Questions tagged [reference-request]

For questions that are requesting specific literature references

Filter by
Sorted by
Tagged with
4
votes
1answer
1k 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 ...
7
votes
1answer
258 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 ...
4
votes
1answer
196 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 ...
5
votes
1answer
123 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 ...
2
votes
1answer
82 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 ...
7
votes
1answer
526 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 ...
9
votes
1answer
247 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 ...
2
votes
0answers
140 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 ...
5
votes
1answer
534 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 ...
10
votes
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 ...
2
votes
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 ...
5
votes
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-...
6
votes
7answers
329 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 ...
3
votes
2answers
117 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
votes
1answer
161 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
votes
1answer
156 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 ...
6
votes
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 ...
9
votes
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 ...
3
votes
1answer
206 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 ...
4
votes
0answers
111 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
2answers
109 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 ...
2
votes
1answer
351 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 ...
5
votes
1answer
189 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 ...
4
votes
2answers
776 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.
5
votes
1answer
365 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 - ...
2
votes
1answer
76 views

Jordan's Paper on the Jordan Canonical Form

In which paper, did Jordan introduce/prove the Jordan canonical form?
2
votes
1answer
421 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 ...
6
votes
2answers
22k 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 ...
2
votes
0answers
148 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 ...
3
votes
1answer
301 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 ...
3
votes
5answers
882 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 ...
4
votes
2answers
390 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 ...
3
votes
1answer
70 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,...
2
votes
1answer
129 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 Physiques et ...
5
votes
1answer
2k views

Did Srinivasa Ramanujan have a surviving sibling?

Wiki says 'After his death, his brother Tirunarayanan chronicled Ramanujan's remaining handwritten notes consisting of formulae on singular moduli, hypergeometric series and continued fractions and ...
4
votes
0answers
116 views

Historical evidence for claim that we use base 10 because of the number of fingers

It is a common belief that we use a base 10 representation of integers because we have 10 fingers. Does there exist historical evidence which supports the claim that this is true and that the number ...
3
votes
1answer
115 views

Origin of the smooth but nowhere real analytic function built with dyadic rationals

I found the following interesting function and its analysis at Non-analytic smooth function article in Wikipedia. I include a screen capture below for those who don't wish to navigate away: I could ...
4
votes
1answer
237 views

Do these trigonometric identities belong to Antonio Cagnoli?

I'm new to this stack community, please bear with me as I try to explain my question properly. Recently I came across with these trigonometric identities (where $ \omega + \phi + \psi = 180^\circ $): ...
1
vote
2answers
120 views

On the creation of analytical geometry

Of all mathematical creations, the one of using graphs to describe planes and 3D space seem to me the most strange ones. My head almost can't admit that space can be represent by three numbers. If I'...
0
votes
1answer
307 views

mathematicians attempts at proving Euclid postulate

Is there a list of all the people who attempted to prove the parallel postulate (also known as the fifth postulate or the Euclid axiom) in Euclidean geometry? Wikipedia has a page on the subject but ...
2
votes
1answer
119 views

Who discovered the Virial Theorem?

Who first discovered the Virial Theorem? Who first wrote it down? When? Where? My guess: a 19th century thermodynamicist
1
vote
0answers
102 views

Looking for Cantor's correspondence

I am trying to collect all available letters written or received by Cantor or written between his colleagues about Cantor. I have searched already the literature given below. But I would like to ...
0
votes
0answers
77 views

The Original Proofs of The Stable Manifold Theorem

The book "Differential Equations and Dynamical Systems" by Lawrence Perko says that the first proofs of the Stable Manifold Theorem are from Hadamard in 1901, Perron in 1928, and Liapunov and Perron. ...
1
vote
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 ...
1
vote
2answers
99 views

Whether Euclid considered squares to be rectangles

When I look up 'that which is right-angled but not equilateral' there are translations that show the word before the above phrase to 'oblong', some that show 'rectangle' and some that show both ...
7
votes
1answer
331 views

How were variables used and understood in (particularly) 19th century maths?

Context: I have been thinking about Frege's Begriffsschrift, where he introduces a version of what we now think of as the standard quantifier/variable notation. Philosophers who write on Frege tend to ...
6
votes
2answers
1k views

How was the focus/directrix property of conic sections discovered?

I've always thought that defining conic sections by a locus of points w.r.t the ratio of the distance to the focus and directrix was always "too artificial" - how does one actually discover this ...
5
votes
1answer
289 views

Who influenced Gauss in his abstract approach to mathematics?

I have studied that Gauss was one of the firsts mathematicians to defend this idea, about the Abstract Math and the conception of number, claiming that "What is calculated (in the sense of things ...
2
votes
1answer
341 views

Does an English translation of Bombelli's L'Algebra exist?

I'm looking for an English translation of Rafael Bombelli's L'Algebra. From what I can tell after having searched the usual corners of the web, it doesn't exist, but I'm asking here just in case. I'...
3
votes
1answer
188 views

Where can I find the list of problems from the (Chinese) "Nine Chapters on Mathematical Art"?

For the sake of curiosity, I'm interested in the "list of problems" that were laid out in the ancient Chinese text on Math. However, I haven't found a "list" in English anywhere. Only a few excerpts ...