Questions tagged [reference-request]

For questions that are requesting specific literature references

Filter by
Sorted by
Tagged with
2
votes
1answer
68 views

Reference request for Gauss's original discovery of the special property of the $j$ function

In Interchapter VII of his biography of Gauss, W.K. Buhler describes Gauss's discovery of one of the important properties that characterize the $j$ invariant (Klein's absolute invariant; Gauss called ...
1
vote
0answers
60 views

Source of L’Hôpital’s 1696 Calculus textbook

A calculus textbook I’m using references a calculus book of L’Hôpital in which he illustrates his rule, which is taught in many calculus classes. Does anyone have a source as a scanned PDF? I’d love ...
4
votes
1answer
87 views

When were cephalopods assigned to the taxonomic phylum Mollusca?

I am fascinated to read about the evolution of cephalopod intelligence while I understand why cephalopods are mollusks (e.g., https://en.wikipedia.org/wiki/Cephalopod), but I cannot easily find when ...
4
votes
0answers
113 views

Who bet against the usefulness of matrix inversion – or is it a myth?

In my linear-algebra and numerics courses, I frequently heard an anecdote about some professor betting – literally, with money – that there would never be any application where computing the actual ...
2
votes
1answer
79 views

Lunar distance measurement reference

While preparing trigonometric exercises for my students, I learned that, in 1771, French astronomers determined the distance of the Moon from the Earth by measuring the appropriate angles from both ...
0
votes
1answer
74 views

Where can I find the historical information or the stats related to Winning WW2 with the minimum actions using The Bombe Machine of Alan Turing?

I am doing a marathon of data visualizations with real world datasets. I am interested in historical war datasets. Does anybody know about the historical data on The Bombe Machine cracking the codes ...
0
votes
1answer
49 views

What monograph on celestial mechanics did Jürgen Moser coauthor the 2nd and considerably expanded English language edition of with Carl Ludwig Siegel?

Comments under the Space SE question How do orbits around Jacobi ellipsoids behave? include: Periodic orbits around a rotating ellipsoid "This paper extends results obtained during the ...
4
votes
0answers
94 views

Where can I read Cauchy's terrible poems?

I hope that the slightly abrasive title is forgivable, as the judgement on this poetry is not mine, but Hans Freudenthal's. Here is the background: in the Dictionary of Scientific Biography, there is ...
1
vote
0answers
50 views

Who first spoke of Euclidean domains?

I am looking at Euclidean domains for the first time and it is a subject that has caught my attention. I wonder, who was the first to talk about this? I've been reading a little and so far the oldest ...
4
votes
0answers
71 views

von Neumann vignette on early computer usage

I'm looking for a vignette about von Neumann. My recollection is as follows but my google-fu is not bringing up anything. von Neumann, having prodigious mathematical capacity even of the most mundane ...
4
votes
1answer
97 views

Original Proof of the Schwarz lemma

The classical Schwarz lemma from one-variable complex analysis states that a holomorphic map $f : \Delta(r) \to \Delta(R)$ between two disks in the complex plane such that $f(0)=0$ satisfies $$|f(z)| \...
0
votes
0answers
34 views

First appearance of relations commutator,anticommutator with quaternion product

My query is the following, what is the first textual reference of the usage of commutator and anticommutator regarding quaternions in a similar way relative how it is done in the wikipedia article of ...
8
votes
3answers
260 views

What does "organic" mean in old texts when describing plane curves and their construction?

I've been reading about 17th and 18th century geometers and their research into plane curves, especially algebraic curves. A term that comes up frequently is "organic". By context it seems ...
4
votes
1answer
188 views

Lost memoir of Évariste Galois

According to the Wikipedia article on Évariste Galois He submitted his memoir on equation theory several times, but it was never published in his lifetime due to various events. Though his first ...
0
votes
0answers
79 views

Platonian geometry illustrated

I recently found out that a lot of Plato's work can be drawn geometrically. See the Cerritos College YouTube video "Platos Divided Line" with the description Cerritos College Professor ...
1
vote
1answer
51 views

First occurrence of the Langevin function in scientific literature

The Langevin function $\mathcal{L}(x) = \mathrm{coth}(x) - \frac{1}{x}$ is named after the French physicist Paul Langevin (1872-1946). The Wikipedia article on the Brillouin and Langevin functions ...
4
votes
0answers
101 views

In which work was Gibbs' Inequality introduced?

Gibbs' inequality $$-\sum\limits_{i=1}^n p_{i} \cdot \log{p_{i}} \le -\sum\limits_{i=1}^n p_{i} \cdot \log{q_{i}}$$ is such a popular thing that I cannot find where it was introduced. My findings I ...
1
vote
0answers
72 views

history of curl and inverting the curl

A man in Tennessee has written to me, asking for a reference about the method in my answer to https://math.stackexchange.com/questions/81405/anti-curl-operator He is writing an article on finite ...
4
votes
1answer
131 views

Original mathematical foundation of Dirac's function

In which paper/book (most likely) by either Sobolev or Schwartz is the Dirac function properly and explicitly substantiated as a functional (tempered distribution), preferably quoting Dirac's name? I ...
2
votes
2answers
184 views

A technical and historical introduction to quantum mechanics

I am curious to understand the history of QM. In particular, how did the physicists conclude that observables can be treated as operators, or the use of complex state spaces, or that Eigenvalues of ...
6
votes
2answers
494 views

A branch of mathematics which refused to be rigorous?

I'm currently in a class on formal mathematics/formal logic/axiomatic set theory. Someone asked, "At the end of the day, as mathematicians, why do we care about rigor?" My professor gave an ...
1
vote
1answer
151 views

G. Washington notes on geometry

Do you know if there is a pdf file containing President George Washington's notes on geometry and surveying somewhere in the Internet? I recall reading a few weeks ago that those notes had been ...
0
votes
0answers
58 views

On the Euler line

Do you know of some books or papers dealing with the history of the Euler line? Was L. Euler the first mathematician that notice its existence? Are there any interesting paragraphs out there ...
2
votes
0answers
73 views

Is there a modern equivalence of Asimov's book "The new intelligent man's guide to science"?

I enjoyed Asimov's "The new intelligent man's guide to science" very much when I was a teenager. I noticed that he later published "Asimov's New Guide to Science", however that was ...
1
vote
1answer
75 views

Stories about the consequences of statistical simplification?

I am currently preparing a presentation about the value of more complex (specically: non-Gaussian) statistical inference. I thought it might be interesting to start the presentation with a small real-...
4
votes
1answer
164 views

($\varepsilon$, $\delta$)-definition of limit by Weierstrass

I am looking for the original ($\varepsilon$, $\delta$)-definition of limit by Weierstrass, but I cannot find an exact quote or a reference. I saw that somewhere it was claimed that this definition ...
1
vote
0answers
98 views

Fourth powers and quartic equations before Descartes

How did mathematicians interpret quartic equations and fourth powers before Descartes propose to perform elementary arithmetic on line segments? I ask this because it seems strange to me that ...
3
votes
0answers
74 views

Where can I find the complete papers of abstracts published by P. G. Tait in Proc. Roy. Soc. Edinburgh in 1880?

I am interested in looking up P. G. Tait's flawed proof of the four-colour theorem, published in 1880. The citation that I have seen is: P. G. Tait, On the colouring of maps, Proc. Roy. Soc. ...
3
votes
0answers
62 views

What is the source of Hopf's (boundary) lemma?

In an introductory course on PDE's I got as a project to prove and present a version of Hopf's (boundary) lemma. Namely: Let $\Omega \subset R^{d}$ be an non-empty open connected set with a twice ...
0
votes
0answers
42 views

Old Indian and Chinese references

It is been some years since I completed my graduate studies in mathematics at a Spanish university. I remember one of the most pleasant and enriching moments I experienced was when reading Euclid´s ...
1
vote
1answer
81 views

Is there an English translation of Newton’s De Analysi?

I’m looking for an English translation of Newton’s De analysi. (Alas, my Latin is weak.) I’m rather dismayed by the fact that I can’t appear to find one. How is it possible that one of the most ...
1
vote
0answers
56 views

Who extended the Banach fixed point theorem from the context of normed spaces to the context of metric spaces?

It is well known that Banach's fixed-point theorem was initially conceived as a fixed-point theorem for applications defined in normed spaces (see [1]). This theorem was conceived in 1922 by Stefan ...
2
votes
0answers
84 views

President James A. Garfield and the Pythagorean proposition

As some of you may recall, President James A. Garfield published at some point of his life a proof of the celebrated Pythagorean proposition. I am interested in acquiring a pdf copy of President ...
2
votes
0answers
115 views

Reference request for some fragments of Gauss with dubious origin

Gauss's results on the interconnection between the different values of the arithmetic-geometric mean of two complex numbers as recorded in his private notebooks led him to introduce foundational ...
3
votes
0answers
139 views

The origins of $\det(I+AB)=\det(I+BA)$

I am looking for the earliest published source that gives and perhaps proves the identity $\det(I+AB)=\det(I+BA)$ where $A$ and $B$ are just rectangular matrices of finite dimensions (as opposed to ...
2
votes
3answers
95 views

Book to know about development of mathematical concepts

I am looking for a book that describes the historical development of mathematics from the ancient times to our advanced developed concept. Along with the derivation and mathematical concepts as ...
3
votes
1answer
68 views

Books about the development/history of gravitational theory

I am looking for a book about the history of gravitational theory. It should obviously include discussions of Newton, Einstein, and their theories, and hopefully it would include the work of other ...
8
votes
1answer
186 views

History of irreducible polynomials and motivation for them

I've been thinking about the history of the irreducible polynomials and why they were introduced. I found What is the origin of polynomials and notation for them?, but it's about polynomials in ...
0
votes
0answers
32 views

First paper in derived speeds after collision in relativistic dynamics

In the one dimensional relativistic collision, do you know which is the first paper in which the final speeds in terms of initial rates and rest masses are derived? I found the derivation on Wikipedia ...
0
votes
0answers
39 views

Who was the first one to rigorously show that quantum fields are operator-valued distributions?

Any Wightman-based approach to Axiomatical Quantum Field Theory states that quantum fields are (operator-valued) distributions. Is there a first rigorous proof of this fact which became trivial as ...
0
votes
1answer
83 views

Is there any book or site where John von Neumann's collected philosophical writings are presented?

I was wondering if von Neuman has any philosophical writings beside his writings on the relation of computers to the human mind and vice versa.
1
vote
0answers
75 views

Finding sources for "computers will become so powerful that special functions will become obsolete" as a zeitgeist

In Why are special functions special [Physics Today 54, 11 (2007); eprint], Michael Berry makes the following observations: This continuing and indeed increasing reliance on special functions is a ...
3
votes
0answers
91 views

Origin of notation "R with a stroke on the leg" for the square-root (℞)

The following text from Ars magna (1545) by Girolamo Cardano is known as the inception of complex numbers: "imaginaberis ℞ m 15" (You will imagine the square root of minus 15): The "R&...
10
votes
2answers
194 views

Who introduced the divisibility symbol $a\vert b$ ("$a$ divides $b$") and when?

I have just stumbled across this post and became curious about the same question, namely the part regarding the origin/history of the vertical bar symbol $a\vert b$ that we use to denote "a ...
1
vote
0answers
56 views

The earliest origins of science and math

I'd like to have a broad understanding of how various societies in the world developed pre-scientific understanding. There are a lot of resources for ancient Greece. There are even a few for what ...
2
votes
1answer
128 views

The origins of differential homological algebra

Differential homological algebra in its initial formulation is due to Eilenberg and Moore, who first published the homological version of the Eilenberg–Moore spectral sequence in 1965 (and the ...
2
votes
1answer
83 views

In which article did the physicist Sheldon Glashow introduce his electroweak theory?

In which article did Glashow introduce (1961?) a unified description of the electromagnetic and weak interactions, i.e., the electroweak interaction that earned him the Nobel prize in physics?
2
votes
1answer
265 views

Was Rayleigh the first to derive the drag equation?

I was reading about The Drag Equation: $$ F_D = \frac{1}{2} \rho v^2 C_D A $$ where: $ F_D $ is the drag force $ \rho $ is the mass density of the fluid $ v $ is the flow velocity relative to the ...
7
votes
1answer
225 views

Where to pursue a PhD in history of mathematics in Europe?

This is more a soft question, and I am not sure where I should place it so I ask for excuses if this is not the right place, but I could not find any other that seemed more suitable. I would like to ...
1
vote
0answers
95 views

Quotation reference: "functions which can be evaluated under 1 sec are as good as analytically available"

I have a vague memory of a (possibly-apocryphal) quote by a physicist (I remember it as being Giorgio Parisi, which could be wrong), saying something to the effect of "any function which can be ...

1
2 3 4 5 6