Questions tagged [reference-request]
For questions that are requesting specific literature references
348
questions
2
votes
1
answer
89
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 ...
- 121
3
votes
1
answer
151
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 ...
- 5,718
-4
votes
1
answer
217
views
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 ...
- 3,615
4
votes
1
answer
248
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 ...
- 457
3
votes
0
answers
114
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,\...
- 5,229
-1
votes
1
answer
79
views
Who first distinguished number theory and numerology? [duplicate]
Who first distinguished number theory and numerology?
- 5,229
3
votes
0
answers
91
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 ...
- 261
3
votes
0
answers
106
views
Pre-20th century sources on information theory?
What are some pre-19th or pre-20th century sources on information theory? Do they exist?
- 5,229
4
votes
0
answers
125
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 ...
- 141
10
votes
2
answers
325
views
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 ...
- 211
3
votes
1
answer
243
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 ...
- 4,307
3
votes
1
answer
3k
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.
...
6
votes
1
answer
230
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 ...
- 227
5
votes
2
answers
332
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 ...
- 411
3
votes
1
answer
511
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 ...
- 83
4
votes
1
answer
2k
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 multiplication in the Fourier domain).
The ...
- 3,949
7
votes
1
answer
376
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 ...
- 343
4
votes
1
answer
217
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 ...
- 4,307
5
votes
1
answer
151
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 ...
- 153
3
votes
3
answers
4k
views
What is the origin of Arabic numerals
I was taught that the numerals {0,1,2,...,9} are from the Arabic alphabet. But they look completely different from today's Arabic letters. I wonder what is the origin of Arabic numerals?
Edit: The web ...
- 795
2
votes
1
answer
88
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 ...
- 2,387
7
votes
1
answer
651
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 ...
- 73
10
votes
1
answer
290
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 ...
- 103
2
votes
0
answers
147
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 ...
- 121
5
votes
1
answer
900
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 ...
- 83
10
votes
1
answer
260
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 ...
- 203
2
votes
1
answer
3k
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 ...
- 3,949
8
votes
3
answers
578
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-...
- 5,718
6
votes
7
answers
368
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 ...
- 162
3
votes
2
answers
128
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 ...
- 1,717
3
votes
1
answer
169
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 ...
- 5,718
3
votes
1
answer
176
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 ...
7
votes
6
answers
793
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 ...
- 639
11
votes
2
answers
1k
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 ...
- 693
3
votes
1
answer
242
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 ...
- 204
4
votes
0
answers
157
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 ...
1
vote
2
answers
168
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 ...
- 639
2
votes
1
answer
401
views
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 ...
- 4,307
5
votes
1
answer
200
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 ...
- 355
4
votes
2
answers
1k
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.
user7532
6
votes
1
answer
444
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 - ...
- 639
2
votes
1
answer
89
views
Jordan's Paper on the Jordan Canonical Form
In which paper, did Jordan introduce/prove the Jordan canonical form?
- 486
3
votes
1
answer
618
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 the pioneers regarding a rigorous foundation towards real and complex ...
- 258
10
votes
2
answers
37k
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 ...
user7921
3
votes
1
answer
283
views
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 ...
- 4,307
3
votes
1
answer
379
views
What was the main language in science/mathematics between 1850 and 1950 and beyond
The second half of 19th century and first half of 20th century are golden age of modern mathematics and science, as many important ideas and theories were proposed and developed within that period of ...
- 795
3
votes
5
answers
1k
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 ...
- 795
4
votes
2
answers
450
views
What mathematical techniques Gauss used in order to tessellate the unit disk?
This question is a continuation of my previously posted question: Was Gauss aware of the non-euclidean implications of his work on moduler forms?, and is based on the information given in John ...
- 4,307
3
votes
1
answer
96
views
Whereabouts of oldest extant source for Apollonius’ *Conics*, Books I - IV
Regarding Conics, it is widely written, e.g. Rutger's site, that:
The first four books have come down to us in the original Ancient Greek, but books V-VII are known only from an Arabic translation,...
- 6,679
4
votes
1
answer
216
views
Reference - Schwarz's Proof of Clairaut's Theorem
Where can I find a copy (online) of Schwarz's paper that proved Clairaut's theorem for mixed partial derivatives?
His paper is: Schwarz, H. A., "Communication", Archives des Sciences ...
- 486