Assumption Quote by David Hilbert
“Mathematics is a presuppositionless science. To found it I do not need God, as does Kronecker, or the assumption of a special faculty of our understanding attuned to the principle of mathematical induction, as does Poincaré, or the primal intuition of Brouwer, or, finally, as do Russell and Whitehead, axioms of infinity, reducibility, or completeness, which in fact are actual, contentual assumptions that cannot be compensated for by consistency proofs.”
About This Quote
Source Book: Foundations of Mathematics, David Hilbert, 1925
Mathematics can be built without relying on any prior assumptions, divine or philosophical, by using pure logical deduction.
In simple terms: Math needs no prior assumptions.
Key Takeaway
Build math from pure logic.
Themes
logic
philosophy
mathematics
foundations
Mood
analytical
reflective
Type
philosophical
academic
instructive
When to use this quote
- teaching math
- research in foundations
- philosophical debate
- educational curricula
Key Concepts
formalism
axiomatic method
foundationalism
Questions to Reflect On
- Is pure logic sufficient for all mathematical truths?
- How do we handle concepts that resist formalization?
A Different Perspective
Some argue intuition or empirical insight is essential for mathematical discovery.
![“[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)
![“[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)
