Questions tagged [reference-request]

For questions that are requesting specific literature references

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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 {\...
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473 views

What did Fermat do as a lawyer?

Fermat is easily one of the best known mathematicians of all time. We all know about Fermat's Last Theorem, Fermat's Little Theorem, his quadrature rule, his invention of probability theory, etc. ...
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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 ...
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1answer
123 views

Who posed the separable quotient problem (and when)?

The (infinte dimensional) separable quotient problem asks whether every infinite dimensional Banach space has a separable infinite dimensional quotient. In the literature I have seen that is problem ...
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1answer
259 views

When was $e$ first observed to not be a Liouville number?

When and by who was it first observed that the transcendental number $e$ is NOT a Liouville number? This fact is stated in a lot of web pages, and a proof can be found in the Mathematics Stack ...
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100 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 ...
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1answer
148 views

Books that we can know when which theorem was discovered by whom

There are many textbooks which states mathematical theorems, but in them, by whom and when the theorems are discovered is not explained. Do you know good references for this? If this scope is too ...
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369 views

Is Spivak right in what he says about Galileo?

On chapter 9 of M. Spivak's book on calculus there is an exercise in which Spivak asks the reader to prove that Galileo "got his facts wrong". More specifically, Spivak asks one to to show if a body ...
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1answer
865 views

What are Philolaos' “even-odd” numbers?

Number, indeed, has two proper kinds (ιδια ειδη), odd and even, and a third mixed together from both, the even-odd(αρτιοπέριττον). Of each of the two kinds there are many shapes, of which each ...
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2answers
810 views

History of PDE's in the 19th Century

I've been asked to write an essay on whether the work on PDE's in the 19th century belonged to applied or pure mathematics. Does anyone know of any useful sources I could use?
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376 views

English translation of Heisenberg's papers

Strangely, many of Heisenberg's very important scientific papers are not translated into English. For example, this one seems not to have been translated. Where can I get the translated ones?
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6answers
999 views

Examples of abstract proofs that turned out to be false

I found this question that discusses abstract theories that later found application. I am interested in accepted (at least at one point in time) abstract theories that: was contradicted by attempts ...
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1answer
54 views

First use of the term/name "curved exponential family"?

Question: What was the first recorded use of someone calling exponential families (in probability/statistics) for which the dimension of the natural parameter space is strictly less than the dimension ...
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2answers
85 views

Has Alphonse Pyramus de Candolle's "Géographie botanique raisonné" ever been translated into German or English?

Alphones Pyramus de Candolle (1806-1893), the son of Augustin-Pyrame de Candolle (1778-1841), has been an important figure (as was his father) in the development of plant geography. The younger ...
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446 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 ...
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149 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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229 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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1answer
520 views

History of the origins and development of problems of finding maximum and minimum values of quantities

I am aware that perhaps the earliest source concerning problems of maximum and minimum values occurs in Euclid's Elements. After Euclid, Archimedes of Syracuse and Apollonius of Perga seem to consider ...
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2answers
162 views

Is there any evidence supporting this claim about Cassini and his ovals?

The Wikipedia article for Cassini ovals claims in the introduction that "Cassini believed that the Sun traveled around the Earth on one of these ovals, with the Earth at one focus of the oval." This ...
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313 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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1answer
102 views

On a paper by Georg Pick

Has any of you ever read the paper in which Georg Pick made public his famous formula? If so, would you be so kind as to tell me what it is that one can find in the introduction of it? The complete ...
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91 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{...
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1answer
3k views

Where did Galileo say "All truths are easy to understand once they are discovered. The point is to discover them."?

I've heard it claimed Galileo said or wrote: All truths are easy to understand once they are discovered. The point is to discover them. Where did he say this?
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1answer
670 views

Euler's works after blindness

There are many sources which say that Euler produced, on average, one mathematical paper every week in the year $1775$. Some even say he produced almost half his total works despite the total ...
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4answers
720 views

Biographies on 20th Century physicists

I've recently finished reading Helge Kragh's Quantum Generations and am looking forward to something to read next. I am hoping to find biographies or more information about certain physicists such as ...
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204 views

What are some good (and reasonably academic) books on 18th and 19th century British mathematics?

In addition to the general topical interest indicated in the title, I am also curious about British mathematics of the period viewed through the lens of competition with the rest of Europe (and ...
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60 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 ...
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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, ...
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85 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 ...
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177 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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1answer
108 views

reference need about History of prime number development

Im trying to connect my study to a breif history of prime numbers . Also im interesting in reading history of numbers how they come and how they developed . So can any one suggest for this question a ...
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1answer
82 views

Reference for "Auszug aus einem Briefe von L. Kronecker an R. Dedekind"

While I was looking for a source about Kronecker's Jugendtraum, I found this document: Auszug aus einem Briefe von L. Kronecker an R. Dedekind vom 15. März 1880. The bottom of the given page has a ...
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1answer
73 views

Is reference cited by Rene Descarte available?

In 1634 Descarte wrote to Mersenne : let me tell you about an experiment that was published not long ago in Leurechon’s Mathematical Games. It involves a large cannon placed on flat ground, ...
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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 ...
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1answer
331 views

How did Kepler make his discovery?

It is often said that he used Tycho's data. But the apparent motion of a planet is chaotic, right? The reason is simply that we are living on and observing from the earth, but not the sun. So, how ...
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1answer
124 views

proofs of mathematical claims in the 16th, 17th and 18th cent

I know that starting from the 19th century the style of mathematical proof was more and more formal and inductive. However, I am trying to find reference (article or books) that analyze the way which ...
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2answers
269 views

Poincare Quote Regarding Instability

Poincare wrote (english translation of the french) in 1903: ``A very small cause that escapes our notice determines a considerable effect that we cannot fail to see, and then we say that the effect is ...
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3answers
273 views

History of Foundation of Mathematics

I know that studying the evolution and history of a certain subject is a way of resolving the complexity of that subject. So I want to ask about references that describe the history and evolution of ...
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2answers
366 views

Did Bruns establish that the 3 body problem has no non-trivial conservation laws?

I'm reading Colin Pask's book Magnificent Principia and in 16.7.2 he states that the difficulty of the 3 body problem is in part tied to the lack of additional conservation laws at our disposal. In ...
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1answer
388 views

How were Millennium Problems chosen? (according to what criteria)

I am making a presentation about Millennium Problems. There are 7 Millennium Problems but a lot of unsolved mathematics problems are also waiting to be solved. I know that these problems are much more ...
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1k views

Is there any complete works of Abel, Lagrange, Jacobi and Gauss translated into English?

Is there any source which has the complete works of Abel, Lagrange, Jacobi and Gauss which has been translated into English? I'm asking for separate books for these mathematicians not necessarily a ...
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2answers
209 views

Biography of Galois in English

Note: This was first posted at Mathematics Stack Exchange, from which I was redirected here. Forgive me if this violates any crossposting rules I'm not currently aware of. Currently, I'm starting ...
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1answer
122 views

Which paper/book did d'Alembert publish his essay on the theory of winds in?

This source claims that "d'Alembert won the prize of the Prussian Academy of Sciences with his essay on winds", and this source claims that "A prize essay on the theory of winds in 1746 led to ...
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1answer
225 views

Abraham's electromagnetism book and its story

Max Abraham is well known for his electromagnetic mass theory, and his book Theorie der Elektrizität is said to be read widely around 1900. I am trying to find this book, but the editions look like a ...
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453 views

Where can I find the original presentation of the proof, due to Grothendieck, of the $\bar\partial$-Poincaré lemma?

In complex geometry, there is the a lemma, analogous to the Poincaré lemma in (real) differential geometry, which states that a $(p,q)$-form that is $\bar\partial$-closed is locally $\bar\partial$-...
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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, ...
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1answer
37k views

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 \triangleq ...
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952 views

Where did Rayleigh derive the ultraviolet catastrophe?

Where can I find this paper: J.W. Strutt, Verh. d. deutsch. phys. Ges. 2, 65 (1900). It is presumably where Rayleigh derived the black-body radiation formula (the incorrect one that has ultraviolet ...
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1answer
199 views

What were standard university texts in algebra in the mid 19th century?

Dedekind in 1872 wrote that equations like $\sqrt{2}\cdot\sqrt{3}=\sqrt{6}$ ``to the best of my knowledge have never been established before'' (Continuity and Irrational Numbers, p. 22). This was ...
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156 views

Origins and history of branched covering

During my research on branched coverings of the projective plane, I am interested to know the origins and history of branched coverings of the projective plane and the projective line, together with ...