--- title: "Meaning & Key Takeaway of: Mathematics may be defined as the economy…" description: "\"Mathematics may be defined as the economy of counting. There is no problem in the whole of mathematics which cannot be solved by direct counting.\" — Er..." image: "https://sms4smile.com/quotes/i/061/ernst-mach-15026_counting_mathematics-may-be-defined-as-the-econom_610001.png" --- # Mathematics may be defined as the economy of counting… ![“Mathematics may be defined as the economy of counting. There is no problem in the whole of mathematics which cannot be solved by direct counting.” quote by Ernst Mach](https://sms4smile.com/quotes/i/061/ernst-mach-15026_counting_mathematics-may-be-defined-as-the-econom_610001.png) [Download](https://sms4smile.com/quotes/i/061/ernst-mach-15026_counting_mathematics-may-be-defined-as-the-econom_610001.png) [Open image](https://sms4smile.com/quotes/i/061/ernst-mach-15026_counting_mathematics-may-be-defined-as-the-econom_610001.png) > “Mathematics may be defined as the economy of counting. There is no problem in the whole of mathematics which cannot be solved by direct counting.” [Ernst Mach](https://sms4smile.com/quotes/author/ernst-mach/) ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. Mathematics can be reduced to counting; every problem has a solution through enumeration. **In simple terms:** Counting can solve any math problem. Key Takeaway Use enumeration to simplify problems. Themes mathematics problem solving logic Mood analytical inquisitive Type philosophical inspirational When to use this quote - teaching - research - software development - data analysis - education Key Concepts combinatorics number theory algorithmic thinking Questions to Reflect On - When is counting insufficient? - How to handle infinite possibilities? A Different Perspective Not all problems are practical to count directly. ★ ★ ★ ★ ★ No ratings yet [Economy](https://sms4smile.com/quotes/about/economy/) [Math](https://sms4smile.com/quotes/about/math/) [Mathematics](https://sms4smile.com/quotes/about/mathematics/) [Problem](https://sms4smile.com/quotes/about/problem/) ## Related quotes > [I'm sure that some of them will be very hard and I'll have a sense of achievement again, but nothing will mean the same…](https://sms4smile.com/quotes/andrew-wiles/i-m-sure-that-some-of-them-will-be-very-hard-and-i-ll-have-a-sense-of/) [Andrew Wiles](https://sms4smile.com/quotes/author/andrew-wiles/) > [The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.](https://sms4smile.com/quotes/andrew-wiles/the-definition-of-a-good-mathematical-problem-is-the-mathematics-it/) [Andrew Wiles](https://sms4smile.com/quotes/author/andrew-wiles/) > [Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then suchand such another…](https://sms4smile.com/quotes/bertrand-russell/pure-mathematics-consists-entirely-of-assertions-to-the-effect-that-2/) [Bertrand Russell](https://sms4smile.com/quotes/author/bertrand-russell/) > [“Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such…](https://sms4smile.com/quotes/bertrand-russell/pure-mathematics-consists-entirely-of-assertions-to-the-effect-that/) [Bertrand Russell](https://sms4smile.com/quotes/author/bertrand-russell/) > [Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is…](https://sms4smile.com/quotes/bertrand-russell/mathematics-may-be-defined-as-the-subject-in-which-we-never-know-what/) [Bertrand Russell](https://sms4smile.com/quotes/author/bertrand-russell/) > [Mathematics is often defined as the science of space and number . . . it was not until the recent resonance of computers and…](https://sms4smile.com/quotes/lynn-steen/mathematics-is-often-defined-as-the-science-of-space-and-number-it/) [Lynn Steen](https://sms4smile.com/quotes/author/lynn-steen/) > [Why do I tire of counting sheep?](https://sms4smile.com/quotes/owl-city/why-do-i-tire-of-counting-sheep/) [Owl City](https://sms4smile.com/quotes/author/owl-city/) > [One foot in front of the other, counting tiles on the floor so I don't have to focus the blur of painted smiles, fake…](https://sms4smile.com/quotes/ellen-hopkins/one-foot-in-front-of-the-other-counting-tiles-on-the-floor-so-i-don-t/) [Ellen Hopkins](https://sms4smile.com/quotes/author/ellen-hopkins/) > [Suddenly the full long wail of a ship's horn surged through the open window and flooded the dim room - a cry of boundless,…](https://sms4smile.com/quotes/yukio-mishima/suddenly-the-full-long-wail-of-a-ship-s-horn-surged-through-the-open/) [Yukio Mishima](https://sms4smile.com/quotes/author/yukio-mishima/) > [“were counting on her. 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People are counting on that.](https://sms4smile.com/quotes/sarah-barthel/we-have-to-be-innovative-we-have-to-be-fresh-we-have-to-be-new-people/) [Sarah Barthel](https://sms4smile.com/quotes/author/sarah-barthel/) > [If my campaign is not in the debate, we will not be talking about how we really fix this problem of endless and expanding…](https://sms4smile.com/quotes/jill-stein/if-my-campaign-is-not-in-the-debate-we-will-not-be-talking-about-how/) [Jill Stein](https://sms4smile.com/quotes/author/jill-stein/) ## More by Ernst Mach > [Physics is experience, arranged in economical order.](https://sms4smile.com/quotes/ernst-mach/physics-is-experience-arranged-in-economical-order/) [Ernst Mach](https://sms4smile.com/quotes/author/ernst-mach/) > [Science itself, therefore, may be regarded as a minimal problem, consisting of the completest possible presentment of facts with the least possible expenditure of…](https://sms4smile.com/quotes/ernst-mach/science-itself-therefore-may-be-regarded-as-a-minimal-problem/) [Ernst Mach](https://sms4smile.com/quotes/author/ernst-mach/) > [In reality, the law always contains less than the fact itself, because it does not reproduce the fact as a whole but only in…](https://sms4smile.com/quotes/ernst-mach/in-reality-the-law-always-contains-less-than-the-fact-itself-because/) [Ernst Mach](https://sms4smile.com/quotes/author/ernst-mach/) > [The presentations and conceptions of the average man of the world are formed and dominated, not by the full and pure desire for knowledge…](https://sms4smile.com/quotes/ernst-mach/the-presentations-and-conceptions-of-the-average-man-of-the-world-are/) [Ernst Mach](https://sms4smile.com/quotes/author/ernst-mach/) > [“To us investigators, the concept 'soul' is irrelevant and a matter for laughter.”](https://sms4smile.com/quotes/ernst-mach/to-us-investigators-the-concept-soul-is-irrelevant-and-a-matter-for/) [Ernst Mach](https://sms4smile.com/quotes/author/ernst-mach/) > [Scientists must use the simplest means of arriving at their results and exclude everything not perceived by the senses.](https://sms4smile.com/quotes/ernst-mach/scientists-must-use-the-simplest-means-of-arriving-at-their-results/) [Ernst Mach](https://sms4smile.com/quotes/author/ernst-mach/) > [Personally, people know themselves very poorly.](https://sms4smile.com/quotes/ernst-mach/personally-people-know-themselves-very-poorly/) [Ernst Mach](https://sms4smile.com/quotes/author/ernst-mach/) > [“But we must not forget that all things in the world are connected with one another and depend on one another, and that we…](https://sms4smile.com/quotes/ernst-mach/but-we-must-not-forget-that-all-things-in-the-world-are-connected/) [Ernst Mach](https://sms4smile.com/quotes/author/ernst-mach/) > [If our dreams were more regular, more connected, more stable, they would also have more practical importance for us.](https://sms4smile.com/quotes/ernst-mach/if-our-dreams-were-more-regular-more-connected-more-stable-they-would/) [Ernst Mach](https://sms4smile.com/quotes/author/ernst-mach/) > [Strange as it may sound, the power of mathematics rests on its evasion of all unnecessary thought and on its wonderful saving of mental…](https://sms4smile.com/quotes/ernst-mach/strange-as-it-may-sound-the-power-of-mathematics-rests-on-its-evasion/) [Ernst Mach](https://sms4smile.com/quotes/author/ernst-mach/) > [The acquisition of the most elementary truth does not devolve upon the individual alone: it is pre-effected in the development of the race.](https://sms4smile.com/quotes/ernst-mach/the-acquisition-of-the-most-elementary-truth-does-not-devolve-upon/) [Ernst Mach](https://sms4smile.com/quotes/author/ernst-mach/) > [The history of the development of mechanics is quite indispensable to a full comprehension of the science in its present condition. It also affords…](https://sms4smile.com/quotes/ernst-mach/the-history-of-the-development-of-mechanics-is-quite-indispensable-to/) [Ernst Mach](https://sms4smile.com/quotes/author/ernst-mach/) > [The task which we have set ourselves is simply to show why and for what purpose we hold that standpoint during most of our…](https://sms4smile.com/quotes/ernst-mach/the-task-which-we-have-set-ourselves-is-simply-to-show-why-and-for/) [Ernst Mach](https://sms4smile.com/quotes/author/ernst-mach/) > [All this, the positive and physical essence of mechanics, which makes its chief and highest interest for a student of nature, is in existing…](https://sms4smile.com/quotes/ernst-mach/all-this-the-positive-and-physical-essence-of-mechanics-which-makes/) [Ernst Mach](https://sms4smile.com/quotes/author/ernst-mach/) > [Science is the most complete presentment of facts with the least expenditure of thought](https://sms4smile.com/quotes/ernst-mach/science-is-the-most-complete-presentment-of-facts-with-the-least/) [Ernst Mach](https://sms4smile.com/quotes/author/ernst-mach/) [Explore all 44 Ernst Mach quotes ](https://sms4smile.com/quotes/author/ernst-mach/) ## More Counting quotes > [If my campaign is not in the debate, we will not be talking about how we really fix this problem of endless and expanding…](https://sms4smile.com/quotes/jill-stein/if-my-campaign-is-not-in-the-debate-we-will-not-be-talking-about-how/) [Jill Stein](https://sms4smile.com/quotes/author/jill-stein/) > [We have to be innovative, we have to be fresh, we have to be new. People are counting on that.](https://sms4smile.com/quotes/sarah-barthel/we-have-to-be-innovative-we-have-to-be-fresh-we-have-to-be-new-people/) [Sarah Barthel](https://sms4smile.com/quotes/author/sarah-barthel/) > [There is us living the Cuban experience that we believe is ours. We do not believe that it is perfect, but it has been…](https://sms4smile.com/quotes/alejandro-castro-espin/there-is-us-living-the-cuban-experience-that-we-believe-is-ours-we-do/) [Alejandro Castro Espin](https://sms4smile.com/quotes/author/alejandro-castro-espin/) > [I don't count my sit-ups. I only start counting when it starts hurting. That is when I start counting, because then it really counts.…](https://sms4smile.com/quotes/muhammad-ali/i-don-t-count-my-sit-ups-i-only-start-counting-when-it-starts-hurting/) [Muhammad Ali](https://sms4smile.com/quotes/author/muhammad-ali/) > [They're counting on your patriotism to distract you from their plunder. They're counting on you to be standing at attention with your hand over…](https://sms4smile.com/quotes/bill-moyers/they-re-counting-on-your-patriotism-to-distract-you-from-their/) [Bill Moyers](https://sms4smile.com/quotes/author/bill-moyers/) > [“were counting on her. She couldn’t let them down.”](https://sms4smile.com/quotes/laurie-leclair/were-counting-on-her-she-couldn-t-let-them-down/) [Laurie LeClair](https://sms4smile.com/quotes/author/laurie-leclair/) > [Suddenly the full long wail of a ship's horn surged through the open window and flooded the dim room - a cry of boundless,…](https://sms4smile.com/quotes/yukio-mishima/suddenly-the-full-long-wail-of-a-ship-s-horn-surged-through-the-open/) [Yukio Mishima](https://sms4smile.com/quotes/author/yukio-mishima/) > [One foot in front of the other, counting tiles on the floor so I don't have to focus the blur of painted smiles, fake…](https://sms4smile.com/quotes/ellen-hopkins/one-foot-in-front-of-the-other-counting-tiles-on-the-floor-so-i-don-t/) [Ellen Hopkins](https://sms4smile.com/quotes/author/ellen-hopkins/) > [Why do I tire of counting sheep?](https://sms4smile.com/quotes/owl-city/why-do-i-tire-of-counting-sheep/) [Owl City](https://sms4smile.com/quotes/author/owl-city/) > [Beware of making a woman cry. God is counting her tears.](https://sms4smile.com/quotes/paulo-coelho/beware-of-making-a-woman-cry-god-is-counting-her-tears/) [Paulo Coelho](https://sms4smile.com/quotes/author/paulo-coelho/) > [Builders insist that success may never come without a compelling personal commitment to something you care about and would be willing to do with…](https://sms4smile.com/quotes/jerry-i-porras/builders-insist-that-success-may-never-come-without-a-compelling/) [Jerry I. Porras](https://sms4smile.com/quotes/author/jerry-i-porras/) > [A business must have a conscience as well as a counting house.](https://sms4smile.com/quotes/montague-burton/a-business-must-have-a-conscience-as-well-as-a-counting-house/) Montague Burton > [The lure in art collecting and its financial rewards, not counting for a moment its aesthetic, cultural and intellectual rewards, is like the trust…](https://sms4smile.com/quotes/steve-martin/the-lure-in-art-collecting-and-its-financial-rewards-not-counting-for/) [Steve Martin](https://sms4smile.com/quotes/author/steve-martin/) > [The best part of our lives we pass in counting on what is to come.](https://sms4smile.com/quotes/william-hazlitt/the-best-part-of-our-lives-we-pass-in-counting-on-what-is-to-come/) [William Hazlitt](https://sms4smile.com/quotes/author/william-hazlitt/) > [For was that all, she thought bleakly, that love ever was? Something that saved one from loneliness? A sort of insurance policy against not…](https://sms4smile.com/quotes/sarah-waters/for-was-that-all-she-thought-bleakly-that-love-ever-was-something/) [Sarah Waters](https://sms4smile.com/quotes/author/sarah-waters/) Browse all 454 Counting quotes ```json { "@context": "https://schema.org", "@graph": [ { "@type": "Quotation", "text": "Mathematics may be defined as the economy of counting. 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