Questions tagged [reference-request]

For questions that are requesting specific literature references

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Einstein and relativity [closed]

What are the best books to learn Einstein's theory of relativity (general and special)? If I understand correctly, Einstein himself wrote once some essays about relativity... Does one obtain a general ...
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48 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 ...
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65 views

Einstein and geometry [duplicate]

Are there any serious biographies of A. Einstein that mention or support the popular accounts of Einstein's early interest in euclidean geometry and the Pythagorean theorem? Would you be so kind as to ...
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1answer
105 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 ...
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2answers
166 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 ...
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306 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 ...
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1answer
146 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 ...
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55 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 ...
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68 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 ...
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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-...
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1answer
147 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 ...
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95 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 ...
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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. ...
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60 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 ...
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37 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 ...
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64 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 ...
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40 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 ...
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82 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 ...
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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 ...
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131 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 ...
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3answers
94 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 ...
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1answer
44 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 ...
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1answer
158 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 ...
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31 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 ...
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35 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 ...
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72 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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90 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&...
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167 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 ...
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55 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 ...
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1answer
120 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
79 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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1answer
191 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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1answer
187 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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94 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 ...
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1answer
185 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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116 views

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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101 views

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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1answer
57 views

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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1answer
115 views

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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1answer
124 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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1answer
70 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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1answer
83 views

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
82 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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515 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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1answer
444 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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1answer
108 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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1answer
323 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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1answer
79 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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50 views

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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