--- title: "Meaning & Key Takeaway of: I have often noticed that when people…" description: "\"I have often noticed that when people come to understand a mathematical proposition in some other way than that of the ordinary demonstration, they pro..." image: "https://sms4smile.com/quotes/i/34d/georg-c-lichtenberg-1087_demonstration_i-have-often-noticed-that-when-people-co_1943543.png" --- # I have often noticed that when people come to understand a… ![“I have often noticed that when people come to understand a mathematical proposition in some other way than that of the ordinary demonstration, they promptly say, "Oh, I see. That's how it must be." This is a sign that they explain it to themselves from within their own system.” quote by Georg C. Lichtenberg](https://sms4smile.com/quotes/i/34d/georg-c-lichtenberg-1087_demonstration_i-have-often-noticed-that-when-people-co_1943543.png) [Download](https://sms4smile.com/quotes/i/34d/georg-c-lichtenberg-1087_demonstration_i-have-often-noticed-that-when-people-co_1943543.png) [Open image](https://sms4smile.com/quotes/i/34d/georg-c-lichtenberg-1087_demonstration_i-have-often-noticed-that-when-people-co_1943543.png) > “I have often noticed that when people come to understand a mathematical proposition in some other way than that of the ordinary demonstration, they promptly say, "Oh, I see. That's how it must be." This is a sign that they explain it to themselves from within their own system.” [Georg C. Lichtenberg](https://sms4smile.com/quotes/author/georg-c-lichtenberg/) ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. Understanding a proposition in a personal way leads to instant confidence, showing internalization of the idea. **In simple terms:** Personal insight creates confidence. Key Takeaway Trust your own reasoning. Themes learning confidence personal insight Mood reflective analytical Type philosophical educational When to use this quote - studying math - self‑teaching - problem solving Key Concepts cognitive restructuring metacognition Questions to Reflect On - How does internal explanation differ from formal proof? - When might confidence be misplaced? A Different Perspective May overlook hidden flaws if not externally checked. ★ ★ ★ ★ ★ No ratings yet [Demonstration](https://sms4smile.com/quotes/about/demonstration/) [Math](https://sms4smile.com/quotes/about/math/) [Mathematics](https://sms4smile.com/quotes/about/mathematics/) [People](https://sms4smile.com/quotes/about/people/) [Understanding](https://sms4smile.com/quotes/about/understanding/) ## Related quotes > [Mathematics is a logical method. . . . Mathematical propositions express no thoughts. In life it is never a mathematical proposition which we need,…](https://sms4smile.com/quotes/ludwig-wittgenstein/mathematics-is-a-logical-method-mathematical-propositions-express-no/) [Ludwig Wittgenstein](https://sms4smile.com/quotes/author/ludwig-wittgenstein/) > [“That’s right, but it’s not a mathematical proposition. It’s a sociological observation and there is always the possibility of exceptions to such observations." -…](https://sms4smile.com/quotes/isaac-asimov/that-s-right-but-it-s-not-a-mathematical-proposition-it-s-a/) [Isaac Asimov](https://sms4smile.com/quotes/author/isaac-asimov/) > [Sooner or later we've all got to confront the reality that we have got to come to understand who we are and what we're…](https://sms4smile.com/quotes/ayad-akhtar/sooner-or-later-we-ve-all-got-to-confront-the-reality-that-we-have/) [Ayad Akhtar](https://sms4smile.com/quotes/author/ayad-akhtar/) > [A lot of women have come to understand that you can't just show up and say I'm unhappy, you have to then go out…](https://sms4smile.com/quotes/cokie-roberts/a-lot-of-women-have-come-to-understand-that-you-can-t-just-show-up/) [Cokie Roberts](https://sms4smile.com/quotes/author/cokie-roberts/) > [“You take a different view of your actions when you come to understand, when you are made to understand every day that your existence…](https://sms4smile.com/quotes/joseph-conrad/you-take-a-different-view-of-your-actions-when-you-come-to-understand/) [Joseph Conrad](https://sms4smile.com/quotes/author/joseph-conrad/) > [“I guess I don't really understand you yet,' I said. 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When we are all covered…](https://sms4smile.com/quotes/karin-altenberg/the-only-way-we-can-come-to-understand-other-beings-is-by-tainting/) Karin Altenberg > [Boy, when you come to study something, and you come to understand it - you know, even if it's just a little discovery that…](https://sms4smile.com/quotes/carolyn-porco/boy-when-you-come-to-study-something-and-you-come-to-understand-it/) [Carolyn Porco](https://sms4smile.com/quotes/author/carolyn-porco/) > [I've come to understand my role. On some level, I provide the context for them to shine. I also know my role is the…](https://sms4smile.com/quotes/kathy-mattea/i-ve-come-to-understand-my-role-on-some-level-i-provide-the-context/) [Kathy Mattea](https://sms4smile.com/quotes/author/kathy-mattea/) ## More by Georg C. Lichtenberg > [If people should ever start to do only what is necessary millions would die of hunger.](https://sms4smile.com/quotes/georg-c-lichtenberg/if-people-should-ever-start-to-do-only-what-is-necessary-millions/) [Georg C. Lichtenberg](https://sms4smile.com/quotes/author/georg-c-lichtenberg/) > [We can see nothing whatever of the soul unless it is visible in the expression of the countenance; one might call the faces at…](https://sms4smile.com/quotes/georg-c-lichtenberg/we-can-see-nothing-whatever-of-the-soul-unless-it-is-visible-in-the/) [Georg C. Lichtenberg](https://sms4smile.com/quotes/author/georg-c-lichtenberg/) > [The wisdom of providence is as much revealed in the rarity of genius, as in the circumstance that not everyone is deaf or blind.](https://sms4smile.com/quotes/georg-c-lichtenberg/the-wisdom-of-providence-is-as-much-revealed-in-the-rarity-of-genius/) [Georg C. 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Lichtenberg](https://sms4smile.com/quotes/author/georg-c-lichtenberg/) > [To live when you do not want to is dreadful, but it would be even more terrible to be immortal when you did not…](https://sms4smile.com/quotes/georg-c-lichtenberg/to-live-when-you-do-not-want-to-is-dreadful-but-it-would-be-even-more/) [Georg C. Lichtenberg](https://sms4smile.com/quotes/author/georg-c-lichtenberg/) > [He who understands the wise is wise already.](https://sms4smile.com/quotes/georg-c-lichtenberg/he-who-understands-the-wise-is-wise-already/) [Georg C. Lichtenberg](https://sms4smile.com/quotes/author/georg-c-lichtenberg/) > [The fruits of philosophy are the important thing, not the philosophy itself. When we ask the time, we don't want to know how watches…](https://sms4smile.com/quotes/georg-c-lichtenberg/the-fruits-of-philosophy-are-the-important-thing-not-the-philosophy/) [Georg C. Lichtenberg](https://sms4smile.com/quotes/author/georg-c-lichtenberg/) > [He who says he hates all kinds of flattery, and says so in earnest, has undoubtedly not as yet become acquainted with all kinds…](https://sms4smile.com/quotes/georg-c-lichtenberg/he-who-says-he-hates-all-kinds-of-flattery-and-says-so-in-earnest-has/) [Georg C. Lichtenberg](https://sms4smile.com/quotes/author/georg-c-lichtenberg/) > [One can live in this world on soothsaying but not on truth saying.](https://sms4smile.com/quotes/georg-c-lichtenberg/one-can-live-in-this-world-on-soothsaying-but-not-on-truth-saying/) [Georg C. Lichtenberg](https://sms4smile.com/quotes/author/georg-c-lichtenberg/) > [Actual aristocracy cannot be abolished by any law: all the law can do is decree how it is to be imparted and who is…](https://sms4smile.com/quotes/georg-c-lichtenberg/actual-aristocracy-cannot-be-abolished-by-any-law-all-the-law-can-do/) [Georg C. Lichtenberg](https://sms4smile.com/quotes/author/georg-c-lichtenberg/) > [One of the greatest and also the commonest of faults is for men to believe that, because they never hear their shortcomings spoken of,…](https://sms4smile.com/quotes/georg-c-lichtenberg/one-of-the-greatest-and-also-the-commonest-of-faults-is-for-men-to/) [Georg C. Lichtenberg](https://sms4smile.com/quotes/author/georg-c-lichtenberg/) > [People who never have any time on their hands are those who do the least.](https://sms4smile.com/quotes/georg-c-lichtenberg/people-who-never-have-any-time-on-their-hands-are-those-who-do-the/) [Georg C. Lichtenberg](https://sms4smile.com/quotes/author/georg-c-lichtenberg/) > [An hour-glass is a reminder not only of time's quick flight, but also of the dust to which we must at last return](https://sms4smile.com/quotes/georg-c-lichtenberg/an-hour-glass-is-a-reminder-not-only-of-time-s-quick-flight-but-also/) [Georg C. Lichtenberg](https://sms4smile.com/quotes/author/georg-c-lichtenberg/) [Explore all 295 Georg C. Lichtenberg quotes ](https://sms4smile.com/quotes/author/georg-c-lichtenberg/) ## More Demonstration quotes > [Every demonstration of God's faithfulness to us is an opportunity for us to testify of Him to others.](https://sms4smile.com/quotes/max-anders/every-demonstration-of-god-s-faithfulness-to-us-is-an-opportunity-for/) [Max Anders](https://sms4smile.com/quotes/author/max-anders/) > [I liked wrestling a lot better than boxing. I remember thinking at that time that wrestling was a pure demonstration of strength, which I…](https://sms4smile.com/quotes/scott-carpenter/i-liked-wrestling-a-lot-better-than-boxing-i-remember-thinking-at/) [Scott Carpenter](https://sms4smile.com/quotes/author/scott-carpenter/) > [The method of not erring is sought by all the world. 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