27
votes
What was the relationship between Einstein and Minkowski?
A good account is Weinstein, Max Born, Albert Einstein and Hermann Minkowski's Space-Time Formalism of Special Relativity. They did no have much of a relationship, what it was is well-summarized by ...
- 78.3k
12
votes
Accepted
What theorem of Sophus Lie on the number of geometries is H. Poincaré referring to?
Poincare refers to the Lie's solution of the so-called problem of space, a.k.a. the Helmholtz , or Riemann-Helmholtz, or Helmholtz-Lie problem of space, which amounts to characterizing all manifolds (...
- 78.3k
11
votes
Accepted
Help translate from German a quote by Hermann Weyl in Space Time Matter
One must firmly protest these orgies of a formalism with which even technicians are getting harassed today.
(Literally: of the formalism, with which one is beginning to harass even technicians today.)...
- 7,779
10
votes
Accepted
What are the references for Riemann's discussion of gravity?
Riemann discussed a "unified field theory", including light, electromagnetism and gravity, in the unpublished paper Neue Mathematische Principien der Naturphilosophie (New Mathematical Principles of ...
- 78.3k
7
votes
Accepted
Did Riemann invent the Riemann curvature tensor?
A short answer: yes, he did.
Riemann's habilitation lecture was aimed at a broad non-mathematical audience,
so he did not use formulas in it, trying to explain everything in words. The curvature ...
- 50.5k
7
votes
Accepted
Did Clifford introduce the "Clifford torus", and for what purpose?
The Clifford torus was introduced by Clifford in 1873, not as embedded into $\mathbb{R}^4$ or $\mathbb{C}^2$, but first projectively and then intrinsically, by identifying the opposite sides of a flat ...
- 78.3k
3
votes
Help translate from German a quote by Hermann Weyl in Space Time Matter
One has to object thoroughly to the orgies of formalism, with which recently even technicians have been bothered.
Man muß ... protestieren -> One has to object to (in the context of legislative ...
- 139
3
votes
Accepted
Who was first to recognize the link between (synthetic) elliptic geometry and geometry on the sphere?
Elliptic geometry is not equivalent to geometry on the sphere because there is non-unique line through antipodal points on the sphere, contrary to one of the axioms. One needs to identify the ...
- 78.3k
3
votes
Material models of Riemann surfaces
Kharkiv University (Ukraine) subscribed to all models made M. Schilling, who probably was a student of Klein, and who run a company making and selling these models. Currently they photograph them and ...
- 50.5k
2
votes
Accepted
How is "soul" meant to be understood in the context of the "Soul Theorem"
http://www.nytimes.com/2008/06/19/science/19gromoll.html:
In the soul theorem, published in 1972, Dr. Gromoll and Dr. Cheeger were studying the properties of certain surfaces that could have flat ...
- 7,779
2
votes
Did the formation of Differential Geometry come before Differential Topology/ Topology in general?
Yes, differential geometry is older. Though he had predecessors, Gauss can be considered the founding father of differential geometry with his book General investigation of curved surfaces, 1827. This ...
- 50.5k
2
votes
What is Metric tensor's origin?
The metric tensor was introduced by Riemann in his lecture:
1854 – Über die Hypothesen, welche der Geometrie zugrunde liegen. There are several English translations, and a comprehensive commentary in ...
- 50.5k
2
votes
What was the relationship between Einstein and Minkowski?
There is a monolithic Einstein myth consolidated by scores of popular books which is a great inconvenience for anybody trying to make some sense of the history. Cornifold's answer and refs already ...
- 2,442
2
votes
Accepted
Reference for "A manifold is a topological space which satisfies a long series of axioms."
It is difficult, if not impossible, to determine which "recent American book" Arnold is referring to, but the statement he makes is certainly correct.
There are some very interesting surveys ...
- 4,090
1
vote
What did Helmholtz mean about crumpling a hemisphere?
I do not know how to give a precise description, nor draw a picture of it, but I can give anecdotal confirmation that such a thing is real.
Namely, if you get a thin, flexible-but-not-stretchy ...
- 1,096
1
vote
What was the relationship between Einstein and Minkowski?
Einstein believed that his insufficiently deferential attitude to his professors was what caused him to end up in the scientific "wilderness", unable to get a job in research. He was ...
- 11
1
vote
Help translate from German a quote by Hermann Weyl in Space Time Matter
Heney L. Beose's translation (last sentence of ch. 1, § 6, p. 54) says:
An emphatic protest must be entered against these orgies of formalism which are threatening the peace of even the technical ...
- 5,440
1
vote
Help translate from German a quote by Hermann Weyl in Space Time Matter
"Man muß gegen die Orgien des Formalismus, mit dem man heute sogar die Techniker zu belästigen beginnt, nachdrücklich protestieren."
Both of the translations you got are 'decent'. Technician is ...
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