Questions tagged [reference-request]
For questions that are requesting specific literature references
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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 the ...
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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 \triangleq ...
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How did Eratosthenes know the Sun was very far away?
Eratosthenes calculated the radius of the Earth from the difference of the lengths of shadows between Aswan and Alexandria were different (see also here). But this could also happen if the Earth were ...
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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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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 & ...
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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 ...
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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 ...
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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)...
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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 (...
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How did Romans do multiplications?
The Romans did not have Indian numerals. Worse still, they did not have the decimal system. Yet, they produced amazing works of engineering and architecture. How was that possible? It's troublesome ...
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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 ...
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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 ...
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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 ...
user4962
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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 ...
user459
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Who was the first to say "Shut up and calculate!"?
The best thing I could find on the internet was this apparently forgotten article from 12 years ago.
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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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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 ...
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Did Einstein say "We cannot solve our problems with the same thinking we used to create them"?
According to various sources on the Web, Albert Einstein is likely to have said or written one of the following:
Probleme kann man niemals mit derselben Denkweise lösen, durch die sie entstanden ...
user7921
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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 ...
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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 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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What was the scientific explanation of earthquakes in the 18th century?
I'd like to know what western scientists thought about the causes of earthquakes in the mid to late 18th century (especially pertaining to the one in Lisbon in 1755). I've read that the ancient Greeks ...
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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, ...
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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 ...
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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 ...
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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. ...
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Did Newton say: "If I have ever made any valuable discoveries, it has been due more to patient attention, than to any other talent"?
I came across the above quote, and found it quite interesting. However, I struggled to find an actual source. Did Newton truly say this?
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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 ...
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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 ...
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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 ...
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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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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-...
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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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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 ...
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Why do we call a linear mapping "linear mapping"?
According to P. M. Cohn's Classic Algebra, for historical reasons we call a linear mapping "linear mapping". What are the historical reasons that led to the adoption of the term "linear ...
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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 ...
user2831
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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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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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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 ...
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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 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 ...
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What research articles were inspired by web comics?
Currently, I'm doing a PhD on the applications of algorithms to generate timelines of textual content. Recently, I found an article entitled StoryFlow: Tracking the Evolution of Stories by S. Liu et ...
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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....
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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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