--- title: "Meaning & Key Takeaway of: This common and unfortunate fact of the…" description: "\"This common and unfortunate fact of the lack of adequate presentation of basic ideas and motivations of almost any mathematical theory is probably due ..." image: "https://sms4smile.com/quotes/i/5ef/mikhail-leonidovich-gromov-570_adequate_this-common-and-unfortunate-fact-of-the_2136881.jpg" --- # This common and unfortunate fact of the lack of adequate… ![“This common and unfortunate fact of the lack of adequate presentation of basic ideas and motivations of almost any mathematical theory is probably due to the binary nature of mathematical perception. Either you have no inkling of an idea, or, once you have understood it, the very idea appears so…” quote by Mikhail Leonidovich Gromov](https://sms4smile.com/quotes/i/5ef/mikhail-leonidovich-gromov-570_adequate_this-common-and-unfortunate-fact-of-the_2136881.jpg) [Download](https://sms4smile.com/quotes/i/5ef/mikhail-leonidovich-gromov-570_adequate_this-common-and-unfortunate-fact-of-the_2136881.jpg) [Open image](https://sms4smile.com/quotes/i/5ef/mikhail-leonidovich-gromov-570_adequate_this-common-and-unfortunate-fact-of-the_2136881.jpg) > “This common and unfortunate fact of the lack of adequate presentation of basic ideas and motivations of almost any mathematical theory is probably due to the binary nature of mathematical perception. Either you have no inkling of an idea, or, once you have understood it, the very idea appears so embarrassingly obvious that you feel reluctant to say it aloud.” [Mikhail Leonidovich Gromov](https://sms4smile.com/quotes/author/mikhail-leonidovich-gromov/) ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. Mathematical ideas often seem either completely obscure or trivially obvious, making them hard to articulate and teach. **In simple terms:** Ideas feel either hidden or obvious, hindering clear explanation. Key Takeaway Recognize and bridge the gap between intuition and formalism. Themes education communication mathematics perception Mood reflective analytical Type pedagogical philosophical When to use this quote - lecture preparation - writing textbooks - peer tutoring - public outreach - curriculum design Key Concepts cognitive bias knowledge transfer epistemic humility Questions to Reflect On - How can we make obvious ideas feel novel? - What strategies help convey hidden concepts without oversimplifying? A Different Perspective Overemphasis on obviousness can discourage deeper inquiry and marginalize beginners. ★ ★ ★ ★ ★ No ratings yet [Binary](https://sms4smile.com/quotes/about/binary/) [Facts](https://sms4smile.com/quotes/about/facts/) [Ideas](https://sms4smile.com/quotes/about/ideas/) [Math](https://sms4smile.com/quotes/about/math/) [Mathematics](https://sms4smile.com/quotes/about/mathematics/) [Motivation](https://sms4smile.com/quotes/about/motivation/) [Nature](https://sms4smile.com/quotes/about/nature/) [Perception](https://sms4smile.com/quotes/about/perception/) [Presentation](https://sms4smile.com/quotes/about/presentation/) [Reluctant](https://sms4smile.com/quotes/about/reluctant/) ## Related quotes > [I don't think there's anything unique about human intellience. 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Barber](https://sms4smile.com/quotes/author/e-j-w-barber/) > [“I live in a binary star system, my two suns being my two sons.”](https://sms4smile.com/quotes/corrado-ghinamo/i-live-in-a-binary-star-system-my-two-suns-being-my-two-sons/) Corrado Ghinamo > [Any sufficiently crisp question can be answered by a single binary digit-0 or 1, yes or no.](https://sms4smile.com/quotes/carl-sagan/any-sufficiently-crisp-question-can-be-answered-by-a-single-binary/) [Carl Sagan](https://sms4smile.com/quotes/author/carl-sagan/) > [Not all bodies are born in male or female. 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