Change Quote by 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 of affine geometry, we have a definite invariant quadratic form, viz. the metrical groundform once and for all as an absolute datum.””
About This Quote
Source Lecture: Differential Geometry, Hermann Weyl, 1921
The quote calls for a mathematical framework that stays unchanged under any linear transformation, using a fixed quadratic form as an absolute reference point.
In simple terms: Create a theory unchanged under linear changes, using a constant quadratic form.
Key Takeaway
Define invariance using a fixed metric.
Themes
geometry
invariance
mathematics
Mood
analytical
theoretical
technical
Type
mathematical
philosophical
When to use this quote
- physics research
- engineering design
- computer graphics
- data analysis
Key Concepts
quadratic forms
linear transformations
metric invariance
Questions to Reflect On
- How does a fixed metric affect modeling curved spaces?
- When is invariance under all linear maps essential?
A Different Perspective
The fixed quadratic form may limit flexibility in non‑Euclidean contexts.
![“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)
![“Without the concepts, methods and results found and developed by previous generations right down to Greek antiquity one cannot understand either the aims or achievements of mathematics in the last 50 years. [Said in 1950]” quote by Hermann Weyl](https://sms4smile.com/quotes/img-quotes/a74/hermann-weyl-16709_achievement_without-the-concepts-methods-and-results_922221.jpg)
