Combination Quote by Hermann Hankel
![“[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/img-quotes/9d5/hermann-hankel-65857_combination_mathematics-is-purely-intellectual-a-pur_2076406.jpg)
“[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.”
About This Quote
Source Philosophical Treatise: Foundations of Mathematics, 1885
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.
![“[On Cantor's work:] The finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.” quote by David Hilbert](https://sms4smile.com/quotes/img-quotes/1dd/david-hilbert-12585_achievement_on-cantor-s-work-the-finest-product-of-m_34708.jpg)
![“Geometry, which should only obey Physics, when united with it sometimes commands it. If it happens that the question which we wish to examine is too complicated for all the elements to be able to enter into the analytical comparison we wish to make, we separate the more inconvenient [elements], we…” quote by Jean le Rond d'Alembert](https://sms4smile.com/quotes/img-quotes/0d9/jean-le-rond-d-alembert-26487_able_geometry-which-should-only-obey-physics_6945.jpg)
