Questions tagged [reference-request]

For questions that are requesting specific literature references

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15 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 ...
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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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1answer
69 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 ...
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1answer
71 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?
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89 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 ...
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171 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 ...
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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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165 views

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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115 views

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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61 views

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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1answer
76 views

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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209 views

What paragraph was written by Emanouil Atanassov to solve problem 6 on the International Mathematical Olympiad in1988?

In the Wikipedia about Vieta jumping, it is stated that "Emanouil Atanassov, Bulgaria, solved the problem [assumed to be the most difficult one on the 1988 International Mathematics Olympiad] in ...
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428 views

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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91 views

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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100 views

In which article/book chapter did Cantor, Hibert, and Poincare formally defined or directly discussed 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, Poincare, and Cantor were ...
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192 views

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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70 views

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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Is there an English translation of Kronecker's proof of Infinitude of primes?

Is any English translation of the following paper available? H. Hasse, Vorlesungen ¨uber Zahlentheorie, Second edition, Springer-Verlag, New York, $1964$ (L. Kronecker, $269–273; 440–442; $ K. Hensel, ...
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224 views

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 (...
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67 views

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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Did Peierles write about Peierls transition in any Journal?

I want a reference to Peierls transition and am looking for the original work by Peierls himself. But none of the citations in the Wikipedia page of Peierls transition is authored by Peierls. So, did ...
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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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2k views

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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232 views

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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261 views

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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85 views

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 the Mathematical Association in 1933 titled "The marquis and the land agent: a tale of the 18th century", G. N. Watson says: My final task is to express my gratitude to ...
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93 views

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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116 views

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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130 views

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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146 views

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 ...
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1answer
71 views

Glass ball drop experiment

Several years ago, I remember reading about an experiment, and I thought it was in Newton's Principia, so the experiment was conducted in that time frame. The experiment involved timing the fall of a ...
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1answer
97 views

Where to get more biographical information about Fritz Peter?

Fritz Peter (1899–1949) is known mainly as one of the authors of the Peter-Weyl theorem. This theorem appears in a paper (Die Vollständigkeit der primitiven Darstellungen einer geschlossenen ...
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113 views

What was the work of Robert Muchielli's, a French psychologist, role in the Rwandan Genocide? [closed]

I read recently in an in-depth book-length study by an investigative journalist on the Rwandan Genocide that the work of the French psychologist, Robert Muchielli, was implicated in organised ...
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165 views

Who axiomatized classical mechanics in 1949?

According to Peter Machamer's "A Brief Historical Introduction to the Philosophy of Science" (The Blackwell Guide to the Philosophy of Science, p. 7) ... classical mechanics was not axiomatized ...
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87 views

Who first proved Fubini's theorem $n$th order integrals?

Who first proved a generalized Fubini theorem for integrals of order $≥3$? An $n$th order integral is $$\underbrace{\underset{x_n}\int\underset{x_{n-1}}\int\ldots\underset{x_1}\int}_{n} f(x_1,x_2,\...
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49 views

Who first distinguished number theory and numerology? [duplicate]

Who first distinguished number theory and numerology?
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78 views

Where does the notion of “three crises of mathematics” come from? [duplicate]

Update: It can be traced back to Fraenkel-Bar-Hillel's Foundations of Set Theory, originally published in 1958. Further discussions can be seen at the linked question. The notion of "three crises ...
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68 views

pre-20th century sources on information theory?

What are some pre-19th or pre-20th century sources on information theory? Do they exist?
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121 views

Reference Request: Comment about Contradictions Proof Method Related to John G. Thompson

I read in a PDF document where the author made a comment that it is “dangerous” to use indirect proof method/contradiction proof method (as far as I can remember, and of course I am paraphrasing) as ...

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