](https://sms4smile.com/quotes/author/stephen-king/) > [The next best thing to being witty one's self, is to be able to be able to quote another's wit.](https://sms4smile.com/quotes/christian-nestell-bovee/the-next-best-thing-to-being-witty-one-s-self-is-to-be-able-to-be/) [Christian Nestell Bovee](https://sms4smile.com/quotes/author/christian-nestell-bovee/) > [I really believe that our past can really hold us back from growth, so the best thing that we can do is MOVE ON…](https://sms4smile.com/quotes/bob-harper/i-really-believe-that-our-past-can-really-hold-us-back-from-growth-so/) [Bob Harper](https://sms4smile.com/quotes/author/bob-harper/) > [The best thing for you to do is shop at your local farmer's market and support the organic growers who are there. Because those…](https://sms4smile.com/quotes/jason-mraz/the-best-thing-for-you-to-do-is-shop-at-your-local-farmer-s-market/) [Jason Mraz](https://sms4smile.com/quotes/author/jason-mraz/) > [The best thing about the term 'performance artist' is that it includes just about everything you might want to do.](https://sms4smile.com/quotes/laurie-anderson/the-best-thing-about-the-term-performance-artist-is-that-it-includes/) [Laurie Anderson](https://sms4smile.com/quotes/author/laurie-anderson/) > [The best things in life are free. Sunsets and sunrises are free. Air is free. Love is free. Death is free. The best things…](https://sms4smile.com/quotes/frederick-lenz/the-best-things-in-life-are-free-sunsets-and-sunrises-are-free-air-is/) [Frederick Lenz](https://sms4smile.com/quotes/author/frederick-lenz/) > [I always wanted to be a player, but I never had the talent to make the big leagues. So I did the next best…](https://sms4smile.com/quotes/charlie-finley/i-always-wanted-to-be-a-player-but-i-never-had-the-talent-to-make-the/) [Charlie Finley](https://sms4smile.com/quotes/author/charlie-finley/) > [I was a 36C or D, and at 5' 1'', I knew that being a small person with big boobs standing in front of…](https://sms4smile.com/quotes/janeane-garofalo/i-was-a-36c-or-d-and-at-5-1-i-knew-that-being-a-small-person-with-big/) [Janeane Garofalo](https://sms4smile.com/quotes/author/janeane-garofalo/) > [Each time I stop somewhere and look out, there are more people sitting there than there were the time I came before. I think…](https://sms4smile.com/quotes/louie-giglio/each-time-i-stop-somewhere-and-look-out-there-are-more-people-sitting/) [Louie Giglio](https://sms4smile.com/quotes/author/louie-giglio/) > [One of the best things that happened for me as a playwright is becoming a comic-book writer.](https://sms4smile.com/quotes/roberto-aguirre-sacasa/one-of-the-best-things-that-happened-for-me-as-a-playwright-is/) [Roberto Aguirre-Sacasa](https://sms4smile.com/quotes/author/roberto-aguirre-sacasa/) > [I don't really know who I am as an actor: the best thing would be to experiment with it for the next 30 years…](https://sms4smile.com/quotes/ben-barnes/i-don-t-really-know-who-i-am-as-an-actor-the-best-thing-would-be-to/) [Ben Barnes](https://sms4smile.com/quotes/author/ben-barnes/) > [The best thing about time passing is the privilege of running out of it, of watching the wave of mortality break over me and…](https://sms4smile.com/quotes/sarah-manguso/the-best-thing-about-time-passing-is-the-privilege-of-running-out-of/) [Sarah Manguso](https://sms4smile.com/quotes/author/sarah-manguso/) > [What was the best thing before sliced bread?](https://sms4smile.com/quotes/george-carlin/what-was-the-best-thing-before-sliced-bread/) [George Carlin](https://sms4smile.com/quotes/author/george-carlin/) > [The best thing about waking up early is seeing the sun rise.](https://sms4smile.com/quotes/bridgit-mendler/the-best-thing-about-waking-up-early-is-seeing-the-sun-rise/) [Bridgit Mendler](https://sms4smile.com/quotes/author/bridgit-mendler/) [Browse all 1,021 Best things quotes ](https://sms4smile.com/quotes/about/best-things/) ```json { "@context": "https://schema.org", "@graph": [ { "@type": "Quotation", "text": "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.", "creator": { "@type": "Person", "name": "Saharon Shelah" }, "isPartOf": { "@id": "https://sms4smile.com/quotes/#website" }, "url": "https://sms4smile.com/quotes/saharon-shelah/given-a-conjecture-the-best-thing-is-to-prove-it-the-second-best/", "about": { "@type": "Thing", "name": "Best things" }, "@id": "https://sms4smile.com/quotes/saharon-shelah/given-a-conjecture-the-best-thing-is-to-prove-it-the-second-best/#quotation", "image": { "@type": "ImageObject", "@id": "https://sms4smile.com/quotes/i/ff8/saharon-shelah-67459_best-things_given-a-conjecture-the-best-thing-is-to_1331678.jpg", "contentUrl": "https://sms4smile.com/quotes/i/ff8/saharon-shelah-67459_best-things_given-a-conjecture-the-best-thing-is-to_1331678.jpg", "url": "https://sms4smile.com/quotes/i/ff8/saharon-shelah-67459_best-things_given-a-conjecture-the-best-thing-is-to_1331678.jpg", "width": 1080, "height": 1080, "caption": "“Given a conjecture, the best thing is to prove it. The second best thing is to disprove it. The third best…” — Saharon Shelah", "creditText": "SMS4Smile Quotes", "creator": { "@id": "https://sms4smile.com/quotes/#organization" } } }, { "@type": "BreadcrumbList", "itemListElement": [ { "@type": "ListItem", "position": 1, "name": "Home", "item": "https://sms4smile.com/" }, { "@type": "ListItem", "position": 2, "name": "Quotes", "item": "https://sms4smile.com/quotes/" }, { "@type": "ListItem", "position": 3, "name": "Saharon Shelah", "item": "https://sms4smile.com/quotes/author/saharon-shelah/" }, { "@type": "ListItem", "position": 4, "name": "Given a conjecture, the best thing...", "item": "https://sms4smile.com/quotes/saharon-shelah/given-a-conjecture-the-best-thing-is-to-prove-it-the-second-best/" } ], "@id": "https://sms4smile.com/quotes/saharon-shelah/given-a-conjecture-the-best-thing-is-to-prove-it-the-second-best/#breadcrumb" }, { "@type": "WebSite", "@id": "https://sms4smile.com/quotes/#website", "name": "SMS4Smile Quotes", "url": "https://sms4smile.com/quotes/", "publisher": { "@id": "https://sms4smile.com/quotes/#organization" } }, { "@type": "Organization", "@id": "https://sms4smile.com/quotes/#organization", "name": "SMS4Smile Quotes", "url": "https://sms4smile.com/quotes/", "logo": { "@type": "ImageObject", "url": "https://sms4smile.com/quotes/wp-content/themes/sq/assets/icons/icon-512.png", "width": 512, "height": 512 } } ] } ```