Questions tagged [reference-request]
For questions that are requesting specific literature references
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questions with no upvoted or accepted answers
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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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Books on elliptic functions
In the end of his address to Annual Meeting of the Mathematical Association in 1933 titled "The marquis and the land agent: a tale of the 18th century", the Association president G. N. ...
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History of group actions as their own structures
I'm interested in when (and how) the modern idea of a group action developed and how group actions became their own algebraic structures.
As far as I can tell in the 19th century group actions were ...
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Chronology of proofs of cubic and biquadratic reciprocity laws
I just want to check if anybody knows a website where one can find a chronology of proofs of more difficult reciprocity theorems (such as the cubic and biquadratic cases) similar to the (already ...
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Early illustrations of topological notions in published work
Since I've not gotten any answers after a bit more than a week, I've now cross-posted to MathOverFlow.
EDIT 2023-08-15: Several commenters here and at MO have asked me to sharpen the original question....
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Does "Metatron's cube" have a history and a serious name in geometry?
This is a figure that I saw while going down the rabbit hole of "Sacred Geometry" back when conspiracy theories and related nonsense were relatively harmless and fun to laugh at. A book ...
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What's the origin of the claim that a single uranium atom fissioning would release enough energy to visibly move a grain of sand?
There's a fairly widespread claim that the energy released by the fission of a single atom of uranium would release enough energy to make a grain of sand visibly jump. Richard Rhodes's The Making of ...
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Where can I read Cauchy's terrible poems?
I hope that the slightly abrasive title is forgivable, as the judgement on this poetry is not mine, but Hans Freudenthal's. Here is the background: in the Dictionary of Scientific Biography, there is ...
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Is there any historical evidence of this quote E.T. Bell attributed to C.G.J. Jacobi?
I read Men of Mathematics by E.T. Bell long ago, and this quote he attributed to Jacobi stuck with me:
Certainly I have sometimes endangered my health from overwork, but what of it? Only cabbages ...
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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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Reflections in the 18th century
It is well known that the theory of reflections was considerably developed during the 19th century with the development of group theory (e.g. Klein) and the theory of transformations. However, I'm ...
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Finding the Letter from Freeman Dyson to Gerald Gabrielse in 2006
In 2006, the renowned physicist Freeman Dyson wrote a letter to his colleague Gerald Gabrielse regarding an advance in precision about measuring the magnetic moment of an electron. An excerpt of his ...
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In which work was Boltzmann's entropy originally introduced?
I get an impression from this enyclopedia entry
that the primary source of the Boltzmann entropy equation $S = k \log W$ might be
1866, Über die Mechanische Bedeutung des Zweiten Hauptsatzes der ...
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Origin of the "teakettle principle" joke?
There's a fairly widely known joke about boiling water (one version is below) that pokes fun at how mathematicians like to reduce new problems to known solutions. I've traced it back to a footnote on ...
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Earliest measurement of proton's mass
I was looking for the earliest experiment or the paper which shows the determination of the mass of proton. In NIST CODATA, the mass of proton is listed as "1.672 621 923 69 x 10$^{-27 }$kg"....
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Who bet against the usefulness of matrix inversion – or is it a myth?
In my linear-algebra and numerics courses, I frequently heard an anecdote about some professor betting – literally, with money – that there would never be any application where computing the actual ...
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von Neumann vignette on early computer usage
I'm looking for a vignette about von Neumann. My recollection is as follows but my google-fu is not bringing up anything.
von Neumann, having prodigious mathematical capacity even of the most mundane ...
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In which work was Gibbs' Inequality introduced?
Gibbs' inequality
$$-\sum\limits_{i=1}^n p_{i} \cdot \log{p_{i}} \le -\sum\limits_{i=1}^n p_{i} \cdot \log{q_{i}}$$
is such a popular thing that I cannot find where it was introduced.
My findings
I ...
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Reference Request: Comment about Contradictions Proof Method Related to John G. Thompson
I read in a PDF document where the author made a comment that it is “dangerous” to use indirect proof method/contradiction proof method (as far as I can remember, and of course I am paraphrasing) as ...
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Earliest drawings of the plots of trigonometric functions
[Even though this question may seem as a duplicate of this question about the History of sine function, I'd like to ask it again - with a more specific title and a more specific focus (on specific ...
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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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What came first: pythagoras number or pythagorean fields?
Which concept was first introduced: the pythagoras number of a field or pythagorean fields? I have not found anything on this matter, but my gut feeling says the latter. One can more directly link the ...
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Is there a comprehensive list of Ancient Greek mathematical writings?
Much of the Ancient Greek's mathematical philosophy texts have survived from antiquity and passed to modern times. Also, texts previously thought to be lost are being occasionally rediscovered (...
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Did the Romans really use the binomial formula to calculate products?
I'm not quite sure if this is the right place to ask this question (in fact, I was redirected to this SE from the Math Stackexchange), but it's probably more fitting than the original posting place.
I ...
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References on the role of diagrams in scientific advancement
A number of diagrammatic formulations have played an important role in the advancement of science. Some embody representations of physical phenomena, while others model mathematical or logical ideas ...
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Who came up with the proof of "Bézout's identity" that uses the well-ordering principle?
Let $a$ and $b$ be two integers not both of which are equal to zero. It is an important and well-known fact that $\text{gcd}(a,b)=ax_{0}+by_{0}$ for some integers $x_{0}$ and $y_{0}$. Even though this ...
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Can not find reference for "uniform convexity implies existence of unique conjugate" mentioned by Pettis
In A proof that every uniformly convex space is reflexive in footnote 3 (available at that link without a paywall), author Billy Pettis mentions that the first half of Lemma 1 in that paper "was ...
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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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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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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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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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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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Literature on Mayan mathematics
I asked this question on math.se and they sent me here.
It is well known that Mayan people used vigesimal (base 20) numeral system, and had had an advanced calendar system.
Except for these facts, I'...
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Who first proved Fubini's theorem $n$th order integrals?
Who first proved a generalized Fubini theorem for integrals of order $≥3$?
An $n$th order integral is $$\underbrace{\underset{x_n}\int\underset{x_{n-1}}\int\ldots\underset{x_1}\int}_{n} f(x_1,x_2,\...
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Pre-20th century sources on information theory?
What are some pre-19th or pre-20th century sources on information theory? Do they exist?
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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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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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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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Where did the divide and conquer method for radix conversion come from?
While doing the tedious work of documenting my software I tried to find the original source of the divide and conquer method for the conversion of numbers of one base to a number in another base (...
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Are Brillouin's papers translated into English?
I mean the Brillouin in the WKB method. I want to read his original paper. But it is in French. Is it translated into English? It should be.
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Who was the first pointing out the $U(1)$-gauge theories common structure?
It is well-known that in each $U(1)$-gauge theory one can define, in analogy with electromagnetism, a 1-form connection and an associated 2-form of curvature on an appropriate (principal) bundle, ...
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Who evaluated the surface of the Torricelli solid/Gabriel's horn
The Torricelli solid/Gabriel's Horn is defined as the rotation-invariant solid delimited by a hyperbola. It appears in De solido hyperbolico acuto where Torricelli proves that it has a finite volume, ...
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History behind Serre's conditions $\mathrm{S}_k$ and $\mathrm{R}_k$ for a commutative Noetherian ring
In 033Q we find defined what some sources call “Serre's conditions $\mathrm{S}_k$ and $\mathrm{R}_k$” (if you don't know what a scheme is, you can read the definition for a commutative Noetherian ring ...
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Zermelo's or Fraenkel's early consideration of something equivalent to countable Replacement
I have now claimed a few times on the internet, based on something (sensible!) I read, that at some point in the 1920s, that Zermelo at one point considered as a set theoretic axiom (schema) something ...
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First use of corner quotes for Gödel numbers
Who first used the corner quotes, ⌜ and ⌝, or $\texttt{\Godelnum}$ with Sam Buss's macro, for the notion of Gödel number?
Quine introduced corner quotes, but did not use them for the notion of Gödel ...
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Questions related to the theorem von Neumann proved in five minutes
I have recently seen this post about the theorem von Neumann proved in five minutes.
Searching for more information about that, it is certain that I can't find any references for what the theorem was.
...
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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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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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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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Earliest Known reference to a female scientist?
According to an uncited Wikipedia paragraph, Merit-Ptah is the earliest known female scientist.
An ancient Egyptian, Merit-Ptah (c. 2700 BC), described in an inscription as "chief physician", is ...
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