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Questions tagged [reference-request]

For questions that are requesting specific literature references

36 questions with no upvoted or accepted answers
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11
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Who first defined the “equal-delta” or “delta over equal” ($\triangleq$) symbol?

The symbol $\triangleq$ is sometimes used in mathematics (and physics) for a definition. It is instantiated for instance in the Unicode Character 'DELTA EQUAL TO' (U+225C). The notation $t \...
7
votes
0answers
244 views

Did Kronecker say that set theory is not mathematics?

I have frequently come across Kronecker's statement about set theory: "I don't know what predominates in Cantor's theory - philosophy or theology, but I am sure that there is no mathematics there." It ...
6
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0answers
212 views

Who gave you infinitesimal epsilon?

As someone reputed among certain historians to have given you the epsilon Cauchy startled me by using $\varepsilon$ to denote an infinitely small number in his 1826 text on differential geometry; see ...
5
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0answers
72 views

Where in Gauss's nachlass did he pose the problem of connectedness of a surface?

On p.98 of the book "Mathematics of the 19th Century: Geometry, Analytic Function Theory", the authors mention a note written by Gauss in 1840: In 1840 Gauss wrote a note in which he introduced the ...
5
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0answers
128 views

Reflections in the 18th century

It is well known that the theory of reflections was considerably developed during the 19th century with the development of group theory (e.g. Klein) and the theory of transformations. However, I'm ...
5
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1answer
204 views

Grothendieck and Elementary Topos

I would like to know some references (if any) for the claim that Grothendieck didn't like the idea of elementary topos.
4
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0answers
105 views

Historical evidence for claim that we use base 10 because of the number of fingers

It is a common belief that we use a base 10 representation of integers because we have 10 fingers. Does there exist historical evidence which supports the claim that this is true and that the number ...
4
votes
0answers
74 views

History of Braids

I am looking for papers or books that describe the history of the development of braid theory, mainly during the 19th and the 20th century. I know Moritz Epple book on the history of the theory of ...
4
votes
0answers
57 views

What came first: pythagoras number or pythagorean fields?

Which concept was first introduced: the pythagoras number of a field or pythagorean fields? I have not found anything on this matter, but my gut feeling says the latter. One can more directly link the ...
3
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0answers
65 views

Who first proved Fubini's theorem $n$th order integrals?

Who first proved a generalized Fubini theorem for integrals of order $≥3$? An $n$th order integral is $$\underbrace{\underset{x_n}\int\underset{x_{n-1}}\int\ldots\underset{x_1}\int}_{n} f(x_1,x_2,\...
3
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0answers
60 views

pre-20th century sources on information theory?

What are some pre-19th or pre-20th century sources on information theory? Do they exist?
3
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0answers
98 views

Reference Request: Comment about Contradictions Proof Method Related to John G. Thompson

I read in a PDF document where the author made a comment that it is “dangerous” to use indirect proof method/contradiction proof method (as far as I can remember, and of course I am paraphrasing) as ...
3
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0answers
133 views

Earliest Known reference to a female scientist?

According to an uncited Wikipedia paragraph, Merit-Ptah is the earliest known female scientist. An ancient Egyptian, Merit-Ptah (c. 2700 BC), described in an inscription as "chief physician", is ...
3
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0answers
92 views

Earliest drawings of the plots of trigonometric functions

[Even though this question may seem as a duplicate of this question about the History of sine function, I'd like to ask it again - with a more specific title and a more specific focus (on specific ...
3
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0answers
61 views

Raymond Cattell and History of Personality Traits Prior 1947

I find that papers reference Raymond Cattell suggesting 16 or 22, etc, traits, by factor analysis (basically regression), including all five of the modern reproducible traits (openness to experience, ...
3
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0answers
127 views

Where did the divide and conquer method for radix conversion come from?

While doing the tedious work of documenting my software I tried to find the original source of the divide and conquer method for the conversion of numbers of one base to a number in another base (...
3
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0answers
89 views

Are Brillouin's papers translated into English?

I mean the Brillouin in the WKB method. I want to read his original paper. But it is in French. Is it translated into English? It should be.
3
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0answers
64 views

Who was the first pointing out the $U(1)$-gauge theories common structure?

It is well-known that in each $U(1)$-gauge theory one can define, in analogy with electromagnetism, a 1-form connection and an associated 2-form of curvature on an appropriate (principal) bundle, ...
2
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0answers
110 views

Several questions about Gauss's mathematical conception of braids

I'm trying to figure out several things about Gauss's thoughts concerning a certain four-strand braid. The reference my questions are based on is mainly Moritz Epple's excellent article "orbits of ...
2
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0answers
88 views

Question about Leibniz's “characteristic numbers” and propositional logic

The wikipedia article on Gottfried Wilhelm Leibniz mentions, in the chapter on symbolic thought, that: "Leibniz saw that the uniqueness of prime factorization suggests a central role for prime numbers ...
2
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0answers
78 views

Etymology of 'qubit'; is there any relation to cubits?

Whilst several not-very-authoritative sources e.g. Wikipedia state that the word qubit was derived, partially, as a play on the word cubit (obviously it also stands for 'quantum bit'), is there any ...
2
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0answers
163 views

Works of mathematician François Viète

I'm searching for a book or an online copy of complete works of the mathematician François Viète, preferably in English. Any help will be appreciated. Thanks.
2
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0answers
59 views

Trying to learn some history of mathematics with parabolic Anderson model (PAM) as theme

I have been recently trying to find context and motivation for my Ph.D. Thesis in probability theory. I have not much background on the history of my theme. I just studied it aiming at solving a ...
2
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0answers
195 views

Reading material suggestion for history of Newton's laws of motion

I intend to review the different concepts related to laws of motion floating around the publication of Principia and hopefully would like to comment on these (It's an essay project). I've gathered ...
1
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0answers
76 views

Looking for Cantor's correspondence

I am trying to collect all available letters written or received by Cantor or written between his colleagues about Cantor. I have searched already the literature given below. But I would like to ...
1
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0answers
77 views

Laplace's characterization of Gauss as “a super-terrestrial spirit in a human body”

The following words concerning Carl Friedrich Gauss are attributed to Laplace in an article from the Mathematics magazine by Teets and Whitehead (The discovery of Ceres: how Gauss became famous, first ...
1
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0answers
327 views

History of the arithmetic mean

The arithmetic mean of a set of points $\{x_1, x_2, ..., x_n\}$ is defined by $$\frac{1}{n}\sum_{i=1}^n x_i.$$ It is remarkable for its ubiquitous use and universal understanding. It represents a ...
1
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0answers
55 views

Carnap's last theory Of probability

According to Bar-Hillel, Carnap's coauthor in a 1952 report on probability, Carnap had, as of 1956 an unpublished but circulated theory distinguishing "random" refers to methods of production of ...
1
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0answers
78 views

Verification of Navier's theory of structures

Jacques Heyman in his article Truesdell and the History of the Theory of Structures, mentions the following: The first full-scale tests on building frames were made in the 1920s in London, and ...
1
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0answers
59 views

Grey Walter and Norbert Wiener Regarding Holism

Grey Walter writes: ``Even in the very simplest system, with two active elements, multiple interconnection between elements give several modes for which simple observation is useless. The study of ...
1
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0answers
62 views

Years to Learn to Build an IC

So, for a couple years now I've been quoting someone that said that it would take about 150 years of education to learn everything it'd take to build an integrated circuit, start to finish. Thing is, ...
1
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0answers
66 views

Is there any online resource on Yitang Zhang's biography?

Where I should look for a biographical note on Yitang Zhang's life. I read the wikipedia article but it does not provide any in depth perception on his life. There is nothing on here. If anybody knows ...
0
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0answers
42 views

The Original Proofs of The Stable Manifold Theorem

The book "Differential Equations and Dynamical Systems" by Lawrence Perko says that the first proofs of the Stable Manifold Theorem are from Hadamard in 1901, Perron in 1928, and Liapunov and Perron. ...
0
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0answers
57 views

Why is the angular momentum written as JJ in quantum mechanics?

Why is $\textbf{J}$ called angular momentum operator? Can anyone explain why the expectation value of J is angular momentum? Here is how $J$ is defined: The rotation operator $$ U(\alpha)=\exp(-i {\...
0
votes
0answers
76 views

Riemann surfaces and covering

Assuming we have a Riemann surface $S$ of degree $n$ and we look at it as a covering of the projective line $\mathbb{P}^1$. If $B$ is the set of branch points of $S$ (when $B$ is a subset in $\mathbb{...
-4
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0answers
63 views

Who first explained why there are 7 days in a week?

Who first explained why there are 7 days in a week?