Questions tagged [reference-request]

For questions that are requesting specific literature references

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1answer
273 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.
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1answer
181 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 - ...
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1answer
62 views

Jordan's Paper on the Jordan Canonical Form

In which paper, did Jordan introduce/prove the Jordan canonical form?
3
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1answer
277 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 pioneers regarding a rigorous foundation towards real and complex ...
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2answers
11k 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 ...
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0answers
99 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 ...
2
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1answer
248 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 ...
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5answers
651 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
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2answers
172 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
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1answer
66 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,...
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1answer
81 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 ...
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1answer
939 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 ...
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0answers
108 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
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1answer
102 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
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1answer
216 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 $): ...
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2answers
106 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'...
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1answer
179 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 ...
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1answer
85 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
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0answers
82 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 ...
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63 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. ...
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2answers
74 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 ...
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1answer
281 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 ...
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2answers
778 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 ...
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1answer
216 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 ...
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1answer
235 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
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1answer
96 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 ...
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57 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 {\...
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2answers
319 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. ...
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88 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 ...
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1answer
108 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 ...
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1answer
236 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 ...
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0answers
82 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 ...
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1answer
139 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 ...
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2answers
261 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
552 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 ...
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2answers
643 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?
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7answers
856 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 ...
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1answer
43 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 ...
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2answers
75 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 ...
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0answers
372 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 ...
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0answers
98 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 ...
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218 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 ...
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1answer
323 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 ...
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2answers
133 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 ...
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267 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 ...
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1answer
70 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 ...
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79 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{...
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1answer
2k 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?
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1answer
502 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 ...
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3answers
266 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 ...