--- title: "Meaning & Key Takeaway of: [Mathematics is] purely intellectual, a…" description: "\"[Mathematics is] purely intellectual, a pure theory of forms, which has for its objects not the combination of quantities or their images, the numbers,..." image: "https://sms4smile.com/quotes/i/9d5/hermann-hankel-65857_combination_mathematics-is-purely-intellectual-a-pur_2076406.png" --- # \[Mathematics is\] purely intellectual, a pure theory of… ![“[Mathematics is] purely intellectual, a pure theory of forms, which has for its objects not the combination of quantities or their images, the numbers, but things of thought to which there could correspond effective objects or relations, even though such a correspondence is not necessary.” quote by Hermann Hankel](https://sms4smile.com/quotes/i/9d5/hermann-hankel-65857_combination_mathematics-is-purely-intellectual-a-pur_2076406.png) [Download](https://sms4smile.com/quotes/i/9d5/hermann-hankel-65857_combination_mathematics-is-purely-intellectual-a-pur_2076406.png) [Open image](https://sms4smile.com/quotes/i/9d5/hermann-hankel-65857_combination_mathematics-is-purely-intellectual-a-pur_2076406.png) > “\[Mathematics is\] purely intellectual, a pure theory of forms, which has for its objects not the combination of quantities or their images, the numbers, but things of thought to which there could correspond effective objects or relations, even though such a correspondence is not necessary.” Hermann Hankel ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. Mathematics studies abstract ideas beyond numbers, focusing on pure thought and potential real-world links. **In simple terms:** Math is about pure ideas, not just numbers. Key Takeaway Appreciate abstract reasoning. Themes abstraction philosophy mathematics Mood analytical inquisitive Type academic philosophical When to use this quote - academic research - theoretical physics - philosophical debate - educational curriculum design Key Concepts ontology epistemology Questions to Reflect On - What value does pure theory bring to applied fields? - Can abstract concepts inspire innovation? A Different Perspective Pure abstraction can seem disconnected from practical needs. ★ ★ ★ ★ ★ No ratings yet [Correspondence](https://sms4smile.com/quotes/about/correspondence/) [Intellectual](https://sms4smile.com/quotes/about/intellectual/) [Mathematics](https://sms4smile.com/quotes/about/mathematics/) ## Related quotes > [Mathematics is purely hypothetical: it produces nothing but conditional propositions.](https://sms4smile.com/quotes/charles-sanders-peirce/mathematics-is-purely-hypothetical-it-produces-nothing-but/) [Charles Sanders Peirce](https://sms4smile.com/quotes/author/charles-sanders-peirce/) > [Mainstream economics scholarship produces theory without facts ("pure theory") and facts without theory ("applied economics").](https://sms4smile.com/quotes/michel-chossudovsky/mainstream-economics-scholarship-produces-theory-without-facts-pure-2/) [Michel Chossudovsky](https://sms4smile.com/quotes/author/michel-chossudovsky/) > [Mainstream economics scholarship produces theory without facts (pure theory) and facts without theory](https://sms4smile.com/quotes/michel-chossudovsky/mainstream-economics-scholarship-produces-theory-without-facts-pure/) [Michel Chossudovsky](https://sms4smile.com/quotes/author/michel-chossudovsky/) > [I believe, indeed, that overemphasis on the purely intellectual attitude, often directed solely to the practical and factual, in our education, has led directly…](https://sms4smile.com/quotes/albert-einstein/i-believe-indeed-that-overemphasis-on-the-purely-intellectual-2/) [Albert Einstein](https://sms4smile.com/quotes/author/albert-einstein/) > [To ask for a purely intellectual proof of the existence of God is like asking for the privilege of being able to see with…](https://sms4smile.com/quotes/meher-baba/to-ask-for-a-purely-intellectual-proof-of-the-existence-of-god-is/) [Meher Baba](https://sms4smile.com/quotes/author/meher-baba/) > [“What they achieved in art and literature is familiar to everybody, but what they did in the purely intellectual realm is even more exceptional.”](https://sms4smile.com/quotes/anonymous/what-they-achieved-in-art-and-literature-is-familiar-to-everybody-but/) [Anonymous](https://sms4smile.com/quotes/author/anonymous/) > [“I have at all times written my writings with my whole heart and soul: I do not know what purely intellectual problems are.”](https://sms4smile.com/quotes/friedrich-nietzsche/i-have-at-all-times-written-my-writings-with-my-whole-heart-and-soul/) [Friedrich Nietzsche](https://sms4smile.com/quotes/author/friedrich-nietzsche/) > [Chess is a fighting game which is purely intellectual and includes chance.](https://sms4smile.com/quotes/richard-reti/chess-is-a-fighting-game-which-is-purely-intellectual-and-includes/) [Richard Reti](https://sms4smile.com/quotes/author/richard-reti/) > [ \[On Cantor's work:\] The finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity. ](https://sms4smile.com/quotes/david-hilbert/on-cantor-s-work-the-finest-product-of-mathematical-genius-and-one-of/) [David Hilbert](https://sms4smile.com/quotes/author/david-hilbert/) > [Modern man, seeking a middle position in the evaluation of sense impression and thought, can, following Plato , interpret the process of understanding nature…](https://sms4smile.com/quotes/wolfgang-pauli/modern-man-seeking-a-middle-position-in-the-evaluation-of-sense/) [Wolfgang Pauli](https://sms4smile.com/quotes/author/wolfgang-pauli/) > [“Subject: This is a work environment and this is harassment Mr. Zaccadelli, I am writing to inform you that your proposition has been rejected.…](https://sms4smile.com/quotes/chelsea-m-cameron/subject-this-is-a-work-environment-and-this-is-harassment-mr/) [Chelsea M. 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In mathematics alone each generations adds…](https://sms4smile.com/quotes/hermann-hankel/in-most-sciences-one-generation-tears-down-what-another-has-built-and/) Hermann Hankel > [Isolated, so-called "pretty theorems" have even less value in the eyes of a modern mathematician than the discovery of a new "pretty flower" has…](https://sms4smile.com/quotes/hermann-hankel/isolated-so-called-pretty-theorems-have-even-less-value-in-the-eyes/) Hermann Hankel Explore all 4 Hermann Hankel quotes ## More Combination quotes > [Anytime there is any lyrical meaning or combination in my mixes, it's very blatant. I'm not trying to make any statement or anything like…](https://sms4smile.com/quotes/girl-talk/anytime-there-is-any-lyrical-meaning-or-combination-in-my-mixes-it-s/) [Girl Talk](https://sms4smile.com/quotes/author/girl-talk/) > [We do not claim that punning is legitimate wit. Wit consists in combination of ideas, punning in combination of words only. 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