Questions tagged [reference-request]

For questions that are requesting specific literature references

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8
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3answers
741 views

Why do we call a linear mapping "linear mapping"?

According to P. M. Cohn's Classic Algebra, for historical reasons we call a linear mapping "linear mapping". What are the historical reasons that led to the adoption of the term "linear ...
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0answers
106 views

What's the origin of the claim that a single uranium atom fissioning would release enough energy to visibly move a grain of sand?

There's a fairly widespread claim that the energy released by the fission of a single atom of uranium would release enough energy to make a grain of sand visibly jump. Richard Rhodes's The Making of ...
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1answer
137 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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1answer
121 views

What is the origin of the "problem of Brahmagupta" of constructing inscribed quadrangle with given sides?

I am looking for a source of the following construction problem: Construct an inscribed quadrangle with given sides. I know it under the name problem of Brahmagupta, but I do not know any evidence ...
4
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0answers
103 views

Earliest measurement of proton's mass

I was looking for the earliest experiment or the paper which shows the determination of the mass of proton. In NIST CODATA, the mass of proton is listed as "1.672 621 923 69 x 10$^{-27 }$kg"....
28
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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 ...
6
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3answers
1k views

What was Richard Courant's saying about mathematical research apart from applications?

I remember reading somewhere (perhaps in The Mathematical Experience) that Richard Courant wrote something to the effect that, without applications to guide the river of mathematical discovery, ...
1
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1answer
94 views

What was Einstein's first publication of the final form of general relativity?

What was Einstein's first published exposition of his final form of general relativity, be it a scientific article or a book? I've been googling the answer for hours now, with no luck, really. The ...
5
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3answers
477 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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0answers
101 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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2answers
569 views

What was Weil's reaction to Deligne's proof?

How did André Weil react when Pierre Deligne finally solved the most important and hardest of the Weil conjectures ? Is there any written account on this ? I guess Serre's and Grothendieck's (...
3
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1answer
91 views

Reference request for Gauss's original discovery of the special property of the $j$ function

In Interchapter VII of his biography of Gauss, W.K. Buhler describes Gauss's discovery of one of the important properties that characterize the $j$ invariant (Klein's absolute invariant; Gauss called ...
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1answer
90 views

Is there any book or site where John von Neumann's collected philosophical writings are presented?

I was wondering if von Neuman has any philosophical writings beside his writings on the relation of computers to the human mind and vice versa.
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2answers
644 views

How did Romans do multiplications?

The Romans did not have Indian numerals. Worse still, they did not have the decimal system. Yet, they produced amazing works of engineering and architecture. How was that possible? It's troublesome ...
5
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2answers
668 views

When was the diving bell invented?

This question comes from my attempts to give a good answer to the previous question, How was difference in water pressure perceived in ancient cultures or the middle ages? I know from my childhood ...
10
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1answer
183 views

What was the scientific explanation of earthquakes in the 18th century?

I'd like to know what western scientists thought about the causes of earthquakes in the mid to late 18th century (especially pertaining to the one in Lisbon in 1755). I've read that the ancient Greeks ...
10
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1answer
1k views

How was curvature originally defined and calculated?

I am interested in the early history of curvature. Who defined it first and when, who came up with the name, how was it calculated before mathematicians used calculus to define $k=|α''(s)|$? Are there ...
18
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3answers
2k views

Source for Hilbert's famous quote "Mathematics in Göttingen? There really is none anymore"

Reportedly this was uttered at a banquet in which Hilbert was seated next to the new Minister of Education, Bernhard Rust, in response to Rust inquiring as to the state of mathematics in Göttingen now ...
6
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1answer
291 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.
6
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2answers
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
82 views

Lunar distance measurement reference

While preparing trigonometric exercises for my students, I learned that, in 1771, French astronomers determined the distance of the Moon from the Earth by measuring the appropriate angles from both ...
4
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0answers
969 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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0answers
57 views

What is the first instance in which Mendeleev published a long-form table as compared with his 8-column table of 1869?

Mendeleev is famous for having published his first periodic table in 1869. This was a short-form or 8-column table. He also published a number of 18 column periodic tables. I am asking for ...
4
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1answer
294 views

Classic mathematics books by British mathematicians

Having recently read a review that expounded on the rigour and depth of books by 'earlier' British mathematicians (mainly analysts) I would like to know more. My own research yielded the following ...
0
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1answer
79 views

Where can I find the historical information or the stats related to Winning WW2 with the minimum actions using The Bombe Machine of Alan Turing?

I am doing a marathon of data visualizations with real world datasets. I am interested in historical war datasets. Does anybody know about the historical data on The Bombe Machine cracking the codes ...
3
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1answer
549 views

Why are complex numbers called 'complex'?

I'm a high school teacher, and I was just wondering why complex numbers are called 'complex'. I have read that Gauss coined the term. But I couldn't find any reference where it was explained. I also ...
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0answers
73 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 ...
4
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1answer
92 views

When were cephalopods assigned to the taxonomic phylum Mollusca?

I am fascinated to read about the evolution of cephalopod intelligence while I understand why cephalopods are mollusks (e.g., https://en.wikipedia.org/wiki/Cephalopod), but I cannot easily find when ...
6
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1answer
2k views

Translations of Luca Pacioli's Summa de arithmetica

Are there any English language (or perhaps German, Dutch or French, but preferably English) translations of Luca Pacioli's 1494 (or later edition) "Summa de arithmetica"? They do not have to ...
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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 ...
4
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0answers
124 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 ...
4
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3answers
1k views

Euler's formula for product of cosines

According to "Squaring the Circle" by Ernest Hobson, this formula $$\theta =\frac{\sin\theta}{\cos\frac\theta2\cdot \cos\frac\theta4\cdot \cos\frac\theta8\dots}$$ for $\theta<\pi$ is due to Euler. ...
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0answers
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 ...
8
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2answers
222 views

Heisenberg's last work on a non-linear generalization of quantum mechanics?

It is claimed here that toward the end of his life Werner Heisenberg worked on a non-linear broadening or generalization of quantum mechanics. What work was that? Was it published? Is it listed in ...
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1answer
1k 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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1answer
52 views

What monograph on celestial mechanics did Jürgen Moser coauthor the 2nd and considerably expanded English language edition of with Carl Ludwig Siegel?

Comments under the Space SE question How do orbits around Jacobi ellipsoids behave? include: Periodic orbits around a rotating ellipsoid "This paper extends results obtained during the ...
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0answers
99 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 ...
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0answers
52 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 ...
4
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1answer
98 views

Original Proof of the Schwarz lemma

The classical Schwarz lemma from one-variable complex analysis states that a holomorphic map $f : \Delta(r) \to \Delta(R)$ between two disks in the complex plane such that $f(0)=0$ satisfies $$|f(z)| \...
4
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0answers
73 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 ...
8
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2answers
363 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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0answers
37 views

First appearance of relations commutator,anticommutator with quaternion product

My query is the following, what is the first textual reference of the usage of commutator and anticommutator regarding quaternions in a similar way relative how it is done in the wikipedia article of ...
1
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1answer
52 views

First occurrence of the Langevin function in scientific literature

The Langevin function $\mathcal{L}(x) = \mathrm{coth}(x) - \frac{1}{x}$ is named after the French physicist Paul Langevin (1872-1946). The Wikipedia article on the Brillouin and Langevin functions ...
8
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3answers
268 views

What does "organic" mean in old texts when describing plane curves and their construction?

I've been reading about 17th and 18th century geometers and their research into plane curves, especially algebraic curves. A term that comes up frequently is "organic". By context it seems ...
4
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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 ...
4
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1answer
192 views

Lost memoir of Évariste Galois

According to the Wikipedia article on Évariste Galois He submitted his memoir on equation theory several times, but it was never published in his lifetime due to various events. Though his first ...
12
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2answers
1k views

Early history of the phase concept in the physical sciences

One of the first distinctions encountered in science education is that substances can assume different states of matter: for example, water can be found as a liquid, as a solid (ice), or as a gas (...
6
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4answers
493 views

Why does the "Principle Of Permanence" have two different definitions?

This question is a sub-question of previous question on MSE. I feel that on this website I have better chances of knowing more things. For quite some time now, I have been searching about the "...
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0answers
82 views

Platonian geometry illustrated

I recently found out that a lot of Plato's work can be drawn geometrically. See the Cerritos College YouTube video "Platos Divided Line" with the description Cerritos College Professor ...
6
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6answers
553 views

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

I've always grappled with anything related to Fourier since my undergrad days. Recently, when revisiting why I learned what I did, I discovered how Fourier's desire to understand the flow of heat ...

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