Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [reference-request]

For questions that are requesting specific literature references

0
votes
0answers
64 views

What was the main language in science/mathematics between 1850 and 1950

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
361 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 ...
3
votes
1answer
90 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
58 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
36 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 ...
3
votes
1answer
152 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
99 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
91 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 ...
3
votes
1answer
153 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 $): ...
0
votes
2answers
53 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
116 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
55 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
67 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
26 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
2answers
65 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
245 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
302 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 ...
4
votes
1answer
150 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
105 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 searching the usual corners of the web, it doesn't exist, but I'm asking here just in case. I'm ...
3
votes
1answer
57 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 ...
0
votes
0answers
53 views

Why is the angular momentum written as JJ in quantum mechanics?

Why is $\textbf{J}$ called angular momentum operator? Can anyone explain why the expectation value of J is angular momentum? Here is how $J$ is defined: The rotation operator $$ U(\alpha)=\exp(-i {\...
6
votes
2answers
168 views

What did Fermat do as a lawyer?

Fermat is easily one of the best known mathematicians of all time. We all know about Fermat's Last Theorem, Fermat's Little Theorem, his quadrature rule, his invention of probability theory, etc. ...
1
vote
0answers
72 views

Laplace's characterization of Gauss as “a super-terrestrial spirit in a human body”

The following words concerning Carl Friedrich Gauss are attributed to Laplace in an article from the Mathematics magazine by Teets and Whitehead (The discovery of Ceres: how Gauss became famous, first ...
2
votes
1answer
55 views

Who posed the separable quotient problem (and when)?

The (infinte dimensional) separable quotient problem asks whether every infinite dimensional Banach space has a separable infinite dimensional quotient. In the literature I have seen that is problem ...
0
votes
0answers
34 views

Who popularized using $x,y$ to label axes and $z$ as complex variable?

I believe although it was Rene Descartes who popularize using $a,b,c$ as constants and $x,y,z$ as variables, he wasn't the one who associated $x$ and $y$ with axes labeling. Also, how did using $z$ ...
3
votes
1answer
105 views

When was $e$ first observed to not be a Liouville number?

When and by who was it first observed that the transcendental number $e$ is NOT a Liouville number? This fact is stated in a lot of web pages, and a proof can be found in the Mathematics Stack ...
4
votes
0answers
66 views

History of Braids

I am looking for papers or books that describe the history of the development of braid theory, mainly during the 19th and the 20th century. I know Moritz Epple book on the history of the theory of ...
2
votes
1answer
135 views

Books that we can know when which theorem was discovered by whom

There are many textbooks which states mathematical theorems, but in them, by whom and when the theorems are discovered is not explained. Do you know good references for this? If this scope is too ...
5
votes
2answers
206 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 ...
4
votes
1answer
199 views

What are Philolaos' “even-odd” numbers?

Number, indeed, has two proper kinds (ιδια ειδη), odd and even, and a third mixed together from both, the even-odd(αρτιοπέριττον). Of each of the two kinds there are many shapes, of which each ...
2
votes
2answers
324 views

History of PDE's in the 19th Century

I've been asked to write an essay on whether the work on PDE's in the 19th century belonged to applied or pure mathematics. I was wondering if anyone knows of any useful sources I could use?
4
votes
7answers
695 views

Examples of abstract proofs that turned out to be false

I found this question that discusses abstract theories that later found application. I am interested in accepted (at least at one point in time) abstract theories that: was contradicted by attempts ...
1
vote
1answer
37 views

First use of the term/name “curved exponential family”?

Question: What was the first recorded use of someone calling exponential families (in probability/statistics) for which the dimension of the natural parameter space is strictly less than the dimension ...
0
votes
2answers
68 views

Has Alphonse Pyramus de Candolle's “Géographie botanique raisonné” ever been translated into German or English?

Alphones Pyramus de Candolle (1806-1893), the son of Augustin-Pyrame de Candolle (1778-1841), has been an important figure (as was his father) in the development of plant geography. The younger ...
1
vote
0answers
179 views

History of the arithmetic mean

The arithmetic mean of a set of points $\{x_1, x_2, ..., x_n\}$ is defined by $$\frac{1}{n}\sum_{i=1}^n x_i.$$ It is remarkable for its ubiquitous use and universal understanding. It represents a ...
2
votes
0answers
58 views

Etymology of 'qubit'; is there any relation to cubits?

Whilst several not-very-authoritative sources e.g. Wikipedia state that the word qubit was derived, partially, as a play on the word cubit (obviously it also stands for 'quantum bit'), is there any ...
5
votes
0answers
201 views

Who gave you infinitesimal epsilon?

As someone reputed among certain historians to have given you the epsilon Cauchy startled me by using $\varepsilon$ to denote an infinitely small number in his 1826 text on differential geometry; see ...
2
votes
1answer
115 views

History of the origins and development of problems of finding maximum and minimum values of quantities

I am aware that perhaps the earliest source concerning problems of maximum and minimum values occurs in Euclid's Elements. After Euclid, Archimedes of Syracuse and Apollonius of Perga seem to consider ...
1
vote
2answers
103 views

Is there any evidence supporting this claim about Cassini and his ovals?

The Wikipedia article for Cassini ovals claims in the introduction that "Cassini believed that the Sun traveled around the Earth on one of these ovals, with the Earth at one focus of the oval." This ...
7
votes
0answers
168 views

Did Kronecker say that set theory is not mathematics?

I have frequently come across Kronecker's statement about set theory: "I don't know what predominates in Cantor's theory - philosophy or theology, but I am sure that there is no mathematics there." It ...
2
votes
1answer
63 views

On a paper by Georg Pick

Has any of you ever read the paper in which Georg Pick made public his famous formula? If so, would you be so kind as to tell me what it is that one can find in the introduction of it? The complete ...
0
votes
0answers
67 views

Riemann surfaces and covering

Assuming we have a Riemann surface $S$ of degree $n$ and we look at it as a covering of the projective line $\mathbb{P}^1$. If $B$ is the set of branch points of $S$ (when $B$ is a subset in $\mathbb{...
1
vote
1answer
460 views

Where did Galileo say “All truths are easy to understand once they are discovered. The point is to discover them.”?

I've heard it claimed Galileo said or wrote: All truths are easy to understand once they are discovered. The point is to discover them. Where did he say this?
6
votes
1answer
244 views

Euler's works after blindness

There are many sources which say that Euler produced, on average, one mathematical paper every week in the year $1775$. Some even say he produced almost half his total works despite the total ...
1
vote
3answers
116 views

Biographies on 20th Century physicists

I've recently finished reading Helge Kragh's Quantum Generations and am looking for what to something to read next. I am hoping to find biographies or more information about certain physicists such as ...
1
vote
2answers
105 views

What are some good (and reasonably academic) books on 18th and 19th century British mathematics?

In addition to the general topical interest indicated in the title, I am also curious about British mathematics of the period viewed through the lens of competition with the rest of Europe (and ...
1
vote
0answers
52 views

Carnap's last theory Of probability

According to Bar-Hillel, Carnap's coauthor in a 1952 report on probability, Carnap had, as of 1956 an unpublished but circulated theory distinguishing "random" refers to methods of production of ...
3
votes
0answers
38 views

Raymond Cattell and History of Personality Traits Prior 1947

I find that papers reference Raymond Cattell suggesting 16 or 22, etc, traits, by factor analysis (basically regression), including all five of the modern reproducible traits (openness to experience, ...
1
vote
0answers
78 views

Verification of Navier's theory of structures

Jacques Heyman in his article Truesdell and the History of the Theory of Structures, mentions the following: The first full-scale tests on building frames were made in the 1920s in London, and ...
2
votes
0answers
107 views

Works of mathematician François Viète

I'm searching for a book or an online copy of complete works of the mathematician François Viète, preferably in English. Any help will be appreciated. Thanks.