--- title: "Meaning & Key Takeaway of: It is well known that the central problem…" description: "\"It is well known that the central problem of the whole of modern mathematics is the study of transcendental functions defined by differential equations..." image: "https://sms4smile.com/quotes/i/70b/felix-klein-38045_certainty_it-is-well-known-that-the-central-proble_423521.png" --- # It is well known that the central problem of the whole of… ![“It is well known that the central problem of the whole of modern mathematics is the study of transcendental functions defined by differential equations.” quote by Felix Klein](https://sms4smile.com/quotes/i/70b/felix-klein-38045_certainty_it-is-well-known-that-the-central-proble_423521.png) [Download](https://sms4smile.com/quotes/i/70b/felix-klein-38045_certainty_it-is-well-known-that-the-central-proble_423521.png) [Open image](https://sms4smile.com/quotes/i/70b/felix-klein-38045_certainty_it-is-well-known-that-the-central-proble_423521.png) > “It is well known that the central problem of the whole of modern mathematics is the study of transcendental functions defined by differential equations.” [Felix Klein](https://sms4smile.com/quotes/author/felix-klein/) ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. The main challenge in modern mathematics is understanding transcendental functions that satisfy differential equations. **In simple terms:** Studying complex functions defined by differential equations is the core problem. Key Takeaway Focus on differential equations to grasp advanced functions. Themes mathematics analysis differential equations transcendental functions Mood analytical inquisitive academic Type educational inspirational When to use this quote - research - advanced coursework - theoretical physics - engineering modeling Key Concepts function theory complex analysis mathematical physics Questions to Reflect On - How do differential equations shape modern scientific models? - What tools help when closed forms are unavailable? A Different Perspective Complex functions may lack closed‑form solutions, limiting explicit analysis. ★ ★ ★ ★ ★ No ratings yet [Certainty](https://sms4smile.com/quotes/about/certainty/) [Differential equations](https://sms4smile.com/quotes/about/differential-equations/) [Education](https://sms4smile.com/quotes/about/education/) [Logic](https://sms4smile.com/quotes/about/logic/) [Mathematics](https://sms4smile.com/quotes/about/mathematics/) [Ontology](https://sms4smile.com/quotes/about/ontology/) [Problem](https://sms4smile.com/quotes/about/problem/) [Reasoning](https://sms4smile.com/quotes/about/reasoning/) [Transcendental](https://sms4smile.com/quotes/about/transcendental/) [Uncertainty](https://sms4smile.com/quotes/about/uncertainty/) ## Related quotes > [“Modern mathematics contains much more than that, of course. 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Its borders are protected by dense thickets of technical terms; its landscapes are a mass of…](https://sms4smile.com/quotes/ivars-peterson/to-most-outsiders-modern-mathematics-is-unknown-territory-its-borders/) [Ivars Peterson](https://sms4smile.com/quotes/author/ivars-peterson/) > [Few realize that the world of modern mathematics is rich with vivid images and provocative ideas.](https://sms4smile.com/quotes/ivars-peterson/few-realize-that-the-world-of-modern-mathematics-is-rich-with-vivid/) [Ivars Peterson](https://sms4smile.com/quotes/author/ivars-peterson/) > [The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than…](https://sms4smile.com/quotes/john-von-neumann/the-calculus-was-the-first-achievement-of-modern-mathematics-and-it/) [John von Neumann](https://sms4smile.com/quotes/author/john-von-neumann/) > [The central problem is always in the midst of the people of God, not in the circumstances surrounding them.](https://sms4smile.com/quotes/francis-schaeffer/the-central-problem-is-always-in-the-midst-of-the-people-of-god-not/) [Francis Schaeffer](https://sms4smile.com/quotes/author/francis-schaeffer/) > [Protein synthesis is a central problem for the whole of biology, and that it is in all probability closely related to gene action.](https://sms4smile.com/quotes/francis-crick/protein-synthesis-is-a-central-problem-for-the-whole-of-biology-and/) [Francis Crick](https://sms4smile.com/quotes/author/francis-crick/) > [Perhaps the central problem we face in all of computer science is how we are to get to the situation where we build on…](https://sms4smile.com/quotes/richard-hamming/perhaps-the-central-problem-we-face-in-all-of-computer-science-is-how/) [Richard Hamming](https://sms4smile.com/quotes/author/richard-hamming/) > [The balancing of present wants against the future is really the central problem of ethics.](https://sms4smile.com/quotes/walter-lippmann/the-balancing-of-present-wants-against-the-future-is-really-the/) [Walter Lippmann](https://sms4smile.com/quotes/author/walter-lippmann/) > [The major credit I think Jim and I deserve ... is for selecting the right problem and sticking to it. It's true that by…](https://sms4smile.com/quotes/francis-crick/the-major-credit-i-think-jim-and-i-deserve-is-for-selecting-the-right/) [Francis Crick](https://sms4smile.com/quotes/author/francis-crick/) ## More by Felix Klein > [Every one who understands the subject will agree that even the basis on which the scientific explanation of nature rests is intelligible only to…](https://sms4smile.com/quotes/felix-klein/every-one-who-understands-the-subject-will-agree-that-even-the-basis/) [Felix Klein](https://sms4smile.com/quotes/author/felix-klein/) > [Mathematics in general is fundamentally the science of self-evident things.](https://sms4smile.com/quotes/felix-klein/mathematics-in-general-is-fundamentally-the-science-of-self-evident/) [Felix Klein](https://sms4smile.com/quotes/author/felix-klein/) > [The developing science departs at the same time more and more from its original scope and purpose and threatens to sacrifice its earlier unity…](https://sms4smile.com/quotes/felix-klein/the-developing-science-departs-at-the-same-time-more-and-more-from/) [Felix Klein](https://sms4smile.com/quotes/author/felix-klein/) > [The teacher manages to get along still with the cumbersome algebraic analysis, in spite of its difficulties and imperfections, and avoids the smooth infinitesimal…](https://sms4smile.com/quotes/felix-klein/the-teacher-manages-to-get-along-still-with-the-cumbersome-algebraic/) [Felix Klein](https://sms4smile.com/quotes/author/felix-klein/) > [Everyone knows what a curve is, until he has studied enough mathematics to become confused through the countless number of possible exceptions.](https://sms4smile.com/quotes/felix-klein/everyone-knows-what-a-curve-is-until-he-has-studied-enough/) [Felix Klein](https://sms4smile.com/quotes/author/felix-klein/) > [Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs.](https://sms4smile.com/quotes/felix-klein/thus-in-a-sense-mathematics-has-been-most-advanced-by-those-who/) [Felix Klein](https://sms4smile.com/quotes/author/felix-klein/) > [The presentation of mathematics in schools should be psychological and not systematic. The teacher, so to speak, should be a diplomat. He must take…](https://sms4smile.com/quotes/felix-klein/the-presentation-of-mathematics-in-schools-should-be-psychological/) [Felix Klein](https://sms4smile.com/quotes/author/felix-klein/) > [Regarding the fundamental investigations of mathematics, there is no final ending ... no first beginning.](https://sms4smile.com/quotes/felix-klein/regarding-the-fundamental-investigations-of-mathematics-there-is-no/) [Felix Klein](https://sms4smile.com/quotes/author/felix-klein/) > [Projective geometry has opened up for us with the greatest facility new territories in our science, and has rightly been called the royal road…](https://sms4smile.com/quotes/felix-klein/projective-geometry-has-opened-up-for-us-with-the-greatest-facility/) [Felix Klein](https://sms4smile.com/quotes/author/felix-klein/) > [The greatest mathematicians, as Archimedes, Newton, and Gauss, always united theory and applications in equal measure.](https://sms4smile.com/quotes/felix-klein/the-greatest-mathematicians-as-archimedes-newton-and-gauss-always/) [Felix Klein](https://sms4smile.com/quotes/author/felix-klein/) > [Among mathematicians in general, three main categories may be distinguished; and perhaps the names logicians, formalists, and intuitionists may serve to characterize them.](https://sms4smile.com/quotes/felix-klein/among-mathematicians-in-general-three-main-categories-may-be/) [Felix Klein](https://sms4smile.com/quotes/author/felix-klein/) [Explore all 12 Felix Klein quotes ](https://sms4smile.com/quotes/author/felix-klein/) ## More Certainty quotes > [A common fallacy in much of the adverse criticism to which science is subjected today is that it claims certainty, infallibility and complete emotional…](https://sms4smile.com/quotes/cyril-norman-hinshelwood/a-common-fallacy-in-much-of-the-adverse-criticism-to-which-science-is/) [Cyril Norman Hinshelwood](https://sms4smile.com/quotes/author/cyril-norman-hinshelwood/) > [Sometimes we have the absolute certainty there's something inside us that's so hideous and monstrous that if we ever search it out we won't…](https://sms4smile.com/quotes/hubert-selby-jr/sometimes-we-have-the-absolute-certainty-there-s-something-inside-us/) [Hubert Selby, Jr](https://sms4smile.com/quotes/author/hubert-selby-jr/) > [The past and the future become unimportant. There is only that moment, and the incredible certainty that everything under the sun has been written…](https://sms4smile.com/quotes/paulo-coelho/the-past-and-the-future-become-unimportant-there-is-only-that-moment/) [Paulo Coelho](https://sms4smile.com/quotes/author/paulo-coelho/) > [In the mental disturbance and effort of writing, what sustains you is the certainty that on every page there is something left unsaid.](https://sms4smile.com/quotes/cesare-pavese/in-the-mental-disturbance-and-effort-of-writing-what-sustains-you-is/) [Cesare Pavese](https://sms4smile.com/quotes/author/cesare-pavese/) > [Of course I doubt. I do not practice a certainty. I practice a faith.](https://sms4smile.com/quotes/robert-breault/of-course-i-doubt-i-do-not-practice-a-certainty-i-practice-a-faith/) [Robert Breault](https://sms4smile.com/quotes/author/robert-breault/) > [The world is a wonderfully weird place, consensual reality is significantly flawed, no institution can be trusted, certainty is a mirage, security a delusion,…](https://sms4smile.com/quotes/tom-robbins/the-world-is-a-wonderfully-weird-place-consensual-reality-is/) [Tom Robbins](https://sms4smile.com/quotes/author/tom-robbins/) > [As a businessman, I know that businesses need certainty.](https://sms4smile.com/quotes/bill-foster/as-a-businessman-i-know-that-businesses-need-certainty/) [Bill Foster](https://sms4smile.com/quotes/author/bill-foster/) > [It is suggested that in domestic violence at least the presence or absence of a firearm, or of any other type of weapon, is…](https://sms4smile.com/quotes/colin-greenwood/it-is-suggested-that-in-domestic-violence-at-least-the-presence-or/) [Colin Greenwood](https://sms4smile.com/quotes/author/colin-greenwood/) > [Every single person who is a member of our party deserves to have certainty. They deserve to know that my attention and focus is…](https://sms4smile.com/quotes/annamie-paul/every-single-person-who-is-a-member-of-our-party-deserves-to-have/) [Annamie Paul](https://sms4smile.com/quotes/author/annamie-paul/) > [The significance and volume of repairs that are needed across the country demand that we give state and local governments the long-term certainty they…](https://sms4smile.com/quotes/sam-graves/the-significance-and-volume-of-repairs-that-are-needed-across-the/) [Sam Graves](https://sms4smile.com/quotes/author/sam-graves/) > [“Death is the one great certainty in life. That’s what my dad used to say. Nothing else is certain. Not love. Not happiness. Not…](https://sms4smile.com/quotes/mila-gray/death-is-the-one-great-certainty-in-life-that-s-what-my-dad-used-to/) [Mila Gray](https://sms4smile.com/quotes/author/mila-gray/) > [ \[I\]f in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge… ](https://sms4smile.com/quotes/roger-bacon/i-f-in-other-sciences-we-should-arrive-at-certainty-without-doubt-and/) [Roger Bacon](https://sms4smile.com/quotes/author/roger-bacon/) > [Do not lose hope; St. Joseph also experienced moments of difficulty, but he never lost faith and was able to overcome them, in the…](https://sms4smile.com/quotes/pope-francis/do-not-lose-hope-st-joseph-also-experienced-moments-of-difficulty-but/) [Pope Francis](https://sms4smile.com/quotes/author/pope-francis/) > [As the future is never known with certainty, the evaluation of the prospective benefits requires the formation of expectations. An acceptable house, partner or…](https://sms4smile.com/quotes/dale-t-mortensen/as-the-future-is-never-known-with-certainty-the-evaluation-of-the/) [Dale T. Mortensen](https://sms4smile.com/quotes/author/dale-t-mortensen/) > [Finding someone that trusted my vision helped me find certainty in who I was.](https://sms4smile.com/quotes/syd/finding-someone-that-trusted-my-vision-helped-me-find-certainty-in/) [Syd](https://sms4smile.com/quotes/author/syd/) [Browse all 1,776 Certainty quotes ](https://sms4smile.com/quotes/about/certainty/) ```json { "@context": "https://schema.org", "@graph": [ { "@type": "Quotation", "text": "It is well known that the central problem of the whole of modern mathematics is the study of transcendental functions defined by differential equations.", "creator": { "@type": "Person", "name": "Felix Klein" }, "isPartOf": { "@id": "https://sms4smile.com/quotes/#website" }, "url": "https://sms4smile.com/quotes/felix-klein/it-is-well-known-that-the-central-problem-of-the-whole-of-modern/", "about": { "@type": "Thing", "name": "Certainty" }, "@id": "https://sms4smile.com/quotes/felix-klein/it-is-well-known-that-the-central-problem-of-the-whole-of-modern/#quotation", "image": { "@type": "ImageObject", "@id": "https://sms4smile.com/quotes/i/70b/felix-klein-38045_certainty_it-is-well-known-that-the-central-proble_423521.png", "contentUrl": "https://sms4smile.com/quotes/i/70b/felix-klein-38045_certainty_it-is-well-known-that-the-central-proble_423521.png", "url": "https://sms4smile.com/quotes/i/70b/felix-klein-38045_certainty_it-is-well-known-that-the-central-proble_423521.png", "width": 1080, "height": 1080, "caption": "“It is well known that the central problem of the whole of modern mathematics is the study of transcendental…” — Felix Klein", "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": "Felix Klein", "item": "https://sms4smile.com/quotes/author/felix-klein/" }, { "@type": "ListItem", "position": 4, "name": "It is well known that the...", "item": "https://sms4smile.com/quotes/felix-klein/it-is-well-known-that-the-central-problem-of-the-whole-of-modern/" } ], "@id": "https://sms4smile.com/quotes/felix-klein/it-is-well-known-that-the-central-problem-of-the-whole-of-modern/#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 } } ] } ```