Questions tagged [reference-request]

For questions that are requesting specific literature references

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In which work was Boltzmann's entropy originally introduced?

I get an impression from this enyclopedia entry that the primary source of the Boltzmann entropy equation $S = k \log W$ might be 1866, Über die Mechanische Bedeutung des Zweiten Hauptsatzes der ...
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What is the earliest use of the $\perp\!\!\!\!\perp$ symbol in statistics to denote statistical independence?

The symbol $\perp\!\!\!\!\perp$ in statistics is a way to denote statistical independence of a collection of random variables. I have seen two forms of it. The first is highly suitable in writing ...
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Source of a Quote by M. Stone on Poincaré and Bourbaki

The quote in question is the following: For Bourbaki, Poincaré was the devil incarnate. For students of chaos and fractals, Poincaré is of course God on Earth. The common reference for this quote ...
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Reference for "A manifold is a topological space which satisfies a long series of axioms."

In On teaching mathematics, Vladimir Igorevich Arnold states "What is a smooth manifold? In a recent American book I read that Poincaré was not acquainted with this (introduced by himself) notion ...
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Fermat et l'équation de Pell

Does any of you happen to own and electronic copy of the paper "Fermat et l'équation de Pell" by A. Weil? If I understand correctly, this paper can be found on pages 413-419 of the third ...
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Doubt on women behind the development of wormhole physics

Ludwig Flamm $[1]$, Albert Einstein-Natan Rosen $[2]$, Hermann Weyl $[3]$, John Wheeler-Fuller $[4,5]$, Homer G. Ellis $[6]$, K. Bronnikov $[7]$, Michael Morris-Kip Thorne$[8]$, M. Visser $[9]$, ...
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Research on Pre-Columbian Polynesian geometry?

Has there been any historical/cultural anthropological research into how Polynesian cultures understood geometry before contact with Europeans? In part what I am interested in is how did the dealing ...
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Can not find reference for "uniform convexity implies existence of unique conjugate" mentioned by Pettis

In A proof that every uniformly convex space is reflexive in footnote 3 (available at that link without a paywall), author Billy Pettis mentions that the first half of Lemma 1 in that paper "was ...
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Reference database for recreational math problems and math puzzles?

Recreational math books contain duplicates for problems. I think, classical examples are SEND + MORE = MONEY and Zebra puzzles. (Though I can't point exact books ...
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5 answers
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Looking for math history but keep finding the same old stuff

I've browsed many math history books, but I've never read too deep into any single one. I always find myself reading the about the same facts and same people over and over -- the set of topics doesn't ...
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Help in locating a portrait of Göttingen's faculty in 1899

Does anybody here own a copy of the poster "Mathematische Gesellschaft: Group Portrait - University of Göttingen (1899)" that Springer Verlag published in 1985? If so, would you be so kind ...
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History of Green's function

Could you give me some references about the history of the Green's function? Thank you in advance for your reply In the study of boundary value problems for differential and difference equations we ...
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Questions related to the theorem von Neumann proved in five minutes

I have recently seen this post about the theorem von Neumann proved in five minutes. Searching for more information about that, it is certain that I can't find any references for what the theorem was. ...
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Publication information on "Recreational Mathematics Magazine"

I'm currently studying Martin Gardner's 1968 repackaging of two of Henry Ernest Dudeney's collections: "536 Puzzles & Curious Problems", and trying to track down all the references in ...
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142 views

Origin of the "teakettle principle" joke?

There's a fairly widely known joke about boiling water (one version is below) that pokes fun at how mathematicians like to reduce new problems to known solutions. I've traced it back to a footnote on ...
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2 answers
175 views

Source documents for Bronstein's Cube of Physics

The "cube of physics" is a quite useful summary of physics, for historical$^1$ and teaching$^2$ purposes, that is best explained (as far as I know) in "Physics On A Cube" by Jeremy ...
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1 answer
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What is the mysterious expression mentioned by Hadamard that Riemann derived properties of zeta function from?

In the Chapter 7 epigraph in Stein and Shakarchi's Complex Analysis, there is a quote, apparently from Hadamard in 1945, saying He proved some important properties of that function, but enunciated ...
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Is there a translation of Kronecker's original work on adjoining a root of a polynomial to a field?

I would be interested in reading how Kronecker formally approached this construction, using the mathematical ideas of his time, and possibly some insight as to what he considered its philosophical ...
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1 answer
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History of difference equations

Could you please give me some references about the history of difference equations. Thank you for your reply
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Source of a Poincaré quote from a Busemann paper

In his paper "The geometry of Finsler spaces" (available at https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-society-new-series/volume-56/issue-1.P1/The-geometry-of-...
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Looking for reference for quote

In graduate school, I remember hearing or seeing the rough quote: Good mathematicians know one branch of math. Great mathematicians know two branches. I'm sure I am somewhat misquoting it, but does ...
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Whose 1930 number theory result is used in characterizing perfect 2-error correcting linear codes?

In Error-Correcting Codes: A Mathematical Introduction (Chapman & Hall, 1998), John Baylis wrote (p.109) Moving on to 2-error correcting linear codes, the condition for perfection of linear codes ...
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1 answer
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(Where) does Plato define perfect number?

I've read several texts suggesting that Plato defines "perfect number" in his Republic, book VIII 546 b. However, there's no definition as we can see from - for example - this translation: &...
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Poisson integral formula

The term Poisson integral formula may refer to any of the related formulas for harmonic (or holomorphic) functions on a disk (or in a ball, half space, etc) in terms of their boundary values. This is ...
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Origins of proof in Mathematics

Why was the idea of writing, formalising and creating new proofs brought about? For example, why even though we have found hundreds of proofs of the Pythagorean Theorem are we still trying to find ...
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What's the origin of the claim that a single uranium atom fissioning would release enough energy to visibly move a grain of sand?

There's a fairly widespread claim that the energy released by the fission of a single atom of uranium would release enough energy to make a grain of sand visibly jump. Richard Rhodes's The Making of ...
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What is the origin of the "problem of Brahmagupta" of constructing inscribed quadrangle with given sides?

I am looking for a source of the following construction problem: Construct an inscribed quadrangle with given sides. I know it under the name problem of Brahmagupta, but I do not know any evidence ...
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4 votes
0 answers
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Earliest measurement of proton's mass

I was looking for the earliest experiment or the paper which shows the determination of the mass of proton. In NIST CODATA, the mass of proton is listed as "1.672 621 923 69 x 10$^{-27 }$kg"....
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8 votes
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What was Richard Courant's saying about mathematical research apart from applications?

I remember reading somewhere (perhaps in The Mathematical Experience) that Richard Courant wrote something to the effect that, without applications to guide the river of mathematical discovery, ...
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1 answer
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What was Einstein's first publication of the final form of general relativity?

What was Einstein's first published exposition of his final form of general relativity, be it a scientific article or a book? I've been googling the answer for hours now, with no luck, really. The ...
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3 votes
1 answer
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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 ...
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1 answer
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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 ...
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4 votes
1 answer
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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 ...
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4 votes
0 answers
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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 ...
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2 votes
1 answer
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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 ...
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0 votes
1 answer
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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 ...
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0 votes
1 answer
56 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 ...
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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 ...
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1 vote
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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 ...
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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 ...
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2 votes
1 answer
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Need quote from early 20th century about humanity probably never being able to control (manipulate, see?) a single quantum system

I remember having read a statement, I think by one of the founding fathers of quantum mechanics, that we will probably never be able to control (or manipulate or see or isolate...?) a single quantum ...
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4 votes
1 answer
141 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)| \...
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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 ...
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8 votes
3 answers
289 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 ...
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4 votes
1 answer
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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 ...
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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 ...
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1 vote
1 answer
61 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 ...
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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 ...
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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 ...
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4 votes
1 answer
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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 ...
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