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Questions tagged [reference-request]

For questions that are requesting specific literature references

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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 ...
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Quote on the value (or no value) of a proof before reaching the Q.E.D. (Quod Erat Demonstrandum)?

I recall reading that some of the mathematical gods of the past said that during proving a claim (or reading the proof of the claim), you really know nothing before you have reached the Q.E.D. sign. ...
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2answers
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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-...
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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
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1answer
64 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 ...
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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 ...
2
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1answer
127 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 ...
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3answers
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What are some good references elucidating the discovery/creation of Fourier Series?

I've always grappled with the topic of anything Fourier during my undergrad days. Until recently when revisiting why I learned what I did, I discovered how Fourier's desire to understand the flow of ...
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1answer
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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 ...
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0answers
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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 ...
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2answers
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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 ...
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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 of ...
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1answer
158 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 ...
3
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1answer
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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
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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
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Jordan's Paper on the Jordan Canonical Form

In which paper, did Jordan introduce/prove the Jordan canonical form?
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1answer
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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
401 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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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 ...
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1answer
207 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
495 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
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2answers
127 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 ...
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1answer
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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
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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
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1answer
275 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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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
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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
188 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
62 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
128 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
62 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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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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0answers
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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
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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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253 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
399 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
160 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
140 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 ...
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1answer
72 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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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
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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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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
69 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
112 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
69 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
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1answer
136 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
228 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
234 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
376 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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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 ...