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Origin of exact and closed differential expressions
In differential geometry and other fields, an expression involving differentials can be closed or exact. In $\mathbb R^2\setminus\{0\}$ for example, $dr$ is exact whereas $d\theta$ is closed but not exact. What is the origin of these terms? Note…
Mikhail Katz
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First occurrence of hyperboloid paraboloid
The ancient greeks considered surfaces such as cones, but did they study the hyperbolic paraboloid? What is the first occurrence of such surface in history?
coudy
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When were arrows first used to visualise vectors?
I guess the use of arrows to visualise vectors came before the general notion of vectors, so a more precise question is: when where arrows first used to visualise physical (or mathematical) quantities which are nowadays considered to be vectors? For…
Michael Bächtold
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Why didn't Einstein propose any metric solution to his equations?
I've read about general relativity (GR) recently and something stroke me: Einstein came up with his equations in 1915, linking the metric of spacetime to the distribution of energy (more exactly, to the stress-energy tensor), without providing any…
Weier
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First appearance of the "four triangles and a square" proof of the Pythagorean Theorem
A well-known proof of the Pythagorean Theorem is illustrated in the figure below:
This figure shows a square with side lengths $a + b$, dissected into four right triangles (each with area $\frac 12 ab$) and a square (of side $c$). A basic area…
mweiss
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Cantor, set theory and foundations
Did Georg Cantor ever think that set theory could serve as a foundational system for all of mathematics?
He died in 1918, but Zermelo set theory (just Z, no ZF or ZFC yet) was described in a paper by Zermelo in 1908, ten years before Cantor's…
Alex
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Earliest mention of permutation matrices, or equivalent? More generally, matrices for arbitrary functions between finite sets?
Permutation matrices I assume have a long history, and would be surprised if they were first considered only long after the work of Shur just after 1900, on the representation theory of $S_n$.
Question 1 When were they first considered?
One can…
David Roberts
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Could ancient astronomers have proven heliocentrism?
Could ancient astronomers have proven heliocentrism and, if so, how could they have done so?
Adrien Hingert
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What is the etymology of the term space-time?
I'm looking for the earliest references to the word space-time (in the modern sense), in any language.
The first references would likely be in German, as Raum-Zeit or Raumzeit.
Of course, H. Minkowski is credited as the originator of the idea. I…
John
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Is Koestler's ‘The Sleepwalkers’ still well regarded? Is there a more recent similar source?
Arthur Koestler's The Sleepwalkers is well-known as both a group biography of Copernicus, Brahe, Kepler and Galileo and an account of the revolutionary turn in astronomy that, in Koestler's phrasing, they ‘sleepwalked’ through. I think it's an…
Norman Gray
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When did people first know that the sky was illuminated by the Sun?
During the day, the sky is bright blue and, along with the yellow light from the Sun, it illuminates the surface of the Earth.
What is the earliest recorded knowledge that the sky wasn't self-illuminating, but simply something that was itself…
Ray Butterworth
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What's the history of "left as exercise" or notions similar to that?
It is now common to come across the term "left as exercise" in mathematics textbooks, and from there a comical usage of such terms was developed, typically by applying them to absurdly difficult propositions.
Who is the first one to use such phrase?…
Vincent Phillips
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6
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When did bounties and prize money for open mathematical problems start being a thing?
I'm a science/math journalist [ger] and currently I'm working on an article about the culture of prize money/bounties for solving open mathematical problems (Millennium Prize Problems and such). One section will be about the history of such bounties…
j grk
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Did Kronecker's "ganzen Zahlen" refer to whole numbers as natural numbers or integers?
Maybe this is a question better for German language Stack Exchange, but in the quote attributed to Kronecker:
Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk.
So "ganzen Zahlen" translates I believe to whole numbers,…
qwr
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Why are the symbols E, F, G, L, M, and N used for the coefficients of the fundamental forms?
In differential geometry, if $e_1$ and $e_2$ are bases for a tangent space $T_pM$, then the coefficients of the first fundamental form is:
$$\begin{align}E&:=\left\\F&:=\left\\G&:=\left\end{align}$$
And…
Slate
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