--- title: "Meaning & Key Takeaway of: The dot was introduced as a symbol for…" description: "\"The dot was introduced as a symbol for multiplication by Leibniz. On July 29, 1698, he wrote in a letter to Johann Bernoulli: \"I do not like X as a sym..." image: "https://sms4smile.com/quotes/i/c23/gottfried-leibniz-3585_dots_the-dot-was-introduced-as-a-symbol-for-m_1060192.png" --- # The dot was introduced as a symbol for multiplication by… ![“The dot was introduced as a symbol for multiplication by Leibniz. On July 29, 1698, he wrote in a letter to Johann Bernoulli: "I do not like X as a symbol for multiplication, as it is easily confounded with x.” quote by Gottfried Leibniz](https://sms4smile.com/quotes/i/c23/gottfried-leibniz-3585_dots_the-dot-was-introduced-as-a-symbol-for-m_1060192.png) [Download](https://sms4smile.com/quotes/i/c23/gottfried-leibniz-3585_dots_the-dot-was-introduced-as-a-symbol-for-m_1060192.png) [Open image](https://sms4smile.com/quotes/i/c23/gottfried-leibniz-3585_dots_the-dot-was-introduced-as-a-symbol-for-m_1060192.png) > “The dot was introduced as a symbol for multiplication by Leibniz. On July 29, 1698, he wrote in a letter to Johann Bernoulli: "I do not like X as a symbol for multiplication, as it is easily confounded with x.” [Gottfried Leibniz](https://sms4smile.com/quotes/author/gottfried-leibniz/) ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. Leibniz preferred a symbol that avoided confusion, highlighting the importance of clear notation. **In simple terms:** Clear symbols prevent misunderstanding. Key Takeaway Choose unambiguous symbols. Themes mathematics notation clarity communication history Mood analytical reflective Type academic historical When to use this quote - teaching math - publishing papers - software design Key Concepts symbolic logic educational standards precision Questions to Reflect On - Why is notation clarity vital? - How do symbols affect learning? A Different Perspective Changing symbols can cause resistance. ★ ★ ★ ★ ★ No ratings yet [Dot Introduced](https://sms4smile.com/quotes/about/dot-introduced-2583618/) [Dots](https://sms4smile.com/quotes/about/dots/) [Introduced Symbol](https://sms4smile.com/quotes/about/introduced-symbol-2583619/) [July](https://sms4smile.com/quotes/about/july/) [Leibniz](https://sms4smile.com/quotes/about/leibniz/) [Letters](https://sms4smile.com/quotes/about/letters/) [Mathematics](https://sms4smile.com/quotes/about/mathematics/) [Multiplication](https://sms4smile.com/quotes/about/multiplication/) [Multiplication Leibniz](https://sms4smile.com/quotes/about/multiplication-leibniz-2583616/) [Symbol Multiplication](https://sms4smile.com/quotes/about/symbol-multiplication-2583617/) [Symbols](https://sms4smile.com/quotes/about/symbols/) ## Related quotes > [“Nature has established patterns originating in the return of events, but only for the most part. New illnesses flood the human race, so that…](https://sms4smile.com/quotes/gottfried-leibniz/nature-has-established-patterns-originating-in-the-return-of-events/) [Gottfried Leibniz](https://sms4smile.com/quotes/author/gottfried-leibniz/) > [I was trying to run something to ground that had come to my attention when I was working on the Baroque Cycle. That series,…](https://sms4smile.com/quotes/neal-stephenson/i-was-trying-to-run-something-to-ground-that-had-come-to-my-attention/) [Neal Stephenson](https://sms4smile.com/quotes/author/neal-stephenson/) > [“If there is one thing common to the great modern speculative philosophers, Leibniz, Hegel and Deleuze, it is the risk that re-animating the universe…](https://sms4smile.com/quotes/christian-kerslake/if-there-is-one-thing-common-to-the-great-modern-speculative/) [Christian Kerslake](https://sms4smile.com/quotes/author/christian-kerslake/) > [The myth that the founding of American Republic was based on the philosophy of John Locke could only have been maintained, because the history…](https://sms4smile.com/quotes/robert-trout/the-myth-that-the-founding-of-american-republic-was-based-on-the/) [Robert Trout](https://sms4smile.com/quotes/author/robert-trout/) > [“In 1714, Gottfried Wilhelm Leibniz argued that matter alone could never produce a mind. Leibniz was a German philosopher, mathematician, and scientist who is…](https://sms4smile.com/quotes/david-eagleman/in-1714-gottfried-wilhelm-leibniz-argued-that-matter-alone-could/) [David Eagleman](https://sms4smile.com/quotes/author/david-eagleman/) > [“Morality consists in this for each individual: to attempt each time to extend its region of clear expression, to try to augment its amplitude,…](https://sms4smile.com/quotes/gilles-deleuze/morality-consists-in-this-for-each-individual-to-attempt-each-time-to/) [Gilles Deleuze](https://sms4smile.com/quotes/author/gilles-deleuze/) > [“Leibniz's machine was designed to automate the dreary task of solving moral problems”](https://sms4smile.com/quotes/martin-cohen/leibniz-s-machine-was-designed-to-automate-the-dreary-task-of-solving/) [Martin Cohen](https://sms4smile.com/quotes/author/martin-cohen/) > [Leibniz is at the disadvantage of not having seen it. Or perhaps we should count this as an advantage, for anyone who sees it…](https://sms4smile.com/quotes/neal-stephenson/leibniz-is-at-the-disadvantage-of-not-having-seen-it-or-perhaps-we/) [Neal Stephenson](https://sms4smile.com/quotes/author/neal-stephenson/) > [Navarette, a Chinese missionary, agrees with Leibniz and says that "It is the special providence of God that the Chinese did not know what…](https://sms4smile.com/quotes/matthew-tindal/navarette-a-chinese-missionary-agrees-with-leibniz-and-says-that-it/) [Matthew Tindal](https://sms4smile.com/quotes/author/matthew-tindal/) > [“Leibniz said, Music is the mind counting without being conscious it’s counting. An eclipse is maths; it’s the most beautiful maths there is.”](https://sms4smile.com/quotes/erin-kelly/leibniz-said-music-is-the-mind-counting-without-being-conscious-it-s/) [Erin Kelly](https://sms4smile.com/quotes/author/erin-kelly/) > [“Because children have abounding vitality, because they are in spirit fierce and free, therefore they want things repeated and unchanged. They always say, "Do…](https://sms4smile.com/quotes/g-k-chesterton/because-children-have-abounding-vitality-because-they-are-in-spirit/) [G.K. Chesterton](https://sms4smile.com/quotes/author/g-k-chesterton/) > [“Leibniz's development of the symbols and theory behind calculus, which allows for the precise study and modeling of change, gave mathematicians a weapon with…](https://sms4smile.com/quotes/christopher-steiner/leibniz-s-development-of-the-symbols-and-theory-behind-calculus-which/) [Christopher Steiner](https://sms4smile.com/quotes/author/christopher-steiner/) > [Leibniz accepted the argument that there must be indestructible simple entities if there is to be a complex world, but Epicurean morals and politics…](https://sms4smile.com/quotes/catherine-wilson/leibniz-accepted-the-argument-that-there-must-be-indestructible/) [Catherine Wilson](https://sms4smile.com/quotes/author/catherine-wilson/) > [“Starting from Descartes’ commitment to a few absolutely certain innate ideas and reason’s ability to determine some facts about reality a priori, Leibniz ended…](https://sms4smile.com/quotes/lee-braver/starting-from-descartes-commitment-to-a-few-absolutely-certain-innate/) [Lee Braver](https://sms4smile.com/quotes/author/lee-braver/) > [“The careful observations and the acute reasonings of the Italian geologists of the seventeenth and eighteenth centuries; the speculations of Leibnitz in the 'Protogaea'…](https://sms4smile.com/quotes/thomas-henry-huxley/the-careful-observations-and-the-acute-reasonings-of-the-italian/) [Thomas Henry Huxley](https://sms4smile.com/quotes/author/thomas-henry-huxley/) ## More by Gottfried Leibniz > [There are two famous labyrinths where our reason very often goes astray. One concerns the great question of the free and the necessary, above…](https://sms4smile.com/quotes/gottfried-leibniz/there-are-two-famous-labyrinths-where-our-reason-very-often-goes/) [Gottfried Leibniz](https://sms4smile.com/quotes/author/gottfried-leibniz/) > [Either there are no corporeal substances, and bodies are merely phenomena which are true or consistent with each other, such as a rainbow or…](https://sms4smile.com/quotes/gottfried-leibniz/either-there-are-no-corporeal-substances-and-bodies-are-merely/) [Gottfried Leibniz](https://sms4smile.com/quotes/author/gottfried-leibniz/) > [The present is saturated with the past and pregnant with the future.](https://sms4smile.com/quotes/gottfried-leibniz/the-present-is-saturated-with-the-past-and-pregnant-with-the-future/) [Gottfried Leibniz](https://sms4smile.com/quotes/author/gottfried-leibniz/) > [Make me the the master of education, and I will undertake to change the world.](https://sms4smile.com/quotes/gottfried-leibniz/make-me-the-the-master-of-education-and-i-will-undertake-to-change/) [Gottfried Leibniz](https://sms4smile.com/quotes/author/gottfried-leibniz/) > [All the different classes of beings which taken together make up the universe are, in the ideas of God who knows distinctly their essential…](https://sms4smile.com/quotes/gottfried-leibniz/all-the-different-classes-of-beings-which-taken-together-make-up-the/) [Gottfried Leibniz](https://sms4smile.com/quotes/author/gottfried-leibniz/) > [I hold that the mark of a genuine idea is that its possibility can be proved, either a priori by conceiving its cause or…](https://sms4smile.com/quotes/gottfried-leibniz/i-hold-that-the-mark-of-a-genuine-idea-is-that-its-possibility-can-be/) [Gottfried Leibniz](https://sms4smile.com/quotes/author/gottfried-leibniz/) > [The monad, of which we shall speak here, is nothing but a simple substance which enters into compounds; simple, that is to say, without…](https://sms4smile.com/quotes/gottfried-leibniz/the-monad-of-which-we-shall-speak-here-is-nothing-but-a-simple/) [Gottfried Leibniz](https://sms4smile.com/quotes/author/gottfried-leibniz/) > [There is no way in which a simple substance could begin in the course of nature, since it cannot be formed by means of…](https://sms4smile.com/quotes/gottfried-leibniz/there-is-no-way-in-which-a-simple-substance-could-begin-in-the-course/) [Gottfried Leibniz](https://sms4smile.com/quotes/author/gottfried-leibniz/) > [In symbols one observes an advantage in discovery which is greatest when they express the exact nature of a thing briefly and, as it…](https://sms4smile.com/quotes/gottfried-leibniz/in-symbols-one-observes-an-advantage-in-discovery-which-is-greatest/) [Gottfried Leibniz](https://sms4smile.com/quotes/author/gottfried-leibniz/) > [There is nothing without reason.](https://sms4smile.com/quotes/gottfried-leibniz/there-is-nothing-without-reason/) [Gottfried Leibniz](https://sms4smile.com/quotes/author/gottfried-leibniz/) > [God, possessing supreme and infinite wisdom, acts in the most perfect manner, not only metaphysically, but also morally speaking, and ... with respect to…](https://sms4smile.com/quotes/gottfried-leibniz/god-possessing-supreme-and-infinite-wisdom-acts-in-the-most-perfect/) [Gottfried Leibniz](https://sms4smile.com/quotes/author/gottfried-leibniz/) > [It can have its effect only through the intervention of God, inasmuch as in the ideas of God a monad rightly demands that God,…](https://sms4smile.com/quotes/gottfried-leibniz/it-can-have-its-effect-only-through-the-intervention-of-god-inasmuch/) [Gottfried Leibniz](https://sms4smile.com/quotes/author/gottfried-leibniz/) > [I do not conceive of any reality at all as without genuine unity.](https://sms4smile.com/quotes/gottfried-leibniz/i-do-not-conceive-of-any-reality-at-all-as-without-genuine-unity/) [Gottfried Leibniz](https://sms4smile.com/quotes/author/gottfried-leibniz/) > [The pleasure we obtain from music comes from counting, but counting unconsciously. Music is nothing but unconscious arithmetic.](https://sms4smile.com/quotes/gottfried-leibniz/the-pleasure-we-obtain-from-music-comes-from-counting-but-counting/) [Gottfried Leibniz](https://sms4smile.com/quotes/author/gottfried-leibniz/) > [If we were magically shrunk and put into someone's brain while she was thinking, we would see all the pumps, pistons, gears and levers…](https://sms4smile.com/quotes/gottfried-leibniz/if-we-were-magically-shrunk-and-put-into-someone-s-brain-while-she/) [Gottfried Leibniz](https://sms4smile.com/quotes/author/gottfried-leibniz/) [Explore all 127 Gottfried Leibniz quotes ](https://sms4smile.com/quotes/author/gottfried-leibniz/) ## More Dots quotes > [The prophet who fails to present a bearable alternative and yet preaches doom is part of the trap that he postulates. Not only does…](https://sms4smile.com/quotes/margaret-mead/the-prophet-who-fails-to-present-a-bearable-alternative-and-yet/) [Margaret Mead](https://sms4smile.com/quotes/author/margaret-mead/) > [Stefan: "Indian with a dot, not a feather.](https://sms4smile.com/quotes/patricia-briggs/stefan-indian-with-a-dot-not-a-feather/) [Patricia Briggs](https://sms4smile.com/quotes/author/patricia-briggs/) > [“Make it a quest to never give up even when the dots seem as if they are difficult to connect.”](https://sms4smile.com/quotes/charlena-jackson/make-it-a-quest-to-never-give-up-even-when-the-dots-seem-as-if-they/) [Charlena Jackson](https://sms4smile.com/quotes/author/charlena-jackson/) > [At seventy-three I learned a little about the real structure of animals, plants, birds, fishes and insects. Consequently when I am eighty I'll have…](https://sms4smile.com/quotes/hokusai/at-seventy-three-i-learned-a-little-about-the-real-structure-of/) [Hokusai](https://sms4smile.com/quotes/author/hokusai/) > [People, I am actually fairly smart. Why has this not occurred to anyone? The information is all out there, if you go looking for…](https://sms4smile.com/quotes/tom-clancy/people-i-am-actually-fairly-smart-why-has-this-not-occurred-to-anyone/) [Tom Clancy](https://sms4smile.com/quotes/author/tom-clancy/) > [Meaning. If you're going to die, you want to find meaning in life. You want to connect the dots.](https://sms4smile.com/quotes/franny-billingsley/meaning-if-you-re-going-to-die-you-want-to-find-meaning-in-life-you/) [Franny Billingsley](https://sms4smile.com/quotes/author/franny-billingsley/) > [A tiny blue dot set in a sunbeam. Here it is. That's where we live. That's home. We humans are one species and this…](https://sms4smile.com/quotes/carl-sagan/a-tiny-blue-dot-set-in-a-sunbeam-here-it-is-that-s-where-we-live-that/) [Carl Sagan](https://sms4smile.com/quotes/author/carl-sagan/) > [If you're going climbing with young people, you get very, very used to seeing your climbing partner as a tiny little dot.](https://sms4smile.com/quotes/chris-bonington/if-you-re-going-climbing-with-young-people-you-get-very-very-used-to/) [Chris Bonington](https://sms4smile.com/quotes/author/chris-bonington/) > [“Zebras dream of polka-dots”](https://sms4smile.com/quotes/phil-caruso/zebras-dream-of-polka-dots/) [Phil Caruso](https://sms4smile.com/quotes/author/phil-caruso/) > [My life is a dot lost among thousands of other dots.](https://sms4smile.com/quotes/yayoi-kusama/my-life-is-a-dot-lost-among-thousands-of-other-dots/) [Yayoi Kusama](https://sms4smile.com/quotes/author/yayoi-kusama/) > [I was an infinitely hot and dense dot.](https://sms4smile.com/quotes/mark-leyner/i-was-an-infinitely-hot-and-dense-dot/) [Mark Leyner](https://sms4smile.com/quotes/author/mark-leyner/) > [Aight baby show me the exact spot, meet me at Hoyt & Schemethorn at 3 on the dot](https://sms4smile.com/quotes/jeru-the-damaja/aight-baby-show-me-the-exact-spot-meet-me-at-hoyt-schemethorn-at-3-on/) [Jeru the Damaja](https://sms4smile.com/quotes/author/jeru-the-damaja/) > [Let man then contemplate nature in full and lofty majesty, and turn his eyes away from the mean objects which surround him. Let him…](https://sms4smile.com/quotes/blaise-pascal/let-man-then-contemplate-nature-in-full-and-lofty-majesty-and-turn/) [Blaise Pascal](https://sms4smile.com/quotes/author/blaise-pascal/) > [Anybody who takes Martin Luther King seriously has got to go beyond the standard understanding of who he was, has to connect those dots.](https://sms4smile.com/quotes/cornel-west/anybody-who-takes-martin-luther-king-seriously-has-got-to-go-beyond/) [Cornel West](https://sms4smile.com/quotes/author/cornel-west/) > [Somebody can paint with a fine brush like Monet and do millions of little dots or somebody can splatter it up there like Kandinsky…](https://sms4smile.com/quotes/patrick-wilson/somebody-can-paint-with-a-fine-brush-like-monet-and-do-millions-of/) [Patrick Wilson](https://sms4smile.com/quotes/author/patrick-wilson/) [Browse all 309 Dots quotes ](https://sms4smile.com/quotes/about/dots/) ```json { "@context": "https://schema.org", "@graph": [ { "@type": "Quotation", "text": "The dot was introduced as a symbol for multiplication by Leibniz. 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