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On the history of Haar measure
Haar measure is a well-known concept in measure theory.
Many books are perfectly dedicated to present its existence and uniqueness such as measure theory for D. Cohn.
I am looking for a good reference on the history of Haar measure.
Neil hawking
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How did J. J. Thomson establish the particle nature of the electron?
In its article about how the electron was discovered, Wikipedia says that Thomson and his students performed experiments which suggested that cathode rays were negatively charged "particles". But even after reading about his experiments I am unable…
user662650
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7
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Were ancient Romans so bad at computations before Arab numerals?
It is often said that Romans (see below) had a terrible number system, which made computations a mess. I do believe this, but I'm suspicious of the claim that nobody had better ways to do computations until Fibonacci brought Eastern techniques to…
seldon
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7
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When and how did the notion/idea of physical constant emerge?
Physical constants (e.g. c, h, G, alpha and so on) play a central role in our scientific theories and they have yet drawn much of controversial flavor into questions concerning the foundational status of those theories. From a historical point of…
Louis
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7
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The relationship between solvability of ruler and compass problems and solvability of algebraic equations by radicals
Galois obtained necessary and sufficient conditions for an algebraic equation (in one variable) to be solvable by extraction of a chain of square roots. A beautiful application of this is to the problem of solvability of geometric problems by ruler…
nwr
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7
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2 answers
Who coined the term random variable?
Who is the first person defined the concept of a random variable?
hanugm
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7
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3 answers
How did Newton measure forces in his experiments to establish the laws of motion?
I wanted to know about the experiments that Newton performed which led to the formulation of laws of motion. In particular I am interested in the following:
How did he measure the forces in order to discover that the net force was directly…
user194517
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7
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Which physicist is this quote attributed to?
There is a quote from a 19-20th century scientist that goes (and I am paraphrasing):
New scientific theories are never accepted until old scientist die.
Who is this cynical quote attributed to, and what is the exact phrasing of the quote?
Based…
cms
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7
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History of a contour integral method for summing series
A folklore result I have seen used in evaluations of infinite sums is the following clever use of the residue theorem:
$$\begin{align*}\sum_{1}^\infty f(k)&=\frac1{2\pi i}\oint f(z)\pi\cot\pi z\,\mathrm dz\\\sum_{1}^\infty (-1)^k f(k)&=\frac1{2\pi…
kolobok
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7
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1 answer
Why is there little scholarship devoted to Book II of Newton's Principia?
Books I and III seem to receive the bulk of attention by Newton scholars, and historians more generally. However, I'm sure an in-depth study of Book II would shed light on Newton as a thinker -- for that reason it must be of import, no?
Rain
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7
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How did Einstein know the Avogadro Number?
Wikipedia says the Avogadro number was determined by Perrin in 1908. But Einstein used the value
$$N=6\times 10^{23}$$
as early as 1905 in order to estimate the size of the fluctuations of an molecule. How did he know it?
Addendum: Of course, the…
Eric David Kramer
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7
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Who are the top mathematicians who were ignored due to their unconventional approach?
A perfect example would be Srinivasa Ramanujan.
It is known that the conventional community throughout history have been close-minded towards great men of science and mathematics (e.g., Galileo).
Srinivasa Ramanujan being one of them. Einstein is…
Travis Wells
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7
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Did Cambridge change their BSc policy for Ramanujan?
I found this quote at Quora:
In March 1916 Ramanujan graduated from Cambridge with a Bachelor of Science by Research (This degree was later renamed as Ph.D. from 1920) for his work on Highly composite numbers.
Given how important his paper on…
students
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7
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0 answers
How did early physicists experimentally assign electronic transitions in atoms?
The spectrum of hydrogen was very well studied by the mid-19th century. However, if one were doing experimental spectroscopy for more complex atoms, one would see plenty of spectral lines in the spectra of sodium or potassium. A diagram for lithium…
AChem
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7
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The "Universal Information Society" of the XIX century?
From the inaugural lecture of J.J. Sylvester at Oxford, December 12, 1885, "On the method of reciprocants as containing an exhaustive theory of the singularities of curves", Collected Mathematical Papers, Vol. 4, 278-302 (in Collected Papers it is…
Pasha Zusmanovich
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