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 ...
Conifold's user avatar
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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 (...
Conifold's user avatar
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11 votes
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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.)...
Francois Ziegler's user avatar
11 votes
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Who do I blame for non-Euclidean geometry?

Technically, the first was Lobachevski (published in 1829-30). Bolyai was independent (published in 1832). Gauss discovered it independently of both (not published). A more complicated research is ...
Alexandre Eremenko's user avatar
10 votes
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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Riemann discussed a "unified field theory", including light, electromagnetism and gravity, in the unpublished paper Neue Mathematische Principien der Naturphilosophie (New Mathematical Principles of ...
Conifold's user avatar
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8 votes
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How did the exponential map of Riemannian geometry get its name?

History does not often develop in the order of textbook expositions. Today the exponential map is introduced early in both Riemannian geometry and Lie group theory, but many results it is used to ...
Conifold's user avatar
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8 votes
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What is the origin of the use of "g" for a Riemannian metric?

You are guessing correctly. Riemann did not use $g$ for the metric tensor, he writes things like $ds^2$ or $\sum dx^2$ instead, see his 1854 lecture "On the Hypotheses which lie at the Bases of ...
Conifold's user avatar
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7 votes
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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 ...
Alexandre Eremenko's user avatar
7 votes
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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 ...
Conifold's user avatar
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5 votes

Who do I blame for non-Euclidean geometry?

Usually this is attributed to, in alphabetical order, Bolyai, Gauss, and Lobachevski all working at about the same time in the first third of the 19th century. This certainly predates Riemann. A ...
Mikhail Katz's user avatar
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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 ...
Angelo Fuchs's user avatar
3 votes

Who do I blame for non-Euclidean geometry?

Regarding first developments in non- euclidean geometry, Eugenio Beltrami considered Lobachevsky-Bolyai geometry as nothing else but euclidean geometry on a space with (constant) negative curvature. ...
Margaret Friedland's user avatar
3 votes
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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 ...
Conifold's user avatar
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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 ...
Alexandre Eremenko's user avatar
2 votes
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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 ...
Francois Ziegler's user avatar
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 ...
sand1's user avatar
  • 2,387
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 ...
Alexandre Eremenko's user avatar
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 ...
Alexandre Eremenko's user avatar
2 votes
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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 ...
user6530's user avatar
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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 ...
paul garrett's user avatar
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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 ...
Eric Baird's user avatar
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 ...
Geremia's user avatar
  • 5,329
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 ...
Andre M. Pietroschek's user avatar

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