Questions tagged [reference-request]
For questions that are requesting specific literature references
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Did Srinivasa Ramanujan have a surviving sibling?
Wiki says 'After his death, his brother Tirunarayanan chronicled Ramanujan's remaining handwritten notes consisting of formulae on singular moduli, hypergeometric series and continued fractions and ...
Freeman.
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Historical evidence for claim that we use base 10 because of the number of fingers
It is a common belief that we use a base 10 representation of integers because we have 10 fingers.
Does there exist historical evidence which supports the claim that this is true and that the number ...
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Origin of the smooth but nowhere real analytic function built with dyadic rationals
I found the following interesting function and its analysis at Non-analytic smooth function article in Wikipedia. I include a screen capture below for those who don't wish to navigate away:
I could ...
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Do these trigonometric identities belong to Antonio Cagnoli?
I'm new to this stack community, please bear with me as I try to explain my question properly. Recently I came across with these trigonometric identities (where $ \omega + \phi + \psi = 180^\circ $):
...
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On the creation of analytical geometry
Of all mathematical creations, the one of using graphs to describe planes and 3D space seem to me the most strange ones. My head almost can't admit that space can be represent by three numbers.
If I'...
user7532
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mathematicians attempts at proving Euclid postulate
Is there a list of all the people who attempted to prove the parallel postulate (also known as the fifth postulate or the Euclid axiom) in Euclidean geometry? Wikipedia has a page on the subject but ...
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Who discovered the Virial Theorem?
Who first discovered the Virial Theorem? Who first wrote it down? When? Where?
My guess: a 19th century thermodynamicist
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Looking for Cantor's correspondence
I am trying to collect all available letters written or received by Cantor or written between his colleagues about Cantor. I have searched already the literature given below. But I would like to ...
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The Original Proofs of The Stable Manifold Theorem
The book "Differential Equations and Dynamical Systems" by Lawrence Perko says that the first proofs of the Stable Manifold Theorem are from Hadamard in 1901, Perron in 1928, and Liapunov and Perron. ...
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What is the first instance in which Mendeleev published a long-form table as compared with his 8-column table of 1869?
Mendeleev is famous for having published his first periodic table in 1869. This was a short-form or 8-column table.
He also published a number of 18 column periodic tables. I am asking for ...
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Whether Euclid considered squares to be rectangles
When I look up
'that which is right-angled but not equilateral'
there are translations that show the word before the above phrase to 'oblong', some that show 'rectangle' and some that show both ...
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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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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 ...
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Who influenced Gauss in his abstract approach to mathematics?
I have studied that Gauss was one of the firsts mathematicians to defend this idea, about the Abstract Math and the conception of number, claiming that "What is calculated (in the sense of things ...
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Does an English translation of Bombelli's L'Algebra exist?
I'm looking for an English translation of Rafael Bombelli's L'Algebra. From what I can tell after having searched the usual corners of the web, it doesn't exist, but I'm asking here just in case.
I'...
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Where can I find the list of problems from the (Chinese) "Nine Chapters on Mathematical Art"?
For the sake of curiosity, I'm interested in the "list of problems" that were laid out in the ancient Chinese text on Math. However, I haven't found a "list" in English anywhere. Only a few excerpts ...
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Why is the angular momentum written as JJ in quantum mechanics?
Why is $\textbf{J}$ called angular momentum operator? Can anyone explain why the expectation value of J is angular momentum?
Here is how $J$ is defined: The rotation operator
$$
U(\alpha)=\exp(-i {\...
user6964
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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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Laplace's characterization of Gauss as "a super-terrestrial spirit in a human body"
The following words concerning Carl Friedrich Gauss are attributed to Laplace in an article from the Mathematics magazine by Teets and Whitehead (The discovery of Ceres: how Gauss became famous, first ...
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Who posed the separable quotient problem (and when)?
The (infinte dimensional) separable quotient problem asks whether every infinite dimensional Banach space has a separable infinite dimensional quotient. In the literature I have seen that is problem ...
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When was $e$ first observed to not be a Liouville number?
When and by who was it first observed that the transcendental number $e$ is NOT a Liouville number?
This fact is stated in a lot of web pages, and a proof can be found in the Mathematics Stack ...
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History of Braids
I am looking for papers or books that describe the history of the development of braid theory, mainly during the 19th and the 20th century. I know Moritz Epple book on the history of the theory of ...
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Books that we can know when which theorem was discovered by whom
There are many textbooks which states mathematical theorems, but in them, by whom and when the theorems are discovered is not explained.
Do you know good references for this?
If this scope is too ...
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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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What are Philolaos' “even-odd” numbers?
Number, indeed, has two proper kinds (ιδια ειδη), odd and even, and a
third mixed together from both, the even-odd(αρτιοπέριττον). Of each
of the two kinds there are many shapes, of which each ...
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History of PDE's in the 19th Century
I've been asked to write an essay on whether the work on PDE's in the 19th century belonged to applied or pure mathematics. Does anyone know of any useful sources I could use?
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English translation of Heisenberg's papers
Strangely, many of Heisenberg's very important scientific papers are not translated into English.
For example, this one seems not to have been translated.
Where can I get the translated ones?
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Invariance principle for stability in the sense of Lyapunov
On Wikipedia this article about the invariance principle and article states that
The general result was independently discovered by J.P. LaSalle (then
at RIAS) and N.N. Krasovskii, who published ...
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Examples of abstract proofs that turned out to be false
I found this question that discusses abstract theories that later found application. I am interested in accepted (at least at one point in time) abstract theories that:
was contradicted by attempts ...
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First use of the term/name "curved exponential family"?
Question: What was the first recorded use of someone calling exponential families (in probability/statistics) for which the dimension of the natural parameter space is strictly less than the dimension ...
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Has Alphonse Pyramus de Candolle's "Géographie botanique raisonné" ever been translated into German or English?
Alphones Pyramus de Candolle (1806-1893), the son of Augustin-Pyrame de Candolle (1778-1841), has been an important figure (as was his father) in the development of plant geography.
The younger ...
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History of the arithmetic mean
The arithmetic mean of a set of points $\{x_1, x_2, ..., x_n\}$ is defined by
$$\frac{1}{n}\sum_{i=1}^n x_i.$$
It is remarkable for its ubiquitous use and universal understanding. It represents a ...
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Etymology of 'qubit'; is there any relation to cubits?
Whilst several not-very-authoritative sources e.g. Wikipedia state that the word qubit was derived, partially, as a play on the word cubit (obviously it also stands for 'quantum bit'), is there any ...
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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 ...
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History of the origins and development of problems of finding maximum and minimum values of quantities
I am aware that perhaps the earliest source concerning problems of maximum and minimum values occurs in Euclid's Elements. After Euclid, Archimedes of Syracuse and Apollonius of Perga seem to consider ...
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Is there any evidence supporting this claim about Cassini and his ovals?
The Wikipedia article for Cassini ovals claims in the introduction that "Cassini believed that the Sun traveled around the Earth on one of these ovals, with the Earth at one focus of the oval." This ...
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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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On a paper by Georg Pick
Has any of you ever read the paper in which Georg Pick made public his famous formula? If so, would you be so kind as to tell me what it is that one can find in the introduction of it?
The complete ...
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Riemann surfaces and covering
Assuming we have a Riemann surface $S$ of degree $n$ and we look at it as a covering of the projective line $\mathbb{P}^1$. If $B$ is the set of branch points of $S$ (when $B$ is a subset in $\mathbb{...
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Where did Galileo say "All truths are easy to understand once they are discovered. The point is to discover them."?
I've heard it claimed Galileo said or wrote:
All truths are easy to understand once they are discovered. The point is to discover them.
Where did he say this?
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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 ...
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Biographies on 20th Century physicists
I've recently finished reading Helge Kragh's Quantum Generations and am looking forward to something to read next. I am hoping to find biographies or more information about certain physicists such as ...
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What are some good (and reasonably academic) books on 18th and 19th century British mathematics?
In addition to the general topical interest indicated in the title, I am also curious about British mathematics of the period viewed through the lens of competition with the rest of Europe (and ...
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Carnap's last theory Of probability
According to Bar-Hillel, Carnap's coauthor in a 1952 report on probability, Carnap had, as of 1956 an unpublished but circulated theory distinguishing "random" refers to methods of production of ...
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Raymond Cattell and History of Personality Traits Prior 1947
I find that papers reference Raymond Cattell suggesting 16 or 22, etc, traits, by factor analysis (basically regression), including all five of the modern reproducible traits (openness to experience, ...
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Verification of Navier's theory of structures
Jacques Heyman in his article Truesdell and the History of the Theory of Structures, mentions the following:
The first full-scale tests on building frames were made in the 1920s
in London, and ...
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Looking for specific book about renaissance physics
I read a book a while ago about the history of physics in the renaissance, which treated it as an alternation between physical-causal descriptions (eg. inertia obtains because air molecules are pushed ...
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Works of mathematician François Viète
I'm searching for a book or an online copy of complete works of the mathematician François Viète, preferably in English.
Any help will be appreciated.
Thanks.
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reference need about History of prime number development
Im trying to connect my study to a breif history of prime numbers . Also im interesting in reading history of numbers how they come and how they developed .
So can any one suggest for this question a ...
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Reference for "Auszug aus einem Briefe von L. Kronecker an R. Dedekind"
While I was looking for a source about Kronecker's Jugendtraum, I found this document: Auszug aus einem Briefe von L. Kronecker an R. Dedekind vom 15. März 1880.
The bottom of the given page has a ...
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