Questions tagged [reference-request]

For questions that are requesting specific literature references

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22 views

Did Peierles write about Peierls transition in any Journal?

I want a reference to Peierls transition and am looking for the original work by Peierls himself. But none of the citations in the Wikipedia page of Peierls transition is authored by Peierls. So, did ...
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2answers
319 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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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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2k views

What was Kolmogorov’s point of view in the philosophy of mathematics?

Today the standard interpretation of intuitionistic logic is the Brouwer-Heyting-Kolmogorov-interpretation which was presented independently by Arend Heyting and Andrei Nikolajewitsch Kolmogorow. ...
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128 views

Natura non facit saltus (nature does not make jumps), who said that?

The sentence is Latin for nature doesn't make jumps. It refers to the fact that, in most physical processes, quantities vary continuously. The principle was used by Leibniz, Kant and Darwin among ...
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755 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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83 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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110 views

What is the origin of the term (non-)derogatory matrix?

A non-derogatory matrix $A$ is one, whose minimal polynomial $m(z)$ equals its characteristic polynomial $p(z)$, where we apply the convention $p(z) = det(zI-A)$, while a matrix is derogatory, if they ...
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1answer
65 views

What are the sources for Democritus’ experiment of dividing a shell down to its atoms?

It is common to find accounts of Democritus explaining his thought experiment to demonstrate the existence of atoms by taking a piece of rock/shell/cheese, and breaking it in smaller and smaller bits ...
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How did Eratosthenes know the distance between Aswan and Alexandria?

In his well-known measurement of the Earth, and according to Cleomedes, Eratosthenes estimated in 5000 stades the distance between Aswan and Alexandria. Modern accounts state that he calculated the ...
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Books on elliptic functions

In the end of his address to the Mathematical Association in 1933 titled "The marquis and the land agent: a tale of the 18th century", G. N. Watson says: My final task is to express my gratitude to ...
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150 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 ...
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77 views

How did Weibull derive the three parameter Weibull distribution?

How did Weibull or any other mathematician arrive at the above expression? I saw the 1951 paper, but it is not clear to me. In 1939 he had published a book called "A Statistical Theory of the Strength ...
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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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108 views

Have orthogonal complex matrices appeared in the literature?

According to https://en.wikipedia.org/wiki/Orthogonal_matrix, https://en.wikipedia.org/wiki/Unitary_matrix, and Friedberg et al.'s Linear Algebra (4th edition), a matrix $A\in F^{n\times n}$ is ...
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3k views

The history and motivation of eigenvectors

I want to understand more about the history of eigenvectors. Was the discovery of eigenvectors inspired from an application to achieve a result in a historical context, was there a phenomenon which ...
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1answer
119 views

Einstein praising Sophus Lie

p. 153 of Raúl M. Falcón Ganfornina and Juan Núñez Valdés, “Mathematical Foundations of Santilli Isotopies,” trans. Alan Aversa, Algebras, Groups, and Geometries 32 (2015): 135–308. quotes (but does ...
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119 views

What is the source of this quote by Einstein on wave–particle duality?

I'm writing a paper which involves a lot of quantum mechanics. As a result of this, I'm finding it necessary to cite the likes of Einstein, Born and Jordan. Particularly in the case of Einstein, due ...
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What was the work of Robert Muchielli's, a French psychologist, role in the Rwandan Genocide? [closed]

I read recently in an in-depth book-length study by an investigative journalist on the Rwandan Genocide that the work of the French psychologist, Robert Muchielli, was implicated in organised ...
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1answer
61 views

Glass ball drop experiment

Several years ago, I remember reading about an experiment, and I thought it was in Newton's Principia, so the experiment was conducted in that time frame. The experiment involved timing the fall of a ...
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1answer
84 views

Where to get more biographical information about Fritz Peter?

Fritz Peter (1899–1949) is known mainly as one of the authors of the Peter-Weyl theorem. This theorem appears in a paper (Die Vollständigkeit der primitiven Darstellungen einer geschlossenen ...
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159 views

Who axiomatized classical mechanics in 1949?

According to Peter Machamer's "A Brief Historical Introduction to the Philosophy of Science" (The Blackwell Guide to the Philosophy of Science, p. 7) ... classical mechanics was not axiomatized ...
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1answer
145 views

Where in Gauss's nachlass apears his sketch of a geometric proof for the biquadratic reciprocity law?

According to p.200-202 of the book "Reciprocity Laws: From Euler to Eisenstein" by Franz Lemmermeyer, there are two proofs for the biquadratic reciprocity law in Gauss's nachlass: one is a cyclotomic ...
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628 views

What is the original source for Abel's quote about Gauss:“He is like the fox, who effaces his tracks in the sand with his tail”?

According to the editor of the German version of Ian Stewart's "The Problems of Mathematics", on page 226 of the biography of Gauß authored by Erich Worbs (C. F. Gauß: Ein Lebensbild. Koehler & ...
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80 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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Books on the history of linear algebra

I'm quite desperate to understand the historical motivation and origin of all of the "geometrical" concepts of linear algebra, namely: The concept of thinking of elements of $\mathbb R^n$ or some ...
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76 views

Where does the notion of “three crises of mathematics” come from? [duplicate]

Update: It can be traced back to Fraenkel-Bar-Hillel's Foundations of Set Theory, originally published in 1958. Further discussions can be seen at the linked question. The notion of "three crises of ...
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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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323 views

Who was L. Aubry?

In his magnificent book Number Theory: An approach through history, from Hammurapi to Legendre, André Weil quotes the article Solution de quelques questions d'analyse indéterminée, by L. Aubry (Sphinx-...
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104 views

Biographical informations on Igor Ado

Ado's Theorem is a very reelvant result in Lie theory (every finite-dimensional Lie algebra is isomorphic to a matrix Lie algebra). I've been, however, unable to find anything more than very basics ...
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118 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 ...
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181 views

Reference Request: Did Descartes leave solving the quintic as an exercise to his readers?

In this document by Jim Brown it is claimed (on Section 3, pg 5) that: [Descartes] believed that all polynomials of degree $>4$ could be solved with the same methods as had been applied to the ...
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4k views

An English copy of One Hundred Authors Against Einstein?

I've been trying to find the famous article, "One hundred authors against Einstein" (100 Autoren gegen Einstein), of various objections to special relativity, which is quite often referenced, but ...
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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 \...
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1answer
323 views

When/Why did Septagon change to Heptagon?

I graduated high school in 1980, and as a second career, am helping HS students with their math. I just finished my 6th year of this, and have just one question about the change noted in the title. ...
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1answer
58 views

First occurrence of the Bloch sphere in the scientific literature

The Bloch sphere is a geometric representation of a single qubit. I am having trouble figuring out when it came into common usage in the scientific literature. The wikipedia article, as at the time of ...
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115 views

Source for Felix Klein quote about curves

Hubbard and Hubbard (in "Vector Calculus...") attribute the following quote to Felix Klein: "Everyone knows what a curve is, until he has studied enough mathematics to become confused through the ...
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1answer
248 views

Source of claim that Leibniz discovered separation of variables for ODEs in 1691?

Claims I'm evaluating I've read in multiple sources that Leibniz formulated separation of variables for ODEs in 1691. A couple example sources are below. Mathematical Thought from Ancient to Modern ...
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218 views

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 ...
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1answer
710 views

Who came up with the convolution theorem?

I am looking for the earliest reference which proposed the convolution theorem which is often utilized in signal processing (i.e., convolution becomes a multiplication in the Fourier domain). The ...
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1answer
108 views

Euler's Derivation of Euler's Method for ODEs

I am looking for an English translation of Euler's derivation of Euler's method for ODEs, namely the update $$ y_{n+1} = y_n + h f(y_n, t_n) $$ What motivated Euler to consider this problem, and how ...
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651 views

What was the main language in science/mathematics before 1850

I know that English is the most popular language to write scientific/mathematical papers after World War 2. I also know that in the second half of 19th century and first half of 20th century, German ...
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11k views

Did Einstein say “We cannot solve our problems with the same thinking we used to create them”?

According to various sources on the Web, Albert Einstein is likely to have said or written one of the following: Probleme kann man niemals mit derselben Denkweise lösen, durch die sie entstanden ...
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66 views

Where to find some early discussions of the Equinox(es)?

Said quickly, solstices are rather perceptible while the equinox is a mental construction. Archeoastronomical evidence shows that neolithic people already had knowledge about the solsticial points on ...
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245 views

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 ...
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1answer
176 views

What theorem of Sophus Lie on the number of geometries is H. Poincaré referring to?

In this quotation from Henri Poincaré's essay "Non-Euclidean Geometry" published in Nature in 1892 (No. 1165, Vol 45, p. 406), he refers to a theorem of Sophus Lie. Does anyone know a source for this ...
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135 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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240 views

Earliest Instances of a Slope/Direction Field for a First-Order ODE

Background When first encountering slope fields in calculus or elementary differential equations, students often ask "What is the purpose?" A concise answer is that slope fields provide a way to ...
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1answer
393 views

How did the early chemists determine the atomic weight of hydrogen?

In early history, the relative atomic weight of hydrogen was assigned as 1 (exactly) and all other elements were compared against hydrogen. What is difficult to find who determined the absolute atomic ...

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