---
title: "2 Axioms Quotes By Hermann Weyl"
description: "2 Axioms quotes by Hermann Weyl. Plus more from Hermann Weyl and more Axioms sayings from other authors."
image: "https://sms4smile.com/quotes/i/522/hermann-weyl-16709_axioms_by-refraining-from-reducing-multiplicati_1505622.png"
---

> [“By refraining from reducing multiplication to addition we are enabled through these axioms to banish continuity, which is so difficult to fix precisely, from the logical structure of geometry.”](https://sms4smile.com/quotes/hermann-weyl/by-refraining-from-reducing-multiplication-to-addition-we-are-enabled/)

[Hermann Weyl](https://sms4smile.com/quotes/author/hermann-weyl/)

[Image](https://sms4smile.com/quotes/i/522/hermann-weyl-16709_axioms_by-refraining-from-reducing-multiplicati_1505622.png)

> [The constructs of the mathematical mind are at the same time free and necessary. The individual mathematician feels free to define his notions and set up his axioms as he pleases. But the question is will he get his fellow…](https://sms4smile.com/quotes/hermann-weyl/the-constructs-of-the-mathematical-mind-are-at-the-same-time-free-and/)

[Hermann Weyl](https://sms4smile.com/quotes/author/hermann-weyl/)

[Image](https://sms4smile.com/quotes/i/962/hermann-weyl-16709_accidents_the-constructs-of-the-mathematical-mind_2947610.png)

## Other authors on Axioms

- [Mokokoma Mokhonoana 76 quotes](https://sms4smile.com/quotes/about/axioms/mokokoma-mokhonoana/)

## More by Hermann Weyl

> [For mathematics, even to the logical forms in which it moves, is entirely dependent on the concept of natural number.](https://sms4smile.com/quotes/hermann-weyl/for-mathematics-even-to-the-logical-forms-in-which-it-moves-is/)

[Hermann Weyl](https://sms4smile.com/quotes/author/hermann-weyl/)

> [Mathematics has the inhuman quality of starlight, brilliant and sharp, but cold.](https://sms4smile.com/quotes/hermann-weyl/mathematics-has-the-inhuman-quality-of-starlight-brilliant-and-sharp/)

[Hermann Weyl](https://sms4smile.com/quotes/author/hermann-weyl/)

> [The introduction of numbers as coordinates by reference to the particular division scheme of the open one-dimensional continuum is an act of violence whose…](https://sms4smile.com/quotes/hermann-weyl/the-introduction-of-numbers-as-coordinates-by-reference-to-the/)

[Hermann Weyl](https://sms4smile.com/quotes/author/hermann-weyl/)

> [“Our generation is witness to a development of physical knowledge such as has not been seen since the days of Kepler, Galileo and Newton,…](https://sms4smile.com/quotes/hermann-weyl/our-generation-is-witness-to-a-development-of-physical-knowledge-such/)

[Hermann Weyl](https://sms4smile.com/quotes/author/hermann-weyl/)

> [“the problem is then to develop a theory of invariance with respect to arbitrary linear transformations, in which, however, in contra-distinction to the case…](https://sms4smile.com/quotes/hermann-weyl/the-problem-is-then-to-develop-a-theory-of-invariance-with-respect-to/)

[Hermann Weyl](https://sms4smile.com/quotes/author/hermann-weyl/)

> [Before you generalize, formalize, and axiomatize there must be mathematical substance.](https://sms4smile.com/quotes/hermann-weyl/before-you-generalize-formalize-and-axiomatize-there-must-be/)

[Hermann Weyl](https://sms4smile.com/quotes/author/hermann-weyl/)

> [The whole is always more, is more capable of a much greater variety of wave states, than the combination of its parts. ... In…](https://sms4smile.com/quotes/hermann-weyl/the-whole-is-always-more-is-more-capable-of-a-much-greater-variety-of/)

[Hermann Weyl](https://sms4smile.com/quotes/author/hermann-weyl/)

> [You can not apply mathematics as long as words still becloud reality.](https://sms4smile.com/quotes/hermann-weyl/you-can-not-apply-mathematics-as-long-as-words-still-becloud-reality/)

[Hermann Weyl](https://sms4smile.com/quotes/author/hermann-weyl/)

> [Not only in geometry, but to a still more astonishing degree in physics, has it become more and more evident that as soon as…](https://sms4smile.com/quotes/hermann-weyl/not-only-in-geometry-but-to-a-still-more-astonishing-degree-in/)

[Hermann Weyl](https://sms4smile.com/quotes/author/hermann-weyl/)

> [The introduction of numbers as coordinates is an act of violence.](https://sms4smile.com/quotes/hermann-weyl/the-introduction-of-numbers-as-coordinates-is-an-act-of-violence/)

[Hermann Weyl](https://sms4smile.com/quotes/author/hermann-weyl/)

> [“The goal of mathematics is the symbolic comprehension of the infinite with human, that is finite, means.”](https://sms4smile.com/quotes/hermann-weyl/the-goal-of-mathematics-is-the-symbolic-comprehension-of-the-infinite/)

[Hermann Weyl](https://sms4smile.com/quotes/author/hermann-weyl/)

> [God exists because arithmetic is consistent - the Devil exists because we can't prove it!](https://sms4smile.com/quotes/hermann-weyl/god-exists-because-arithmetic-is-consistent-the-devil-exists-because/)

[Hermann Weyl](https://sms4smile.com/quotes/author/hermann-weyl/)

> [Without the concepts, methods and results found and developed by previous generations right down to Greek antiquity one cannot understand either the aims or…](https://sms4smile.com/quotes/hermann-weyl/without-the-concepts-methods-and-results-found-and-developed-by/)

[Hermann Weyl](https://sms4smile.com/quotes/author/hermann-weyl/)

> [Besides language and music, mathematics is one of the primary manifestations of the free creative power of the human mind.](https://sms4smile.com/quotes/hermann-weyl/besides-language-and-music-mathematics-is-one-of-the-primary/)

[Hermann Weyl](https://sms4smile.com/quotes/author/hermann-weyl/)

> [Our mathematics of the last few decades has wallowed in generalities and formalizations.](https://sms4smile.com/quotes/hermann-weyl/our-mathematics-of-the-last-few-decades-has-wallowed-in-generalities/)

[Hermann Weyl](https://sms4smile.com/quotes/author/hermann-weyl/)

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