--- title: "Meaning & Key Takeaway of: [Mathematics] unceasingly calls forth the…" description: "\"[Mathematics] unceasingly calls forth the faculties of observation and comparison; one of its principal weapons is induction: it has frequent recourse ..." image: "https://sms4smile.com/quotes/i/301/james-joseph-sylvester-23602_boundless_mathematics-unceasingly-calls-forth-the_447035.jpg" --- # \[Mathematics\] unceasingly calls forth the faculties of… ![“[Mathematics] unceasingly calls forth the faculties of observation and comparison; one of its principal weapons is induction: it has frequent recourse to trial and verification; and it affords a boundless scope for the exercise of the highest efforts of imagination and invention.” quote by James Joseph Sylvester](https://sms4smile.com/quotes/i/301/james-joseph-sylvester-23602_boundless_mathematics-unceasingly-calls-forth-the_447035.jpg) [Download](https://sms4smile.com/quotes/i/301/james-joseph-sylvester-23602_boundless_mathematics-unceasingly-calls-forth-the_447035.jpg) [Open image](https://sms4smile.com/quotes/i/301/james-joseph-sylvester-23602_boundless_mathematics-unceasingly-calls-forth-the_447035.jpg) > “\[Mathematics\] unceasingly calls forth the faculties of observation and comparison; one of its principal weapons is induction: it has frequent recourse to trial and verification; and it affords a boundless scope for the exercise of the highest efforts of imagination and invention.” [James Joseph Sylvester](https://sms4smile.com/quotes/author/james-joseph-sylvester/) ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. Mathematics demands observation, comparison, and induction, using trial, verification, imagination, and invention to expand knowledge. **In simple terms:** Math requires careful observation, testing, and creative thinking. Key Takeaway Embrace systematic testing and imagination in problem solving. Themes analysis creativity logic imagination methodology Mood curious analytical inspired Type philosophical educational When to use this quote - research - education - engineering - scientific inquiry - product development Key Concepts induction verification trial and error conceptual thinking Questions to Reflect On - How can you balance rigorous testing with creative speculation? - When does imagination become a hindrance? A Different Perspective Complex problems may resist simple induction; intuition alone can mislead. ★ ★ ★ ★ ★ No ratings yet [Boundless](https://sms4smile.com/quotes/about/boundless/) [Comparison](https://sms4smile.com/quotes/about/comparison/) [Effort](https://sms4smile.com/quotes/about/effort/) [Exercise](https://sms4smile.com/quotes/about/exercise/) [Imagination](https://sms4smile.com/quotes/about/imagination/) [Induction](https://sms4smile.com/quotes/about/induction/) [Invention](https://sms4smile.com/quotes/about/invention/) [Mathematics](https://sms4smile.com/quotes/about/mathematics/) [Observation](https://sms4smile.com/quotes/about/observation/) [Scope](https://sms4smile.com/quotes/about/scope/) [Trials](https://sms4smile.com/quotes/about/trials/) [Weapons](https://sms4smile.com/quotes/about/weapons/) ## Related quotes > [In law, as in every other branch of knowledge, the truths given by induction tend to form the premises for new deductions. The lawyers…](https://sms4smile.com/quotes/benjamin-n-cardozo/in-law-as-in-every-other-branch-of-knowledge-the-truths-given-by/) [Benjamin N. Cardozo](https://sms4smile.com/quotes/author/benjamin-n-cardozo/) > [“in the first part, the master-faculties are Observation and Memory, so in the second, the master-faculty is the Discursive Reason.”](https://sms4smile.com/quotes/dorothy-l-sayers/in-the-first-part-the-master-faculties-are-observation-and-memory-so/) [Dorothy L. Sayers](https://sms4smile.com/quotes/author/dorothy-l-sayers/) > [The chicken noticed that the farmer came every day to feed it. It predicted that the farmer would continue to bring food every day.…](https://sms4smile.com/quotes/bertrand-russell/the-chicken-noticed-that-the-farmer-came-every-day-to-feed-it-it/) [Bertrand Russell](https://sms4smile.com/quotes/author/bertrand-russell/) > [A great part of its theories derives an additional charm from the peculiarity that important propositions, with the impress of simplicity on them, are…](https://sms4smile.com/quotes/carl-friedrich-gauss/a-great-part-of-its-theories-derives-an-additional-charm-from-the/) [Carl Friedrich Gauss](https://sms4smile.com/quotes/author/carl-friedrich-gauss/) > [On teacher education: induction into current mandates must not turn into seduction away from best practice.](https://sms4smile.com/quotes/andy-hargreaves/on-teacher-education-induction-into-current-mandates-must-not-turn/) [Andy Hargreaves](https://sms4smile.com/quotes/author/andy-hargreaves/) > [“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/) > [Both induction and deduction, reasoning from the particular and the general, and back again from the universal to the specific, form the essence to…](https://sms4smile.com/quotes/hans-christian-von-baeyer/both-induction-and-deduction-reasoning-from-the-particular-and-the/) [Hans Christian von Baeyer](https://sms4smile.com/quotes/author/hans-christian-von-baeyer/) > [ The only hope \[of science\] ... is in genuine induction. ](https://sms4smile.com/quotes/francis-bacon/the-only-hope-of-science-is-in-genuine-induction/) [Francis Bacon](https://sms4smile.com/quotes/author/francis-bacon/) > [In every science, after having analysed the ideas, expressing the more complicated by means of the more simple, one finds a certain number that…](https://sms4smile.com/quotes/giuseppe-peano/in-every-science-after-having-analysed-the-ideas-expressing-the-more/) [Giuseppe Peano](https://sms4smile.com/quotes/author/giuseppe-peano/) > [There is nothing which an untrained mind shows itself more hopelessly incapable, than in drawing the proper general conclusions from its own experience. And…](https://sms4smile.com/quotes/john-stuart-mill/there-is-nothing-which-an-untrained-mind-shows-itself-more-hopelessly/) [John Stuart Mill](https://sms4smile.com/quotes/author/john-stuart-mill/) > [“There’s an empty shelf here with your name and dates?” “There is. And it was beginning to sound nice. But then I got called…](https://sms4smile.com/quotes/victoria-schwab/there-s-an-empty-shelf-here-with-your-name-and-dates-there-is-and-it/) [Victoria Schwab](https://sms4smile.com/quotes/author/victoria-schwab/) > [Induction makes you feel guilty for getting something out of nothing, and it is artificial, but it is one of the greatest ideas of…](https://sms4smile.com/quotes/herbert-wilf/induction-makes-you-feel-guilty-for-getting-something-out-of-nothing/) [Herbert Wilf](https://sms4smile.com/quotes/author/herbert-wilf/) > [Induction for deduction, with a view to construction.](https://sms4smile.com/quotes/auguste-comte/induction-for-deduction-with-a-view-to-construction/) [Auguste Comte](https://sms4smile.com/quotes/author/auguste-comte/) > [One might get the impression that I recommend a new methodology which replaces induction by counterinduction and uses a multiplicity of theories, metaphysical views,…](https://sms4smile.com/quotes/paul-feyerabend/one-might-get-the-impression-that-i-recommend-a-new-methodology-which/) [Paul Feyerabend](https://sms4smile.com/quotes/author/paul-feyerabend/) > [Finding a mechanism does not bypass the problem of induction.](https://sms4smile.com/quotes/simon-blackburn/finding-a-mechanism-does-not-bypass-the-problem-of-induction/) [Simon Blackburn](https://sms4smile.com/quotes/author/simon-blackburn/) ## More by James Joseph Sylvester > [ ...There is no study in the world which brings into more harmonious action all the faculties of the mind than \[mathematics\], ... or, like… ](https://sms4smile.com/quotes/james-joseph-sylvester/there-is-no-study-in-the-world-which-brings-into-more-harmonious/) [James Joseph Sylvester](https://sms4smile.com/quotes/author/james-joseph-sylvester/) > [Number, place, and combination . . . the three intersecting but distinct spheres of thought to which all mathematical ideas admit of being referred.](https://sms4smile.com/quotes/james-joseph-sylvester/number-place-and-combination-the-three-intersecting-but-distinct/) [James Joseph Sylvester](https://sms4smile.com/quotes/author/james-joseph-sylvester/) > [ The world of ideas which it \[mathematics\] discloses or illuminates, the contemplation of divine beauty and order which it induces, the harmonious connexion of… ](https://sms4smile.com/quotes/james-joseph-sylvester/the-world-of-ideas-which-it-mathematics-discloses-or-illuminates-the/) [James Joseph Sylvester](https://sms4smile.com/quotes/author/james-joseph-sylvester/) > [The object of pure physics is the unfolding of the laws of the intelligible world; the object of pure mathematics that of unfolding the…](https://sms4smile.com/quotes/james-joseph-sylvester/the-object-of-pure-physics-is-the-unfolding-of-the-laws-of-the/) [James Joseph Sylvester](https://sms4smile.com/quotes/author/james-joseph-sylvester/) > [As the prerogative of Natural Science is to cultivate a taste for observation, so that of Mathematics is, almost from the starting point, to…](https://sms4smile.com/quotes/james-joseph-sylvester/as-the-prerogative-of-natural-science-is-to-cultivate-a-taste-for/) [James Joseph Sylvester](https://sms4smile.com/quotes/author/james-joseph-sylvester/) > [The early study of Euclid made me a hater of geometry.](https://sms4smile.com/quotes/james-joseph-sylvester/the-early-study-of-euclid-made-me-a-hater-of-geometry/) [James Joseph Sylvester](https://sms4smile.com/quotes/author/james-joseph-sylvester/) > [Aspiring to these wide generalizations, the analysis of quadratic functions soars to a pitch from whence it may look proudly down on the feeble…](https://sms4smile.com/quotes/james-joseph-sylvester/aspiring-to-these-wide-generalizations-the-analysis-of-quadratic/) [James Joseph Sylvester](https://sms4smile.com/quotes/author/james-joseph-sylvester/) > [“Mathematics is not a book confined within a cover and bound between brazen clasps, whose contents it need only patience to ransack; it is…](https://sms4smile.com/quotes/james-joseph-sylvester/mathematics-is-not-a-book-confined-within-a-cover-and-bound-between/) [James Joseph Sylvester](https://sms4smile.com/quotes/author/james-joseph-sylvester/) > [ The object of pure Physic\[s\] is the unfolding of the laws of the intelligible world; the object of pure Mathematic\[s\] that of unfolding the… ](https://sms4smile.com/quotes/james-joseph-sylvester/the-object-of-pure-physic-s-is-the-unfolding-of-the-laws-of-the/) [James Joseph Sylvester](https://sms4smile.com/quotes/author/james-joseph-sylvester/) > [Chemistry has the same quickening and suggestive influence upon the algebraist as a visit to the Royal Academy, or the old masters may be…](https://sms4smile.com/quotes/james-joseph-sylvester/chemistry-has-the-same-quickening-and-suggestive-influence-upon-the/) [James Joseph Sylvester](https://sms4smile.com/quotes/author/james-joseph-sylvester/) > [The theory of ramification is one of pure colligation, for it takes no account of magnitude or position; geometrical lines are used, but these…](https://sms4smile.com/quotes/james-joseph-sylvester/the-theory-of-ramification-is-one-of-pure-colligation-for-it-takes-no/) [James Joseph Sylvester](https://sms4smile.com/quotes/author/james-joseph-sylvester/) > [The object of pure Mathematic (is) that of unfolding the laws of human intelligence.](https://sms4smile.com/quotes/james-joseph-sylvester/the-object-of-pure-mathematic-is-that-of-unfolding-the-laws-of-human/) [James Joseph Sylvester](https://sms4smile.com/quotes/author/james-joseph-sylvester/) > [May not music be described as the mathematics of the sense, mathematics as music of the reason?](https://sms4smile.com/quotes/james-joseph-sylvester/may-not-music-be-described-as-the-mathematics-of-the-sense/) [James Joseph Sylvester](https://sms4smile.com/quotes/author/james-joseph-sylvester/) > [So long as a man remains a gregarious and sociable being, he cannot cut himself off from the gratification of the instinct of imparting…](https://sms4smile.com/quotes/james-joseph-sylvester/so-long-as-a-man-remains-a-gregarious-and-sociable-being-he-cannot/) [James Joseph Sylvester](https://sms4smile.com/quotes/author/james-joseph-sylvester/) > [May not music be described as the mathematics of the sense, mathematics as music of the reason? The musician feels mathematics, the mathematician thinks…](https://sms4smile.com/quotes/james-joseph-sylvester/may-not-music-be-described-as-the-mathematics-of-the-sense-2/) [James Joseph Sylvester](https://sms4smile.com/quotes/author/james-joseph-sylvester/) [Explore all 25 James Joseph Sylvester quotes ](https://sms4smile.com/quotes/author/james-joseph-sylvester/) ## More Boundless quotes > [While the world of reality has its limits, the world of your imagination is without boundaries](https://sms4smile.com/quotes/wayne-dyer/while-the-world-of-reality-has-its-limits-the-world-of-your/) [Wayne Dyer](https://sms4smile.com/quotes/author/wayne-dyer/) > [In my forties, my optimism was boundless. I had really good health and tremendous success which allowed me to do anything I wanted.](https://sms4smile.com/quotes/patricia-cornwell/in-my-forties-my-optimism-was-boundless-i-had-really-good-health-and/) [Patricia Cornwell](https://sms4smile.com/quotes/author/patricia-cornwell/) > [The insolence of base minds in success is boundless; and would scarce admit of a comparison, did not they themselves furnish us with one…](https://sms4smile.com/quotes/laurence-sterne/the-insolence-of-base-minds-in-success-is-boundless-and-would-scarce/) [Laurence Sterne](https://sms4smile.com/quotes/author/laurence-sterne/) > [The heart that breaks open can contain the whole universe... All is registered in the 'boundless heart' of the bodhisattva. Through our deepest and…](https://sms4smile.com/quotes/joanna-macy/the-heart-that-breaks-open-can-contain-the-whole-universe-all-is/) [Joanna Macy](https://sms4smile.com/quotes/author/joanna-macy/) > [Every time someone tried to explain to me there are limits to what one man can do, I pointed to the boundless sky and…](https://sms4smile.com/quotes/jaiprakash-gaur/every-time-someone-tried-to-explain-to-me-there-are-limits-to-what/) Jaiprakash Gaur > [I was much more into romance as a teenager and it's been a kind of new discovery for me to learn about sci-fi adventure.…](https://sms4smile.com/quotes/olivia-wilde/i-was-much-more-into-romance-as-a-teenager-and-it-s-been-a-kind-of/) [Olivia Wilde](https://sms4smile.com/quotes/author/olivia-wilde/) > [In the early days the Cubism' method of grasping an object was to go round and round it. The Futurists declared that one had…](https://sms4smile.com/quotes/gino-severini/in-the-early-days-the-cubism-method-of-grasping-an-object-was-to-go/) [Gino Severini](https://sms4smile.com/quotes/author/gino-severini/) > [Keep your rivers flowing as they will, and you will continue to know the most important of all freedoms-the boundless scope of the human…](https://sms4smile.com/quotes/david-r-brower/keep-your-rivers-flowing-as-they-will-and-you-will-continue-to-know/) [David R. Brower](https://sms4smile.com/quotes/author/david-r-brower/) > [He was sailing over a boundless expanse of sea, with a blood-red sky above, and the angry waters, lashed into fury beneath, boiling and…](https://sms4smile.com/quotes/charles-dickens/he-was-sailing-over-a-boundless-expanse-of-sea-with-a-blood-red-sky/) [Charles Dickens](https://sms4smile.com/quotes/author/charles-dickens/) > [In political activity, then, men sail a boundless and bottomless sea; there is neither harbour for shelter nor floor for anchorage, neither starting-place nor…](https://sms4smile.com/quotes/michael-joseph-oakeshott/in-political-activity-then-men-sail-a-boundless-and-bottomless-sea/) [Michael Joseph Oakeshott](https://sms4smile.com/quotes/author/michael-joseph-oakeshott/) > [To take a single step beyond the boundaries specially drawn around the powers of Congress is to take possession of a boundless field of…](https://sms4smile.com/quotes/thomas-jefferson/to-take-a-single-step-beyond-the-boundaries-specially-drawn-around/) [Thomas Jefferson](https://sms4smile.com/quotes/author/thomas-jefferson/) > [Vain are the thousand creeds That move men's hearts, unutterably vain; Worthless as withered weeds, Or idlest froth amid the boundless main.](https://sms4smile.com/quotes/emily-bronte/vain-are-the-thousand-creeds-that-move-men-s-hearts-unutterably-vain/) [Emily Bronte](https://sms4smile.com/quotes/author/emily-bronte/) > [“The field of boundless emptiness is what exists from the very beginning. You must purify, cure, grind down, or brush away all the tendencies…](https://sms4smile.com/quotes/yi-wu-taigen-leighton/the-field-of-boundless-emptiness-is-what-exists-from-the-very/) Yi Wu Taigen Leighton > [Free will appears unfettered, deliberate; it is boundlessly free, wandering, the spirit. But fate is a necessity; unless we believe that world history is…](https://sms4smile.com/quotes/friedrich-nietzsche/free-will-appears-unfettered-deliberate-it-is-boundlessly-free/) [Friedrich Nietzsche](https://sms4smile.com/quotes/author/friedrich-nietzsche/) > [Not everyone possesses boundless energy or a conspicuous talent. We are not equally blessed with great intellect or physical beauty or emotional strength. But…](https://sms4smile.com/quotes/gigi-graham/not-everyone-possesses-boundless-energy-or-a-conspicuous-talent-we/) [Gigi Graham](https://sms4smile.com/quotes/author/gigi-graham/) [Browse all 327 Boundless quotes ](https://sms4smile.com/quotes/about/boundless/) ```json { "@context": "https://schema.org", "@graph": [ { "@type": "Quotation", "text": "[Mathematics] unceasingly calls forth the faculties of observation and comparison; one of its principal weapons is induction: it has frequent recourse to trial and verification; and it affords a boundless scope for the exercise of the highest efforts of imagination and invention.", "creator": { "@type": "Person", "name": "James Joseph Sylvester" }, "isPartOf": { "@id": "https://sms4smile.com/quotes/#website" }, "url": "https://sms4smile.com/quotes/james-joseph-sylvester/mathematics-unceasingly-calls-forth-the-faculties-of-observation-and/", "about": { "@type": "Thing", "name": "Boundless" }, "@id": "https://sms4smile.com/quotes/james-joseph-sylvester/mathematics-unceasingly-calls-forth-the-faculties-of-observation-and/#quotation", "image": { "@type": "ImageObject", "@id": "https://sms4smile.com/quotes/i/301/james-joseph-sylvester-23602_boundless_mathematics-unceasingly-calls-forth-the_447035.jpg", "contentUrl": "https://sms4smile.com/quotes/i/301/james-joseph-sylvester-23602_boundless_mathematics-unceasingly-calls-forth-the_447035.jpg", "url": "https://sms4smile.com/quotes/i/301/james-joseph-sylvester-23602_boundless_mathematics-unceasingly-calls-forth-the_447035.jpg", "width": 1080, "height": 1080, "caption": "“[Mathematics] unceasingly calls forth the faculties of observation and comparison; one of its principal…” — James Joseph Sylvester", "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": "James Joseph Sylvester", "item": "https://sms4smile.com/quotes/author/james-joseph-sylvester/" }, { "@type": "ListItem", "position": 4, "name": "[Mathematics] unceasingly calls forth the faculties...", "item": "https://sms4smile.com/quotes/james-joseph-sylvester/mathematics-unceasingly-calls-forth-the-faculties-of-observation-and/" } ], "@id": "https://sms4smile.com/quotes/james-joseph-sylvester/mathematics-unceasingly-calls-forth-the-faculties-of-observation-and/#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 } } ] } ```