--- title: "Meaning & Key Takeaway of: I was reminded of the Sydney Harris…" description: "\"I was reminded of the Sydney Harris cartoon that said 'adding two numbers that have not been added before does not constitute a mathematical breakthrou..." image: "https://sms4smile.com/quotes/i/eaf/ronald-graham-34796_breakthrough_i-was-reminded-of-the-sydney-harris-cart_1640224.jpg" --- # I was reminded of the Sydney Harris cartoon that said… ![“I was reminded of the Sydney Harris cartoon that said 'adding two numbers that have not been added before does not constitute a mathematical breakthrough'.” quote by Ronald Graham](https://sms4smile.com/quotes/i/eaf/ronald-graham-34796_breakthrough_i-was-reminded-of-the-sydney-harris-cart_1640224.jpg) [Download](https://sms4smile.com/quotes/i/eaf/ronald-graham-34796_breakthrough_i-was-reminded-of-the-sydney-harris-cart_1640224.jpg) [Open image](https://sms4smile.com/quotes/i/eaf/ronald-graham-34796_breakthrough_i-was-reminded-of-the-sydney-harris-cart_1640224.jpg) > “I was reminded of the Sydney Harris cartoon that said 'adding two numbers that have not been added before does not constitute a mathematical breakthrough'.” [Ronald Graham](https://sms4smile.com/quotes/author/ronald-graham/) ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. The cartoon humorously points out that recombining known numbers isn’t a true breakthrough. **In simple terms:** Combining known numbers isn’t innovative. Key Takeaway Seek genuine novelty, not just recombination. Themes innovation mathematics humor Mood lighthearted thoughtful Type educational philosophical When to use this quote - research proposals - teaching methods - algorithm design - patent filing Key Concepts creativity problem solving Questions to Reflect On - What counts as a real breakthrough? - How to value incremental improvements? A Different Perspective Not all new results are groundbreaking. ★ ★ ★ ★ ★ No ratings yet [Breakthrough](https://sms4smile.com/quotes/about/breakthrough/) [Innovation](https://sms4smile.com/quotes/about/innovation/) [Mathematics](https://sms4smile.com/quotes/about/mathematics/) [Science](https://sms4smile.com/quotes/about/science/) [Sydney](https://sms4smile.com/quotes/about/sydney/) ## Related quotes > [“It's not because I want to make out with her." Hold on." He grabbed a pencil and scrawled excitedly at the paper as if…](https://sms4smile.com/quotes/john-green/it-s-not-because-i-want-to-make-out-with-her-hold-on-he-grabbed-a/) [John Green](https://sms4smile.com/quotes/author/john-green/) > [“Hold on." He grabbed a pencil and scrawled excitedly at the paper as if he'd just made a mathematical breakthrough and then looked back…](https://sms4smile.com/quotes/john-green/hold-on-he-grabbed-a-pencil-and-scrawled-excitedly-at-the-paper-as-if/) [John Green](https://sms4smile.com/quotes/author/john-green/) > [“He grabbed a pencil and scrawled excitedly at the paper as if he'd just made a mathematical breakthrough and the looked back back at…](https://sms4smile.com/quotes/john-green/he-grabbed-a-pencil-and-scrawled-excitedly-at-the-paper-as-if-he-d/) [John Green](https://sms4smile.com/quotes/author/john-green/) > [The obvious mathematical breakthrough would be development of an easy way to factor large prime numbers.](https://sms4smile.com/quotes/bill-gates/the-obvious-mathematical-breakthrough-would-be-development-of-an-easy/) [Bill Gates](https://sms4smile.com/quotes/author/bill-gates/) > [The first gig we ever played was at a pub in Sydney called the Annandale Hotel to approximately 12 people.](https://sms4smile.com/quotes/luke-hemmings/the-first-gig-we-ever-played-was-at-a-pub-in-sydney-called-the/) [Luke Hemmings](https://sms4smile.com/quotes/author/luke-hemmings/) > [“The two big cities of Australia are tonally as distinct from each other as Boston is from L.A. or Lyon from Marseilles.”](https://sms4smile.com/quotes/helen-garner/the-two-big-cities-of-australia-are-tonally-as-distinct-from-each/) [Helen Garner](https://sms4smile.com/quotes/author/helen-garner/) > [“but Kyler...yeah, he put the 'oo' in swoon.”](https://sms4smile.com/quotes/jennifer-l-armentrout/but-kyler-yeah-he-put-the-oo-in-swoon/) [Jennifer L. Armentrout](https://sms4smile.com/quotes/author/jennifer-l-armentrout/) > [Rock pools, so-named because they have been hammered out of rocks at the ocean's edge, are one of Sydney's defining characteristics, along with the…](https://sms4smile.com/quotes/raymond-bonner/rock-pools-so-named-because-they-have-been-hammered-out-of-rocks-at/) [Raymond Bonner](https://sms4smile.com/quotes/author/raymond-bonner/) > [Singing at the Opening Ceremonies of the Sydney Olympics in 2000 was amazing and, probably the highlight of this decade is the opening of…](https://sms4smile.com/quotes/olivia-newton-john/singing-at-the-opening-ceremonies-of-the-sydney-olympics-in-2000-was/) [Olivia Newton-John](https://sms4smile.com/quotes/author/olivia-newton-john/) > [“Awareness Makes a Cure Possible.”](https://sms4smile.com/quotes/sydney-davies/awareness-makes-a-cure-possible/) Sydney Davies > [Sydney CBD is the eastern city, Parramatta is the central city and Badgerys will be the third city in greater Sydney.](https://sms4smile.com/quotes/gladys-berejiklian/sydney-cbd-is-the-eastern-city-parramatta-is-the-central-city-and/) [Gladys Berejiklian](https://sms4smile.com/quotes/author/gladys-berejiklian/) > [Sydney is full of the craziest and most talented artists of all kinds.](https://sms4smile.com/quotes/keiynan-lonsdale/sydney-is-full-of-the-craziest-and-most-talented-artists-of-all-kinds/) [Keiynan Lonsdale](https://sms4smile.com/quotes/author/keiynan-lonsdale/) > [I wanted to have a peaceful married life with my wife, so we both moved to Sydney in Australia.](https://sms4smile.com/quotes/rahul-roy/i-wanted-to-have-a-peaceful-married-life-with-my-wife-so-we-both/) [Rahul Roy](https://sms4smile.com/quotes/author/rahul-roy/) > [My first Olympics memory was watching Haile Gebrselassie in Sydney 2000. His sprint finish to defend his title really moved me.](https://sms4smile.com/quotes/mo-farah/my-first-olympics-memory-was-watching-haile-gebrselassie-in-sydney/) [Mo Farah](https://sms4smile.com/quotes/author/mo-farah/) > [“If you want a woman with a tight little kitty, the find one with itty bitty titties!”](https://sms4smile.com/quotes/jennifer-l-armentrout/if-you-want-a-woman-with-a-tight-little-kitty-the-find-one-with-itty/) [Jennifer L. Armentrout](https://sms4smile.com/quotes/author/jennifer-l-armentrout/) ## More by Ronald Graham > [Math is sometimes called the science of patterns.](https://sms4smile.com/quotes/ronald-graham/math-is-sometimes-called-the-science-of-patterns/) [Ronald Graham](https://sms4smile.com/quotes/author/ronald-graham/) > [The ultimate goal of mathematics is to eliminate all need for intelligent thought.](https://sms4smile.com/quotes/ronald-graham/the-ultimate-goal-of-mathematics-is-to-eliminate-all-need-for/) [Ronald Graham](https://sms4smile.com/quotes/author/ronald-graham/) > [Well, as you know, there are 24 hours in every day. And if that's not enough, you've always got the nights!](https://sms4smile.com/quotes/ronald-graham/well-as-you-know-there-are-24-hours-in-every-day-and-if-that-s-not/) [Ronald Graham](https://sms4smile.com/quotes/author/ronald-graham/) > [It wouild be very discouraging if somewhere down the line you could ask a computer if the Riemann hypothesis is correct and it said,…](https://sms4smile.com/quotes/ronald-graham/it-wouild-be-very-discouraging-if-somewhere-down-the-line-you-could/) [Ronald Graham](https://sms4smile.com/quotes/author/ronald-graham/) > [Someone has said that all the great jugglers are dead.](https://sms4smile.com/quotes/ronald-graham/someone-has-said-that-all-the-great-jugglers-are-dead/) [Ronald Graham](https://sms4smile.com/quotes/author/ronald-graham/) > [A lot of the high-level sports are really in your mind.](https://sms4smile.com/quotes/ronald-graham/a-lot-of-the-high-level-sports-are-really-in-your-mind/) [Ronald Graham](https://sms4smile.com/quotes/author/ronald-graham/) > [Someone has remarked that 'An ideal math talk should have one proof and one joke and they should not be the same'.](https://sms4smile.com/quotes/ronald-graham/someone-has-remarked-that-an-ideal-math-talk-should-have-one-proof/) [Ronald Graham](https://sms4smile.com/quotes/author/ronald-graham/) > [Some people think that mathematics is a serious business that must always be cold and dry; but we think mathematics is fun, and we…](https://sms4smile.com/quotes/ronald-graham/some-people-think-that-mathematics-is-a-serious-business-that-must/) [Ronald Graham](https://sms4smile.com/quotes/author/ronald-graham/) > [Juggling is sometimes called the art of controlling patterns, controlling patterns in time and space.](https://sms4smile.com/quotes/ronald-graham/juggling-is-sometimes-called-the-art-of-controlling-patterns/) [Ronald Graham](https://sms4smile.com/quotes/author/ronald-graham/) > [Incidentally, when we're faced with a "prove or disprove," we're usually better off trying first to disprove with a counterexample, for two reasons: A…](https://sms4smile.com/quotes/ronald-graham/incidentally-when-we-re-faced-with-a-prove-or-disprove-we-re-usually/) [Ronald Graham](https://sms4smile.com/quotes/author/ronald-graham/) > [The trouble with integers is that we have examined only the very small ones. Maybe all the exciting stuff happens at really big numbers,…](https://sms4smile.com/quotes/ronald-graham/the-trouble-with-integers-is-that-we-have-examined-only-the-very/) [Ronald Graham](https://sms4smile.com/quotes/author/ronald-graham/) > [AB=1/4((A+B)^2-(A-B)^2) is an amazing identity, and unfortunately, I have to remind my current students how to prove it.](https://sms4smile.com/quotes/ronald-graham/ab-1-4-a-b-2-a-b-2-is-an-amazing-identity-and-unfortunately-i-have-to/) [Ronald Graham](https://sms4smile.com/quotes/author/ronald-graham/) > [It would be very discouraging if somewhere down the line you could ask a computer if the Riemann hypothesis is correct and it said,…](https://sms4smile.com/quotes/ronald-graham/it-would-be-very-discouraging-if-somewhere-down-the-line-you-could/) [Ronald Graham](https://sms4smile.com/quotes/author/ronald-graham/) [Explore all 14 Ronald Graham quotes ](https://sms4smile.com/quotes/author/ronald-graham/) ## More Breakthrough quotes > [Real breakthroughs are not found because you want to develop some new technology, but because you are curious and want to find out how…](https://sms4smile.com/quotes/anton-zeilinger/real-breakthroughs-are-not-found-because-you-want-to-develop-some-new/) [Anton Zeilinger](https://sms4smile.com/quotes/author/anton-zeilinger/) > [The hardware and the software used in the Breakthrough project will be compatible with other telescopes around the world, so they too can search…](https://sms4smile.com/quotes/yuri-milner/the-hardware-and-the-software-used-in-the-breakthrough-project-will/) [Yuri Milner](https://sms4smile.com/quotes/author/yuri-milner/) > [Just like the breakthroughs, the bad stuff always takes you by surprise. (121)](https://sms4smile.com/quotes/gail-giles/just-like-the-breakthroughs-the-bad-stuff-always-takes-you-by/) [Gail Giles](https://sms4smile.com/quotes/author/gail-giles/) > [There are just moments when all the stars are aligned for breakthrough products.](https://sms4smile.com/quotes/john-sculley/there-are-just-moments-when-all-the-stars-are-aligned-for/) [John Sculley](https://sms4smile.com/quotes/author/john-sculley/) > [The founder of any branch must be more ingenious than the common man. However, if his achievement is not carried on by disciples of…](https://sms4smile.com/quotes/bruce-lee/the-founder-of-any-branch-must-be-more-ingenious-than-the-common-man/) [Bruce Lee](https://sms4smile.com/quotes/author/bruce-lee/) > [Brokenness is often the road to breakthrough. Hang in there. Your time is coming.](https://sms4smile.com/quotes/anonymous/brokenness-is-often-the-road-to-breakthrough-hang-in-there-your-time/) [Anonymous](https://sms4smile.com/quotes/author/anonymous/) > [Historic changes and challenges. Breakthroughs in human knowledge and opportunity. And yet, for vast numbers across the globe, the daily realities have not altered.](https://sms4smile.com/quotes/anonymous/historic-changes-and-challenges-breakthroughs-in-human-knowledge-and/) [Anonymous](https://sms4smile.com/quotes/author/anonymous/) > [Obama is hardly the first president to seek rapprochement with our adversaries and reconciliation with our enemies, of course. But his determination to make…](https://sms4smile.com/quotes/stephen-f-hayes/obama-is-hardly-the-first-president-to-seek-rapprochement-with-our/) [Stephen F. Hayes](https://sms4smile.com/quotes/author/stephen-f-hayes/) > [... when things get rough, a breakthrough is just on the other side of the pain.](https://sms4smile.com/quotes/shirley-maclaine/when-things-get-rough-a-breakthrough-is-just-on-the-other-side-of-the/) [Shirley MacLaine](https://sms4smile.com/quotes/author/shirley-maclaine/) > [Tonight, after a breakthrough year for America, our economy is growing and creating jobs at the fastest pace since 1999.](https://sms4smile.com/quotes/barack-obama/tonight-after-a-breakthrough-year-for-america-our-economy-is-growing/) [Barack Obama](https://sms4smile.com/quotes/author/barack-obama/) > [Opposition is just proof that you're close to a major breakthrough keepgoing!](https://sms4smile.com/quotes/rev-run-2/opposition-is-just-proof-that-you-re-close-to-a-major-breakthrough/) [Rev Run](https://sms4smile.com/quotes/author/rev-run-2/) > [ Innovation is not a big breakthrough invention every time. Innovation is a constant thing. But if you don't have an innovative company \[team\], coming… ](https://sms4smile.com/quotes/jack-welch/innovation-is-not-a-big-breakthrough-invention-every-time-innovation/) [Jack Welch](https://sms4smile.com/quotes/author/jack-welch/) > [“A reset isn't going backwards; it's clearing the path to move forward.”](https://sms4smile.com/quotes/alex-rivera/a-reset-isn-t-going-backwards-it-s-clearing-the-path-to-move-forward/) [Alex Rivera](https://sms4smile.com/quotes/author/alex-rivera/) > [The consensus we arrived with States for amending the Constitution to implement GST is a major breakthrough. This alone has the potential to make…](https://sms4smile.com/quotes/narendra-modi/the-consensus-we-arrived-with-states-for-amending-the-constitution-to/) [Narendra Modi](https://sms4smile.com/quotes/author/narendra-modi/) > [Conceivably, blockchains could rely on a number of standards above the Internet's existing standards to allow a smooth bridging from one layer to another.…](https://sms4smile.com/quotes/william-mougayar/conceivably-blockchains-could-rely-on-a-number-of-standards-above-the/) [William Mougayar](https://sms4smile.com/quotes/author/william-mougayar/) [Browse all 507 Breakthrough quotes ](https://sms4smile.com/quotes/about/breakthrough/) ```json { "@context": "https://schema.org", "@graph": [ { "@type": "Quotation", "text": "I was reminded of the Sydney Harris cartoon that said 'adding two numbers that have not been added before does not constitute a mathematical breakthrough'.", "creator": { "@type": "Person", "name": "Ronald Graham" }, "isPartOf": { "@id": "https://sms4smile.com/quotes/#website" }, "url": "https://sms4smile.com/quotes/ronald-graham/i-was-reminded-of-the-sydney-harris-cartoon-that-said-adding-two/", "about": { "@type": "Thing", "name": "Breakthrough" }, "@id": "https://sms4smile.com/quotes/ronald-graham/i-was-reminded-of-the-sydney-harris-cartoon-that-said-adding-two/#quotation", "image": { "@type": "ImageObject", "@id": "https://sms4smile.com/quotes/i/eaf/ronald-graham-34796_breakthrough_i-was-reminded-of-the-sydney-harris-cart_1640224.jpg", "contentUrl": "https://sms4smile.com/quotes/i/eaf/ronald-graham-34796_breakthrough_i-was-reminded-of-the-sydney-harris-cart_1640224.jpg", "url": "https://sms4smile.com/quotes/i/eaf/ronald-graham-34796_breakthrough_i-was-reminded-of-the-sydney-harris-cart_1640224.jpg", "width": 1080, "height": 1080, "caption": "“I was reminded of the Sydney Harris cartoon that said 'adding two numbers that have not been added before…” — Ronald Graham", "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": "Ronald Graham", "item": "https://sms4smile.com/quotes/author/ronald-graham/" }, { "@type": "ListItem", "position": 4, "name": "I was reminded of the Sydney...", "item": "https://sms4smile.com/quotes/ronald-graham/i-was-reminded-of-the-sydney-harris-cartoon-that-said-adding-two/" } ], "@id": "https://sms4smile.com/quotes/ronald-graham/i-was-reminded-of-the-sydney-harris-cartoon-that-said-adding-two/#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 } } ] } ```