Questions tagged [reference-request]
For questions that are requesting specific literature references
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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Historical proofs of the series expression for the Bessel function of the first kind
Introduction
The Bessel function of the first kind $J_n(x)$ ($n \in \mathbb{Z},\ x \in \mathbb{R}$) appeared early among other topics, in Celestial Mechanics, in the series expression of the true ...
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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 ...
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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 ...
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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.
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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 ...
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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&...
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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 ...
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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 ...
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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 ...
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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?
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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 ...
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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 ...
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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 ...
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Some references for Vladimir Arnold's thesis "Mathematics is a part of physics"?
The mathematician Vladimir Arnold claimed that mathematics is a part of physics.
I am aware of Arnold's On Teaching Mathematics where he stated this view, but is there any piece of writing where ...
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What would be some earlier comments on "1+2+3+4=10"?
"1+2+3+4=10" is an arithmetical triviality that is popular as an example of Pythagoreanism. There seems to be no mention of it in ancient Greek texts prior to Speusippus (e.g. ca. 350BCE; ...
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Einstein's handwritten manuscript on General Relativity
The book "The Road to Relativity" by Gutfreund and Renn annotates Einstein's original handwritten manuscript from 1916 - "The Foundation of the General Theory of Relativity." I can ...
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Are there any photographs of the original apparatus used by Hertz to demonstrate the photoelectric effect?
There are many schematics and many photographs of tubes used later but I cannot find a single photograph of the original apparatus. Even the sketches that were made in the late 19th century are ...
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Where exactly did George Brown publish the first paper about Turnstile antennas?
In its most basic form the Turnstile antenna is two half-wave dipole antennas that are perpendicular and driven 90 degrees out of phase. For a recent review see Crossed Dipole Antennas: A review (also ...
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Heisenberg's last work on a non-linear generalization of quantum mechanics?
It is claimed here that toward the end of his life Werner Heisenberg worked on a non-linear broadening or generalization of quantum mechanics. What work was that? Was it published?
Is it listed in ...
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English translation of Xu Yue's Shushu Jiyi?
Is there an english translation of Xu Yue's Shushu Jiyi? This is the work, around 190 CE, often described as containing the first description of the abacus. It is often associated with China's "...
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Are there commented English translations of Pappus's works on conics?
I'm investigating the conics in ancient Greece, I have the works of Apollonius, Diocles and Euclid, written with great commentary (both explaining the math and the historical context) that make them ...
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Origin of identity: $\int\limits_{-\infty}^{\infty} \exp\{ - \pi x^2 - 2 \pi^{1/2} a x\} \,da = \exp\left\{a^2\right\}$
A 1959 paper written by J. Hubbard called "Calculation of Partition Functions" and published in Physical Review Letters contains the following identity (Equation 2):
$$\int\limits_{-\infty}^{...
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What paragraph was written by Emanouil Atanassov to solve problem 6 on the International Mathematical Olympiad in 1988?
From the Wikipedia page about Vieta jumping:
Emanouil Atanassov, Bulgaria, solved the problem [assumed to be the most difficult one on the 1988 International Mathematics Olympiad] in a paragraph and ...
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Who made the first derivation of the angle to maximise projectile range, which turned out to be wrong?
I remember hearing once that the first "proof" that the angle to maximise projectile range gave the correct answer, 45 degrees, but was later found that the proof was wrong. I can't remember ...
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A Reference in Klein's Book
F. Klein mentions a certain Blumenthal in his famous book on the history of mathematics in 19th century with the following verse(when he was talking about the curvature in space):
Die Menschen fassen ...
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In which article/book chapter did Cantor, Hilbert, and Poincaré formally define or directly discusse the term “potential infinity”?
Some media sources say that "Cantor claimed that there would only be potential infinity, not actual infinity"
In addition, the following link claims that Hilbert, Poincaré, and Cantor were ...
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Why are complex numbers called 'complex'?
I'm a high school teacher, and I was just wondering why complex numbers are called 'complex'. I have read that Gauss coined the term. But I couldn't find any reference where it was explained.
I also ...
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When and where was Legendre's Conjecture first published?
When and where did Legendre first publish or write about his conjecture that there is a prime between consecutive square numbers?
$$n^2 < p < (n+1)^2$$
I have looked through edition 1 and 2 of ...
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What was Weil's reaction to Deligne's proof?
How did André Weil react when Pierre Deligne finally solved the most important and hardest of the Weil conjectures ?
Is there any written account on this ?
I guess Serre's and Grothendieck's (...
THC
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What is the original source of the problem of finding equivalent resistance between two nodes in an infinite grid of resistors?
A famous problem in electronics or physics course,is the following---
Consider an infinite 2d grid of resistors having resistance of equal value.Find the resistance between any two nodes in the grid.
...
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Literature on Mayan mathematics
I asked this question on math.se and they sent me here.
It is well known that Mayan people used vigesimal (base 20) numeral system, and had had an advanced calendar system.
Except for these facts, I'...
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What was Kolmogorov’s point of view in the philosophy of mathematics?
Today the standard interpretation of intuitionistic logic is the Brouwer-Heyting-Kolmogorov interpretation which was presented independently by Arend Heyting and Andrei Nikolajewitsch Kolmogorow. ...
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Natura non facit saltus (nature does not make jumps), who said that?
The sentence is Latin for nature doesn't make jumps. It refers to the fact that, in most physical processes, quantities vary continuously.
The principle was used by Leibniz, Kant and Darwin among ...
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Is there any historical evidence of this quote E.T. Bell attributed to C.G.J. Jacobi?
I read Men of Mathematics by E.T. Bell long ago, and this quote he attributed to Jacobi stuck with me:
Certainly I have sometimes endangered my health from overwork, but what of it? Only cabbages ...
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What is the origin of the term (non-)derogatory matrix?
A non-derogatory matrix $A$ is one, whose minimal polynomial $m(z)$ equals its characteristic polynomial $p(z)$, where we apply the convention $p(z) = det(zI-A)$, while a matrix is derogatory, if they ...
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What are the sources for Democritus’ experiment of dividing a shell down to its atoms?
It is common to find accounts of Democritus explaining his thought experiment to demonstrate the existence of atoms by taking a piece of rock/shell/cheese, and breaking it in smaller and smaller bits ...
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How did Eratosthenes know the distance between Aswan and Alexandria?
In his well-known measurement of the Earth, and according to Cleomedes, Eratosthenes estimated in 5000 stades the distance between Aswan and Alexandria. Modern accounts state that he calculated the ...
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Books on elliptic functions
In the end of his address to Annual Meeting of the Mathematical Association in 1933 titled "The marquis and the land agent: a tale of the 18th century", the Association president G. N. ...
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How did Weibull derive the three parameter Weibull distribution?
How did Weibull or any other mathematician arrive at the above expression? I saw the 1951 paper, but it is not clear to me. In 1939 he had published a book called "A Statistical Theory of the Strength ...
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Chronology of proofs of cubic and biquadratic reciprocity laws
I just want to check if anybody knows a website where one can find a chronology of proofs of more difficult reciprocity theorems (such as the cubic and biquadratic cases) similar to the (already ...
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Have orthogonal complex matrices appeared in the literature?
According to https://en.wikipedia.org/wiki/Orthogonal_matrix,
https://en.wikipedia.org/wiki/Unitary_matrix, and
Friedberg et al.'s Linear Algebra (4th edition), a matrix $A\in F^{n\times n}$
is ...
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Einstein praising Sophus Lie
p. 153 of
Raúl M. Falcón Ganfornina and Juan Núñez Valdés, “Mathematical Foundations of Santilli Isotopies,” trans. Alan Aversa, Algebras, Groups, and Geometries 32 (2015): 135–308.
quotes (but does ...
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What is the source of this quote by Einstein on wave–particle duality?
I'm writing a paper which involves a lot of quantum mechanics.
As a result of this, I'm finding it necessary to cite the likes of Einstein, Born and Jordan.
Particularly in the case of Einstein, due ...
Persistence