Questions tagged [reference-request]

For questions that are requesting specific literature references

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48
votes
2answers
5k 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 the ...
28
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1answer
37k 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 \triangleq ...
24
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2answers
569 views

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 (...
19
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4answers
2k 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 ...
19
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1answer
3k 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 ...
18
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3answers
2k 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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4answers
1k 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 ...
12
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3answers
665 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 ...
12
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1answer
405 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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2answers
1k 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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2answers
957 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 & ...
11
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1answer
2k 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 ...
11
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3answers
423 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
388 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 ...
11
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1answer
3k 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 ...
10
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2answers
4k 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 ...
10
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1answer
1k 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 ...
10
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2answers
211 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 ...
10
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1answer
183 views

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 ...
10
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3answers
351 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
347 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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2answers
263 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 ...
10
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0answers
313 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 ...
9
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2answers
473 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. ...
9
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2answers
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. ...
9
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2answers
254 views

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 ...
9
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2answers
644 views

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 ...
9
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1answer
247 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
863 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 ...
9
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3answers
396 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 ...
9
votes
1answer
575 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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4answers
5k 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.
8
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3answers
741 views

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 ...
8
votes
1answer
199 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 ...
8
votes
2answers
222 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 ...
8
votes
1answer
952 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
votes
3answers
268 views

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 ...
8
votes
2answers
366 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
votes
2answers
363 views

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 ...
8
votes
1answer
268 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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1answer
235 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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2answers
168 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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2answers
382 views

Where can I 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
votes
4answers
633 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
votes
1answer
234 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 ...
7
votes
1answer
258 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 ...
7
votes
1answer
526 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
votes
1answer
453 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 $\bar\partial$-...
7
votes
1answer
682 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 ...
7
votes
1answer
331 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 ...

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