--- title: "Meaning & Key Takeaway of: As to the need of improvement there can…" description: "\"“As to the need of improvement there can be no question whilst the reign of Euclid continues. My own idea of a useful course is to begin with arithmeti..." image: "https://sms4smile.com/quotes/i/7d3/oliver-heaviside-26165_algebra_as-to-the-need-of-improvement-there-can_2682136.jpg" --- # As to the need of improvement there can be no question… ![“As to the need of improvement there can be no question whilst the reign of Euclid continues. My own idea of a useful course is to begin with arithmetic, and then not Euclid but algebra. Next, not Euclid , but practical geometry, solid as well as plane; not demonstration, but to make acquaintance…” quote by Oliver Heaviside](https://sms4smile.com/quotes/i/7d3/oliver-heaviside-26165_algebra_as-to-the-need-of-improvement-there-can_2682136.jpg) [Download](https://sms4smile.com/quotes/i/7d3/oliver-heaviside-26165_algebra_as-to-the-need-of-improvement-there-can_2682136.jpg) [Open image](https://sms4smile.com/quotes/i/7d3/oliver-heaviside-26165_algebra_as-to-the-need-of-improvement-there-can_2682136.jpg) > ““As to the need of improvement there can be no question whilst the reign of Euclid continues. My own idea of a useful course is to begin with arithmetic, and then not Euclid but algebra. Next, not Euclid , but practical geometry, solid as well as plane; not demonstration, but to make acquaintance. Then not Euclid , but elementary vectors, conjoined with algebra, and applied to geometry. Addition first; then the scalar product. Elementary calculus should go on simultaneously, and come into vector algebraic geometry after a bit. Euclid might be an extra course for learned men, like Homer ...”” [Oliver Heaviside](https://sms4smile.com/quotes/author/oliver-heaviside/) ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. Heaviside argues that traditional Euclidean geometry should be replaced by a curriculum focused on arithmetic, algebra, practical geometry, vectors, and calculus to better serve modern scientific needs. **In simple terms:** Replace old geometry with modern math topics. Key Takeaway Adopt a modern, applied math curriculum. Themes education mathematics curriculum design modernization practicality Mood thoughtful analytical Type educational philosophical When to use this quote - engineering training - physics education - technical schools - self‑study - curriculum reform Key Concepts vector algebra applied geometry calculus integration pedagogy Questions to Reflect On - How can we balance foundational theory with practical applications? - What modern topics should complement, not replace, Euclid? A Different Perspective Euclidean geometry still underpins many foundational concepts and cannot be entirely discarded. ★ ★ ★ ★ ★ No ratings yet [Acquaintance Euclid](https://sms4smile.com/quotes/about/acquaintance-euclid-2590359/) [Algebra](https://sms4smile.com/quotes/about/algebra/) [Algebra Euclid](https://sms4smile.com/quotes/about/algebra-euclid-2590355/) [Arithmetic](https://sms4smile.com/quotes/about/arithmetic/) [Calculus](https://sms4smile.com/quotes/about/calculus/) [Euclid](https://sms4smile.com/quotes/about/euclid/) [Euclid Continues](https://sms4smile.com/quotes/about/euclid-continues-2590353/) [Euclid Practical](https://sms4smile.com/quotes/about/euclid-practical-2590352/) [Geometry](https://sms4smile.com/quotes/about/geometry/) [Homer](https://sms4smile.com/quotes/about/homer/) [Improvement](https://sms4smile.com/quotes/about/improvement/) [Math](https://sms4smile.com/quotes/about/math/) [Mathematics](https://sms4smile.com/quotes/about/mathematics/) [Practical Geometry](https://sms4smile.com/quotes/about/practical-geometry-2590357/) [Science](https://sms4smile.com/quotes/about/science/) [Vectors](https://sms4smile.com/quotes/about/vectors/) ## Related quotes > [Most new movements start this way: hundreds or thousands of individuals and groups, working in different fields and different locations, start thinking about change…](https://sms4smile.com/quotes/steven-johnson/most-new-movements-start-this-way-hundreds-or-thousands-of/) [Steven Johnson](https://sms4smile.com/quotes/author/steven-johnson/) > [You, Dad, in the large scheme of things, don't matter. I, Dad, don't matter. We're vectors on the grids of cellular life.](https://sms4smile.com/quotes/david-shields/you-dad-in-the-large-scheme-of-things-don-t-matter-i-dad-don-t-matter/) [David Shields](https://sms4smile.com/quotes/author/david-shields/) > [Come, every frustum longs to be a cone, And every vector dreams of matrices. Hark to the gentle gradient of the breeze: It whispers…](https://sms4smile.com/quotes/stanislaw-lem/come-every-frustum-longs-to-be-a-cone-and-every-vector-dreams-of/) [Stanislaw Lem](https://sms4smile.com/quotes/author/stanislaw-lem/) > [The assumption that the square of a unit vector is positive unity leads to an algebra whose characteristic quantities are non-associative.](https://sms4smile.com/quotes/cargill-gilston-knott/the-assumption-that-the-square-of-a-unit-vector-is-positive-unity/) [Cargill Gilston Knott](https://sms4smile.com/quotes/author/cargill-gilston-knott/) > [Words have a universe of qualities other than those of descriptive relation: Hardness, Density, Sound-Shape, Vector-Force, & Degrees of Transparency/Opacity.](https://sms4smile.com/quotes/clark-coolidge/words-have-a-universe-of-qualities-other-than-those-of-descriptive/) [Clark Coolidge](https://sms4smile.com/quotes/author/clark-coolidge/) > [Keith Knight is mapping out a previously unknown vector of the vast cartoon universe.](https://sms4smile.com/quotes/garry-trudeau/keith-knight-is-mapping-out-a-previously-unknown-vector-of-the-vast/) [Garry Trudeau](https://sms4smile.com/quotes/author/garry-trudeau/) > [The vector equilibrium is the true zero reference of the energetic mathematics. Zero pulsation in the vector equilibrium is the nearest approach we will…](https://sms4smile.com/quotes/r-buckminster-fuller/the-vector-equilibrium-is-the-true-zero-reference-of-the-energetic/) [R. Buckminster Fuller](https://sms4smile.com/quotes/author/r-buckminster-fuller/) > [It seems to me that we must make a distinction between what is "objective" and what is "measurable" in discussing the question of physical…](https://sms4smile.com/quotes/roger-penrose/it-seems-to-me-that-we-must-make-a-distinction-between-what-is/) [Roger Penrose](https://sms4smile.com/quotes/author/roger-penrose/) > [New methods always look better than old ones. Neural nets are better than logistic regression, support vector machines are better than neural nets, etc.](https://sms4smile.com/quotes/bradley-efron/new-methods-always-look-better-than-old-ones-neural-nets-are-better/) [Bradley Efron](https://sms4smile.com/quotes/author/bradley-efron/) > [Isn't it time that these most ancient sorrows of ours grew fruitful? Time that we tenderly loosed ourselves from the loved one, and, unsteadily,…](https://sms4smile.com/quotes/rainer-maria-rilke/isn-t-it-time-that-these-most-ancient-sorrows-of-ours-grew-fruitful/) [Rainer Maria Rilke](https://sms4smile.com/quotes/author/rainer-maria-rilke/) > [The physicist who states a law of nature with the aid of a mathematical formula is abstracting a real feature of a real material…](https://sms4smile.com/quotes/hilary-putnam/the-physicist-who-states-a-law-of-nature-with-the-aid-of-a/) [Hilary Putnam](https://sms4smile.com/quotes/author/hilary-putnam/) > [“Vectors never make the same mistake twice,That is why the warrior only risks his heart for something worthwhile.”](https://sms4smile.com/quotes/paulo-coelho/vectors-never-make-the-same-mistake-twice-that-is-why-the-warrior/) [Paulo Coelho](https://sms4smile.com/quotes/author/paulo-coelho/) > [I always loved both 'Breakout' and 'Asteroids' - I thought they were really good games. There was another game called 'Tempest' that I thought…](https://sms4smile.com/quotes/nolan-bushnell/i-always-loved-both-breakout-and-asteroids-i-thought-they-were-really/) [Nolan Bushnell](https://sms4smile.com/quotes/author/nolan-bushnell/) > [Symmetrical equations are good in their place, but ' vector ' is a useless survival, or offshoot from quaternions, and has never been of…](https://sms4smile.com/quotes/lord-kelvin/symmetrical-equations-are-good-in-their-place-but-vector-is-a-useless/) [Lord Kelvin](https://sms4smile.com/quotes/author/lord-kelvin/) > [Happiness is not a state of being. Happiness is a vector, it is movement.](https://sms4smile.com/quotes/neal-shusterman/happiness-is-not-a-state-of-being-happiness-is-a-vector-it-is-movement/) [Neal Shusterman](https://sms4smile.com/quotes/author/neal-shusterman/) ## More by Oliver Heaviside > [We do not dwell in the Palace of Truth. But, as was mentioned to me not long since, "There is a time coming when…](https://sms4smile.com/quotes/oliver-heaviside/we-do-not-dwell-in-the-palace-of-truth-but-as-was-mentioned-to-me-not/) [Oliver Heaviside](https://sms4smile.com/quotes/author/oliver-heaviside/) > [Mathematics is of two kinds, Rigorous and Physical. The former is Narrow: the latter Bold and Broad. To have to stop to formulate rigorous…](https://sms4smile.com/quotes/oliver-heaviside/mathematics-is-of-two-kinds-rigorous-and-physical-the-former-is/) [Oliver Heaviside](https://sms4smile.com/quotes/author/oliver-heaviside/) > [...there is no absolute scale of size in nature, and the small may be as important, or more so than the great.](https://sms4smile.com/quotes/oliver-heaviside/there-is-no-absolute-scale-of-size-in-nature-and-the-small-may-be-as/) [Oliver Heaviside](https://sms4smile.com/quotes/author/oliver-heaviside/) > [Why should I refuse a good dinner simply because I don't understand the digestive processes involved?](https://sms4smile.com/quotes/oliver-heaviside/why-should-i-refuse-a-good-dinner-simply-because-i-don-t-understand/) [Oliver Heaviside](https://sms4smile.com/quotes/author/oliver-heaviside/) > [It is shocking that young people should be addling their brains over mere logical subtleties in Euclid's Elements, trying to understand the proof of…](https://sms4smile.com/quotes/oliver-heaviside/it-is-shocking-that-young-people-should-be-addling-their-brains-over/) [Oliver Heaviside](https://sms4smile.com/quotes/author/oliver-heaviside/) > [“ Ohm found that the results could be summed up in such a simple law that he who runs may read it, and a…](https://sms4smile.com/quotes/oliver-heaviside/ohm-found-that-the-results-could-be-summed-up-in-such-a-simple-law/) [Oliver Heaviside](https://sms4smile.com/quotes/author/oliver-heaviside/) > [Theory is the essence of facts. Without theory scientific knowledge would be only worthy of the madhouse.](https://sms4smile.com/quotes/oliver-heaviside/theory-is-the-essence-of-facts-without-theory-scientific-knowledge/) [Oliver Heaviside](https://sms4smile.com/quotes/author/oliver-heaviside/) > [Mathematics is an experimental science, and definitions do not come first, but later on.](https://sms4smile.com/quotes/oliver-heaviside/mathematics-is-an-experimental-science-and-definitions-do-not-come/) [Oliver Heaviside](https://sms4smile.com/quotes/author/oliver-heaviside/) > [If it is love that makes the world go round, it is self-induction that makes electromagnetic waves go round the world.](https://sms4smile.com/quotes/oliver-heaviside/if-it-is-love-that-makes-the-world-go-round-it-is-self-induction-that/) [Oliver Heaviside](https://sms4smile.com/quotes/author/oliver-heaviside/) > [Electric and magnetic forces. May they live for ever, and never be forgot, if only to remind us that the science of electromagnetics, in…](https://sms4smile.com/quotes/oliver-heaviside/electric-and-magnetic-forces-may-they-live-for-ever-and-never-be/) [Oliver Heaviside](https://sms4smile.com/quotes/author/oliver-heaviside/) > [The best result of mathematics is to be able to do without it.](https://sms4smile.com/quotes/oliver-heaviside/the-best-result-of-mathematics-is-to-be-able-to-do-without-it/) [Oliver Heaviside](https://sms4smile.com/quotes/author/oliver-heaviside/) > [Logic can be patient, for it is eternal.](https://sms4smile.com/quotes/oliver-heaviside/logic-can-be-patient-for-it-is-eternal/) [Oliver Heaviside](https://sms4smile.com/quotes/author/oliver-heaviside/) > [Facts are of not much use, considered as facts. They bewilder by their number and their apparent incoherency. Let them be digested into theory,…](https://sms4smile.com/quotes/oliver-heaviside/facts-are-of-not-much-use-considered-as-facts-they-bewilder-by-their/) [Oliver Heaviside](https://sms4smile.com/quotes/author/oliver-heaviside/) > [Ohm (a distinguished mathematician, be it noted) brought into order a host of puzzling facts connecting electromotive force and electric current in conductors, which…](https://sms4smile.com/quotes/oliver-heaviside/ohm-a-distinguished-mathematician-be-it-noted-brought-into-order-a/) [Oliver Heaviside](https://sms4smile.com/quotes/author/oliver-heaviside/) > [“The following story is true. There was a little boy, and his father said, “Do try to be like other people. Don’t frown.” And…](https://sms4smile.com/quotes/oliver-heaviside/the-following-story-is-true-there-was-a-little-boy-and-his-father/) [Oliver Heaviside](https://sms4smile.com/quotes/author/oliver-heaviside/) [Explore all 22 Oliver Heaviside quotes ](https://sms4smile.com/quotes/author/oliver-heaviside/) ## More Algebra quotes > [“Who cares for Algebra? Who delights in solving math? I only want to live my life Along the creative path.”](https://sms4smile.com/quotes/jennifer-niven/who-cares-for-algebra-who-delights-in-solving-math-i-only-want-to/) [Jennifer Niven](https://sms4smile.com/quotes/author/jennifer-niven/) > [I write emotional algebra.](https://sms4smile.com/quotes/anais-nin/i-write-emotional-algebra/) [Anais Nin](https://sms4smile.com/quotes/author/anais-nin/) > [...the science of calculation also is indispensable as far as the extraction of the square and cube roots: Algebra as far as the quadratic…](https://sms4smile.com/quotes/thomas-jefferson/the-science-of-calculation-also-is-indispensable-as-far-as-the/) [Thomas Jefferson](https://sms4smile.com/quotes/author/thomas-jefferson/) > [Great people create great acts of kindness.](https://sms4smile.com/quotes/miguel-de-cervantes/great-people-create-great-acts-of-kindness/) [Miguel de Cervantes](https://sms4smile.com/quotes/author/miguel-de-cervantes/) > [Algebra applies to the clouds.](https://sms4smile.com/quotes/victor-hugo/algebra-applies-to-the-clouds/) [Victor Hugo](https://sms4smile.com/quotes/author/victor-hugo/) > [ \[On refusing to do nude movie scenes:\] There are certain people who should know what you look like naked. I just don't think your… ](https://sms4smile.com/quotes/julia-roberts/on-refusing-to-do-nude-movie-scenes-there-are-certain-people-who/) [Julia Roberts](https://sms4smile.com/quotes/author/julia-roberts/) > [Hmm. I'm still not very good at algebra. I just can't figure out Y.](https://sms4smile.com/quotes/anonymous/hmm-i-m-still-not-very-good-at-algebra-i-just-can-t-figure-out-y/) [Anonymous](https://sms4smile.com/quotes/author/anonymous/) > [Astronomy, that micography of heaven, is the most magnificent of the sciences. ... Astronomy has its clear side and its luminous side; on its…](https://sms4smile.com/quotes/victor-hugo/astronomy-that-micography-of-heaven-is-the-most-magnificent-of-the/) [Victor Hugo](https://sms4smile.com/quotes/author/victor-hugo/) > [No one fully understands spinors. Their algebra is formally understood but their general significance is mysterious. In some sense they describe the 'square root'…](https://sms4smile.com/quotes/michael-atiyah/no-one-fully-understands-spinors-their-algebra-is-formally-understood/) [Michael Atiyah](https://sms4smile.com/quotes/author/michael-atiyah/) > [Cryptography has generated number theory, algebraic geometry over finite fields, algebra, combinatorics and computers.](https://sms4smile.com/quotes/vladimir-arnold/cryptography-has-generated-number-theory-algebraic-geometry-over/) [Vladimir Arnold](https://sms4smile.com/quotes/author/vladimir-arnold/) > [There's nothing in your life you can't learn from, if you respond with the right attitude.](https://sms4smile.com/quotes/rick-warren/there-s-nothing-in-your-life-you-can-t-learn-from-if-you-respond-with/) [Rick Warren](https://sms4smile.com/quotes/author/rick-warren/) > [ALGEBRA is a general Method of Computation by certain Signs and Symbols which have been contrived for this Purpose, and found convenient.](https://sms4smile.com/quotes/colin-maclaurin/algebra-is-a-general-method-of-computation-by-certain-signs-and/) [Colin Maclaurin](https://sms4smile.com/quotes/author/colin-maclaurin/) > [A child in the 4th grade who's just learning algebra is not imperfect. While there may be a child in the 12th grade who's…](https://sms4smile.com/quotes/frederick-lenz/a-child-in-the-4th-grade-who-s-just-learning-algebra-is-not-imperfect/) [Frederick Lenz](https://sms4smile.com/quotes/author/frederick-lenz/) > [When I was at school, I was terrible at algebra and arithmetic, but I was always the best at English and literature. And acting,…](https://sms4smile.com/quotes/joan-collins/when-i-was-at-school-i-was-terrible-at-algebra-and-arithmetic-but-i/) [Joan Collins](https://sms4smile.com/quotes/author/joan-collins/) > [Algebra goes to the heart of the matter at it ignores the casual nature of particular cases.](https://sms4smile.com/quotes/edward-charles-titchmarsh/algebra-goes-to-the-heart-of-the-matter-at-it-ignores-the-casual/) [Edward Charles Titchmarsh](https://sms4smile.com/quotes/author/edward-charles-titchmarsh/) [Browse all 235 Algebra quotes ](https://sms4smile.com/quotes/about/algebra/) ```json { "@context": "https://schema.org", "@graph": [ { "@type": "Quotation", "text": "“As to the need of improvement there can be no question whilst the reign of Euclid continues. My own idea of a useful course is to begin with arithmetic, and then not Euclid but algebra. Next, not Euclid , but practical geometry, solid as well as plane; not demonstration, but to make acquaintance. Then not Euclid , but elementary vectors, conjoined with algebra, and applied to geometry. Addition first; then the scalar product. Elementary calculus should go on simultaneously, and come into vector algebraic geometry after a bit. Euclid might be an extra course for learned men, like Homer ...”", "creator": { "@type": "Person", "name": "Oliver Heaviside" }, "isPartOf": { "@id": "https://sms4smile.com/quotes/#website" }, "url": "https://sms4smile.com/quotes/oliver-heaviside/as-to-the-need-of-improvement-there-can-be-no-question-whilst-the/", "about": { "@type": "Thing", "name": "Algebra" }, "@id": "https://sms4smile.com/quotes/oliver-heaviside/as-to-the-need-of-improvement-there-can-be-no-question-whilst-the/#quotation", "image": { "@type": "ImageObject", "@id": "https://sms4smile.com/quotes/i/7d3/oliver-heaviside-26165_algebra_as-to-the-need-of-improvement-there-can_2682136.jpg", "contentUrl": "https://sms4smile.com/quotes/i/7d3/oliver-heaviside-26165_algebra_as-to-the-need-of-improvement-there-can_2682136.jpg", "url": "https://sms4smile.com/quotes/i/7d3/oliver-heaviside-26165_algebra_as-to-the-need-of-improvement-there-can_2682136.jpg", "width": 1080, "height": 1080, "caption": "“As to the need of improvement there can be no question whilst the reign of Euclid continues. My own idea of…” — Oliver Heaviside", "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": "Oliver Heaviside", "item": "https://sms4smile.com/quotes/author/oliver-heaviside/" }, { "@type": "ListItem", "position": 4, "name": "“As to the need of improvement...", "item": "https://sms4smile.com/quotes/oliver-heaviside/as-to-the-need-of-improvement-there-can-be-no-question-whilst-the/" } ], "@id": "https://sms4smile.com/quotes/oliver-heaviside/as-to-the-need-of-improvement-there-can-be-no-question-whilst-the/#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 } } ] } ```