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Questions tagged [reference-request]

For questions that are requesting specific literature references

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301 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 ...
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149 views

Books on elliptic functions

In the end of his address to Annual Meeting of the Mathematical Association in 1933 titled "The marquis and the land agent: a tale of the 18th century", Association president G. N. Watson ...
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83 views

Chronology of proofs of cubic and biquadratic reciprocity laws

I just want to check if anybody knows a website where one can find a chronology of proofs of more difficult reciprocity theorems (such as the cubic and biquadratic cases) similar to the (already ...
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96 views

Is there any historical evidence of this quote E.T. Bell attributed to C.G.J. Jacobi?

I read Men of Mathematics by E.T. Bell long ago, and this quote he attributed to Jacobi stuck with me: Certainly I have sometimes endangered my health from overwork, but what of it? Only cabbages ...
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226 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 ...
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187 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 ...
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114 views

Who bet against the usefulness of matrix inversion – or is it a myth?

In my linear-algebra and numerics courses, I frequently heard an anecdote about some professor betting – literally, with money – that there would never be any application where computing the actual ...
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95 views

Where can I read Cauchy's terrible poems?

I hope that the slightly abrasive title is forgivable, as the judgement on this poetry is not mine, but Hans Freudenthal's. Here is the background: in the Dictionary of Scientific Biography, there is ...
4
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72 views

von Neumann vignette on early computer usage

I'm looking for a vignette about von Neumann. My recollection is as follows but my google-fu is not bringing up anything. von Neumann, having prodigious mathematical capacity even of the most mundane ...
4
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101 views

In which work was Gibbs' Inequality introduced?

Gibbs' inequality $$-\sum\limits_{i=1}^n p_{i} \cdot \log{p_{i}} \le -\sum\limits_{i=1}^n p_{i} \cdot \log{q_{i}}$$ is such a popular thing that I cannot find where it was introduced. My findings I ...
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821 views

What paragraph was written by Emanouil Atanassov to solve problem 6 on the International Mathematical Olympiad in 1988?

From the Wikipedia page about Vieta jumping: Emanouil Atanassov, Bulgaria, solved the problem [assumed to be the most difficult one on the 1988 International Mathematics Olympiad] in a paragraph and ...
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123 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 ...
4
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113 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 ...
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59 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 ...
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75 views

Where can I find the complete papers of abstracts published by P. G. Tait in Proc. Roy. Soc. Edinburgh in 1880?

I am interested in looking up P. G. Tait's flawed proof of the four-colour theorem, published in 1880. The citation that I have seen is: P. G. Tait, On the colouring of maps, Proc. Roy. Soc. ...
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62 views

What is the source of Hopf's (boundary) lemma?

In an introductory course on PDE's I got as a project to prove and present a version of Hopf's (boundary) lemma. Namely: Let $\Omega \subset R^{d}$ be an non-empty open connected set with a twice ...
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141 views

The origins of $\det(I+AB)=\det(I+BA)$

I am looking for the earliest published source that gives and perhaps proves the identity $\det(I+AB)=\det(I+BA)$ where $A$ and $B$ are just rectangular matrices of finite dimensions (as opposed to ...
3
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91 views

Origin of notation "R with a stroke on the leg" for the square-root (℞)

The following text from Ars magna (1545) by Girolamo Cardano is known as the inception of complex numbers: "imaginaberis ℞ m 15" (You will imagine the square root of minus 15): The "R&...
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85 views

Literature on Mayan mathematics

I asked this question on math.se and they sent me here. It is well known that Mayan people used vigesimal (base 20) numeral system, and had had an advanced calendar system. Except for these facts, I'...
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95 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,\...
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69 views

pre-20th century sources on information theory?

What are some pre-19th or pre-20th century sources on information theory? Do they exist?
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108 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 ...
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97 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 ...
3
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135 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 ...
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65 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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226 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 (...
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96 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.
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66 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, ...
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73 views

Is there a modern equivalence of Asimov's book "The new intelligent man's guide to science"?

I enjoyed Asimov's "The new intelligent man's guide to science" very much when I was a teenager. I noticed that he later published "Asimov's New Guide to Science", however that was ...
2
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84 views

President James A. Garfield and the Pythagorean proposition

As some of you may recall, President James A. Garfield published at some point of his life a proof of the celebrated Pythagorean proposition. I am interested in acquiring a pdf copy of President ...
2
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115 views

Reference request for some fragments of Gauss with dubious origin

Gauss's results on the interconnection between the different values of the arithmetic-geometric mean of two complex numbers as recorded in his private notebooks led him to introduce foundational ...
2
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103 views

Einstein's handwritten manuscript on General Relativity

The book "The Road to Relativity" by Gutfreund and Renn annotates Einstein's original handwritten manuscript from 1916 - "The Foundation of the General Theory of Relativity." I can ...
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91 views

A Reference in Klein's Book

F. Klein mentions a certain Blumenthal in his famous book on the history of mathematics in 19th century with the following verse(when he was talking about the curvature in space): Die Menschen fassen ...
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138 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 ...
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144 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 ...
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176 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.
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60 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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201 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 ...
2
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1answer
130 views

The origins of differential homological algebra

Differential homological algebra in its initial formulation is due to Eilenberg and Moore, who first published the homological version of the Eilenberg–Moore spectral sequence in 1965 (and the ...
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62 views

Source of L’Hôpital’s 1696 Calculus textbook

A calculus textbook I’m using references a calculus book of L’Hôpital in which he illustrates his rule, which is taught in many calculus classes. Does anyone have a source as a scanned PDF? I’d love ...
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50 views

Who first spoke of Euclidean domains?

I am looking at Euclidean domains for the first time and it is a subject that has caught my attention. I wonder, who was the first to talk about this? I've been reading a little and so far the oldest ...
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72 views

history of curl and inverting the curl

A man in Tennessee has written to me, asking for a reference about the method in my answer to https://math.stackexchange.com/questions/81405/anti-curl-operator He is writing an article on finite ...
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98 views

Fourth powers and quartic equations before Descartes

How did mathematicians interpret quartic equations and fourth powers before Descartes propose to perform elementary arithmetic on line segments? I ask this because it seems strange to me that ...
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56 views

Who extended the Banach fixed point theorem from the context of normed spaces to the context of metric spaces?

It is well known that Banach's fixed-point theorem was initially conceived as a fixed-point theorem for applications defined in normed spaces (see [1]). This theorem was conceived in 1922 by Stefan ...
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75 views

Finding sources for "computers will become so powerful that special functions will become obsolete" as a zeitgeist

In Why are special functions special [Physics Today 54, 11 (2007); eprint], Michael Berry makes the following observations: This continuing and indeed increasing reliance on special functions is a ...
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56 views

The earliest origins of science and math

I'd like to have a broad understanding of how various societies in the world developed pre-scientific understanding. There are a lot of resources for ancient Greece. There are even a few for what ...
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95 views

Quotation reference: "functions which can be evaluated under 1 sec are as good as analytically available"

I have a vague memory of a (possibly-apocryphal) quote by a physicist (I remember it as being Giorgio Parisi, which could be wrong), saying something to the effect of "any function which can be ...
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118 views

What would be some earlier comments on "1+2+3+4=10"?

"1+2+3+4=10" is an arithmetical triviality that is popular as an example of Pythagoreanism. There seems to be no mention of it in ancient Greek texts prior to Speusippus (e.g. ca. 350BCE; ...
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76 views

What is the original source of the problem of finding equivalent resistance between two nodes in an infinite grid of resistors?

A famous problem in electronics or physics course,is the following--- Consider an infinite 2d grid of resistors having resistance of equal value.Find the resistance between any two nodes in the grid. ...
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102 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 ...