Questions tagged [reference-request]

For questions that are requesting specific literature references

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40 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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42 views

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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61 views

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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1answer
67 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 ...
3
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2answers
104 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 ...
3
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1answer
114 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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1answer
109 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 ...
2
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1answer
60 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 ...
3
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1answer
76 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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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
150 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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77 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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1answer
46 views

Who first distinguished number theory and numerology? [duplicate]

Who first distinguished number theory and numerology?
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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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67 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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116 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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2answers
179 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 ...
3
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1answer
142 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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1answer
215 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 ...
5
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1answer
106 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 ...
3
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1answer
243 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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672 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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216 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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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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1answer
107 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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65 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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227 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
164 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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134 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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203 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
345 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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3answers
317 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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7answers
285 views

Pop-sci books that were publicly influential but based on weak science

(I hope this is on-topic on this site) I am wondering what are some of the best examples of popular-science books that had large influence in public, but was based on weak science? By "large ...
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2answers
101 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 ...
3
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2answers
148 views

What are historical applications of geometry to measuring distances beyond human reach?

I am searching for books and articles about applications of Geometry, in particular to the problem of computing distances and lengths which are apparently beyond human reach. As an example, consider ...
3
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1answer
137 views

Clairaut's proposed correction (reported as “D'Alembert's, Clairaut's and Euler's corrections”) to the Newtonian inverse-square law of gravity

From A.P. Yushkevich, "Leonhard Euler, his life and work", in "Development of Leonhard Euler's ideas and contemporary science", Nauka, Moscow, 1988, 15--46 (translation from Russian is mine): "One ...
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3answers
268 views

What are some good references elucidating the discovery/creation of Fourier Series?

I've always grappled with the topic of anything Fourier during my undergrad days. Until recently when revisiting why I learned what I did, I discovered how Fourier's desire to understand the flow of ...
3
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1answer
180 views

Does any extant Greek text prove that the area of an inscribed regular polygon increases with the number of sides?

Does any extant Greek text prove that the area of a regular polygon inscribed in a fixed circle increases with the number of sides in the polygon? I can't find such a proposition in Euclid, but the ...
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0answers
96 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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2answers
68 views

What are some good books that interweave the history of math and art from renaissance onward?

Ever since learning about projective geometry and its birth in the world of art, I’ve been intrigued to learn more about their union and how they influenced each other. I’m specifically looking for ...
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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 ...
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1answer
174 views

Where is the Foucault pendulum in Mainz?

A Foucault pendulum in Mainz is listed on Wikipedia. The article says that it is in School for Business and Technique, Mainz However, I didn't find any information about this pendulum on the ...
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1answer
206 views

Is there anything written by Newton's roommate Wilkins about him?

I've read that John Wilkins was Newton's room-mate and they lived together for 20 years. Is there anything about Newton written by Wilkins? By the way, there is nothing easily found on google.
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1answer
157 views

When and why was inversive geometry created/studied?

I have been revisiting math from my highschool through undergrad. I picked Courant’s excellent What is Mathematics? The flow is well so far. However, in one of the chapters he introduces inversion - ...
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1answer
59 views

Jordan's Paper on the Jordan Canonical Form

In which paper, did Jordan introduce/prove the Jordan canonical form?
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1answer
257 views

An english translation of Cauchy's “Cours d'Analyse”

I am quite interested in the origins of our modern way of understanding analysis. I know that Augustin-Louis Cauchy was one of pioneers regarding a rigorous foundation towards real and complex ...
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2answers
9k 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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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 ...