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Questions tagged [reference-request]

For questions that are requesting specific literature references

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37
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2answers
2k views

Timeline of measurements of the electron's charge

Where can I find a paper or reference that describes the timeline of measurements of the magnitude of the electron's electric charge. For context, Millikan's oil drop experiment in 1908 determined ...
17
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4answers
922 views

Books on the history of linear algebra

I'm quite desperate to understand the historical motivation and origin of all of the "geometrical" concepts of linear algebra, namely: The concept of thinking of elements of $\mathbb R^n$ or some ...
17
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1answer
2k views

Why did Rene Descartes go to Sweden?

The year before he died, mathematician Rene Descartes accepted an invitation to tutor the brilliant 19-year old Queen Christina of Sweden (some thirty years younger). He apparently died from the ...
16
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3answers
1k views

Source for Hilbert's famous quote “Mathematics in Göttingen? There really is none anymore”

Reportedly this was uttered at a banquet in which Hilbert was seated next to the new Minister of Education, Bernhard Rust, in response to Rust inquiring as to the state of mathematics in Göttingen now ...
12
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1answer
343 views

History of a result from Bézout

BÉZOUT'S THEOREM: Let $F$ and $G$ be projective plane curves of degree $m$ and $n$ respectively. Assume $F$ and $G$ have no common component. Then $\displaystyle\sum_{P}I(P,F\cap G)=mn$ $I(P,F\cap G)...
12
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1answer
461 views

Early history of the phase concept in the physical sciences

One of the first distinctions encountered in science education is that substances can assume different states of matter: for example, water can be found as a liquid, as a solid (ice), or as a gas (...
11
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4answers
675 views

What major areas of mathematics have been abandoned?

It seems that the focus of mathematical research moves on every so often, and some areas are not proven wrong, but have just become uninteresting in the current mathematical culture. I was under the ...
11
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3answers
291 views

Historically accurate alternatives to “Men of Mathematics”?

I have heard that the book "Men of Mathematics" by E. Bell is a very entertaining text composed of several biographies of a number of influential mathematicians, and is in fact one of the most popular ...
11
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1answer
2k views

Does anyone know about Ramanujan's method of solving the quartic?

I have read (probably) in Kanigel's book The Man Who Knew Infinity that S. Ramanujan devised his own method of solving the Quartic Equation after he learnt to solve the Cubic Equation. Does anyone ...
11
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0answers
18k views

Who first defined the “equal-delta” or “delta over equal” ($\triangleq$) symbol?

The symbol $\triangleq$ is sometimes used in mathematics (and physics) for a definition. It is instantiated for instance in the Unicode Character 'DELTA EQUAL TO' (U+225C). The notation $t \...
10
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3answers
468 views

What resources are available for lives of recent mathematicians besides E.T. Bell's Men of Mathematics?

I am about halfway through reading E.T. Bell's Men of Mathematics, and I absolutely love it. I'm a mathematician, and I enjoy learning about the lives behind the names that I know and use so often. (I ...
10
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2answers
535 views

What is the original source for Abel's quote about Gauss:“He is like the fox, who effaces his tracks in the sand with his tail”?

According to the editor of the German version of Ian Stewart's "The Problems of Mathematics", on page 226 of the biography of Gauß authored by Erich Worbs (C. F. Gauß: Ein Lebensbild. Koehler & ...
10
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3answers
332 views

Are Leibnizian infinitesimals thought to be logical fictions by Leibniz scholars?

Japanese scholar Hide Ishiguro published a book in 1990 entitled "Leibniz's philosophy of logic and language" (second edition). Of particular interest, as far as the history of mathematics is ...
10
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1answer
266 views

Was the phlogiston theory ahead of its time?

I've always "known" that the phlogiston theory was naive and unsupported by the facts, which is why it was toppled pretty much instantaneously by Lavoisier's discovery of the role of oxygen. However, ...
10
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1answer
254 views

How were Millennium Problems chosen? (according to what criteria)

I am making a presentation about Millennium Problems. There are 7 Millennium Problems but a lot of unsolved mathematics problems are also waiting to be solved. I know that these problems are much more ...
10
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2answers
234 views

Request for good resources on 'history of infinity' topics

I'm writing/starting with my bachelor thesis, the subject is about "infinity": what it is, why do we accept it, etc., but most of all my goal is to give an overview of the history of the ...
9
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1answer
139 views

What theorem of Sophus Lie on the number of geometries is H. Poincaré referring to?

In this quotation from Henri Poincaré's essay "Non-Euclidean Geometry" published in Nature in 1892 (No. 1165, Vol 45, p. 406), he refers to a theorem of Sophus Lie. Does anyone know a source for this ...
9
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1answer
1k views

How did Young perform his double slit experiment?

Thomas Young is famous for his double slit experiment, but I can't seem to find his experimental setup (such as how is prepared the light before it went through the apparatus. Does anyone know his ...
9
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1answer
343 views

Does anyone know the physics student who passed a quantum mechanics oral exam without taking quantum mechanics?

Many years ago I read an interview with a physics professor, where he recounted a funny situation when he was a graduate student at Harvard. When a first year, he was supposed to take the quantum ...
8
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1answer
576 views

Did Gauss say “there have been but three epoch-making mathematicians, Archimedes, Newton and Eisenstein”?

In Wikipedia I found this claim by E.T. Bell in his Men of Mathematics. However in the next paragraph it says that "it is doubtful that Gauss put Eisenstein in the same league as Newton", which makes ...
8
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1answer
630 views

Where did Rayleigh derive the ultraviolet catastrophe?

Where can I find this paper: J.W. Strutt, Verh. d. deutsch. phys. Ges. 2, 65 (1900). It is presumably where Rayleigh derived the black-body radiation formula (the incorrect one that has ultraviolet ...
8
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1answer
728 views

How was curvature originally defined and calculated?

I am interested in the early history of curvature. Who defined it first and when, who came up with the name, how was it calculated before mathematicians used calculus to define $k=|α''(s)|$? Are there ...
8
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2answers
272 views

Did Bruns establish that the 3 body problem has no non-trivial conservation laws?

I'm reading Colin Pask's book Magnificent Principia and in 16.7.2 he states that the difficulty of the 3 body problem is in part tied to the lack of additional conservation laws at our disposal. In ...
8
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1answer
195 views

What are some of the most complete genealogies of scientific and mathematical subject areas?

I am interested in the way scientific and mathematical subject areas developed (and are still developing). One of the great visual tools that can help us gain insight in how these areas developed is ...
8
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3answers
259 views

Are there any canonical books on history of science?

I was looking for some fundamental books on history of science. I picked Thomas Kuhn book "The Structure of Scientific Revolutions" but it's not exactly about history of science - it's more on ...
7
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2answers
249 views

What did Fermat do as a lawyer?

Fermat is easily one of the best known mathematicians of all time. We all know about Fermat's Last Theorem, Fermat's Little Theorem, his quadrature rule, his invention of probability theory, etc. ...
7
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2answers
140 views

What manuscript is depicted in the HSM advertisement?

The following advertisement recently appeared in the sidebar on math.se: Is the Greek script on the left actually from a mathematical manuscript? What is its source?
7
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4answers
563 views

Is there a biography of Ramanujan for mathematicians?

Like many mathematicians, I have long been fascinated by Ramanujan's work and also by what little I know of his life. I would like to learn more, but have found the standard book on this subject (...
7
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2answers
224 views

Where I can find the translated manuscript of Abel?

I am looking for the translated manuscript of Abel where he proved the unsolvability of the quintic. Can anyone give me a pointer? I tried google but nothing came up.
7
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2answers
168 views

Reference Request: Did Descartes leave solving the quintic as an exercise to his readers?

In this document by Jim Brown it is claimed (on Section 3, pg 5) that: [Descartes] believed that all polynomials of degree $>4$ could be solved with the same methods as had been applied to the ...
7
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2answers
3k views

The history and motivation of eigenvectors

I want to understand more about the history of eigenvectors. Was the discovery of eigenvectors inspired from an application to achieve a result in a historical context, was there a phenomenon which ...
7
votes
1answer
196 views

Did Cambridge change their BSc policy for Ramanujan?

I found this quote at Quora: In March 1916 Ramanujan graduated from Cambridge with a Bachelor of Science by Research (This degree was later renamed as Ph.D. from 1920) for his work on Highly ...
7
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1answer
268 views

How were variables used and understood in (particularly) 19th century maths?

Context: I have been thinking about Frege's Begriffsschrift, where he introduces a version of what we now think of as the standard quantifier/variable notation. Philosophers who write on Frege tend to ...
7
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1answer
212 views

History of Coagulation of Milk by Short Waves

In 1968 NASA, through the assistance of the Israel Program for Scientific Translation, translated from Russian the 1964 book "The Earth in the Universe", with chapters written by top Soviet scientists....
7
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0answers
244 views

Did Kronecker say that set theory is not mathematics?

I have frequently come across Kronecker's statement about set theory: "I don't know what predominates in Cantor's theory - philosophy or theology, but I am sure that there is no mathematics there." It ...
6
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4answers
1k views

Who was the first to say “Shut up and calculate!”?

The best thing I could find on the internet was this apparently forgotten aricle from 12 years ago.
6
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3answers
301 views

Who was L. Aubry?

In his magnificent book Number Theory: An approach through history, from Hammurapi to Legendre, André Weil quotes the article Solution de quelques questions d'analyse indéterminée, by L. Aubry (Sphinx-...
6
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3answers
391 views

Why do we call a linear mapping “linear mapping”?

According with the book Classic Algebra by P.M.Cohn for historical reasons we call a linear mapping "linear mapping". What are the historical reasons that created the term "linear mapping"?
6
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1answer
206 views

When and how did the notion/idea of physical constant emerge?

Physical constants (e.g. c, h, G, alpha and so on) play a central role in our scientific theories and they have yet drawn much of controversial flavor into questions concerning the foundational status ...
6
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1answer
99 views

Euler's Derivation of Euler's Method for ODEs

I am looking for an English translation of Euler's derivation of Euler's method for ODEs, namely the update $$ y_{n+1} = y_n + h f(y_n, t_n) $$ What motivated Euler to consider this problem, and how ...
6
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1answer
400 views

Euler's works after blindness

There are many sources which say that Euler produced, on average, one mathematical paper every week in the year $1775$. Some even say he produced almost half his total works despite the total ...
6
votes
1answer
452 views

Why does Aristotle write 'astrology' when Plato writes 'astronomy'?

Checking modern quotes from Aristotle almost everywhere the word astronomy is found to be replacing the original Greek or Latin astrology' (astrologia). In Plato'...
6
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7answers
271 views

Pop-sci books that were publicly influential but based on weak science

(I hope this is on-topic on this site) I am wondering what are some of the best examples of popular-science books that had large influence in public, but was based on weak science? By "large ...
6
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1answer
102 views

What are the earliest known accounts of the demarcation problem (science versus pseudo science)?

The demarcation problem, i.e. the problem of differentiating science from pseudo science has been on my mind recently. This might be considered a philosophy topic for philoSE but since my question has ...
6
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0answers
212 views

Who gave you infinitesimal epsilon?

As someone reputed among certain historians to have given you the epsilon Cauchy startled me by using $\varepsilon$ to denote an infinitely small number in his 1826 text on differential geometry; see ...
5
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2answers
252 views

Is Spivak right in what he says about Galileo?

On chapter 9 of M. Spivak's book on calculus there is an exercise in which Spivak asks the reader to prove that Galileo "got his facts wrong". More specifically, Spivak asks one to to show if a body ...
5
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1answer
114 views

Origins and history of branched covering

During my research on branched coverings of the projective plane, I am interested to know the origins and history of branched coverings of the projective plane and the projective line, together with ...
5
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1answer
86 views

Source for Felix Klein quote about curves

Hubbard and Hubbard (in "Vector Calculus...") attribute the following quote to Felix Klein: "Everyone knows what a curve is, until he has studied enough mathematics to become confused through the ...
5
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2answers
628 views

How was the focus/directrix property of conic sections discovered?

I've always thought that defining conic sections by a locus of points w.r.t the ratio of the distance to the focus and directrix was always "too artificial" - how does one actually discover this ...
5
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1answer
242 views

Where can I find the original presentation of the proof, due to Grothendieck, of the $\bar\partial$-Poincaré lemma?

In complex geometry, there is the a lemma, analogous to the Poincaré lemma in (real) differential geometry, which states that a $(p,q)$-form that is $\bar\partial$-closed is locally $\bar\partial$-...