Questions tagged [reference-request]

For questions that are requesting specific literature references

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24
votes
2answers
481 views

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 (...
2
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1answer
68 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 ...
0
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1answer
83 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.
8
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3answers
585 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
655 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
176 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
votes
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 ...
1
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0answers
60 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 ...
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
285 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
366 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 ...
2
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1answer
79 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
814 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 ...
1
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0answers
55 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
287 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
74 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
votes
1answer
467 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 ...
1
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0answers
71 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
votes
1answer
87 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 ...
4
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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 ...
1
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4answers
669 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
113 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 ...
24
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1answer
35k 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 ...
8
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2answers
194 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 ...
2
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1answer
984 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 ...
0
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1answer
49 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 ...
4
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0answers
94 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
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 ...
4
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1answer
97 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
71 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
319 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 ...
0
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0answers
34 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
vote
1answer
51 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
260 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
208 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
188 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
902 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
votes
4answers
479 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 "...
0
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0answers
79 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
votes
6answers
534 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 ...
3
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3answers
271 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 ...
6
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2answers
494 views

A branch of mathematics which refused to be rigorous?

I'm currently in a class on formal mathematics/formal logic/axiomatic set theory. Someone asked, "At the end of the day, as mathematicians, why do we care about rigor?" My professor gave an ...
3
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1answer
68 views

Books about the development/history of gravitational theory

I am looking for a book about the history of gravitational theory. It should obviously include discussions of Newton, Einstein, and their theories, and hopefully it would include the work of other ...
4
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0answers
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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0answers
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 ...
4
votes
1answer
131 views

Original mathematical foundation of Dirac's function

In which paper/book (most likely) by either Sobolev or Schwartz is the Dirac function properly and explicitly substantiated as a functional (tempered distribution), preferably quoting Dirac's name? I ...
2
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2answers
184 views

A technical and historical introduction to quantum mechanics

I am curious to understand the history of QM. In particular, how did the physicists conclude that observables can be treated as operators, or the use of complex state spaces, or that Eigenvalues of ...
1
vote
1answer
151 views

G. Washington notes on geometry

Do you know if there is a pdf file containing President George Washington's notes on geometry and surveying somewhere in the Internet? I recall reading a few weeks ago that those notes had been ...

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