Questions tagged [reference-request]
For questions that are requesting specific literature references
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Whence Whitehead's essence?
In the article Quine’s New Foundations of The Stanford Encyclopedia of Philosophy (Summer 2019 Edition), Thomas Forster writes:
In [1944] Hailperin gave the first of a number of finite ...
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Was "potency set" used for power set?
Cross posted at Math Overflow
For historical reasons, the English term "power set" in set theory is a translation of the German "Potenzmenge", which is still in use in German ...
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Reference request: What were the problems of accepting zero, negative numbers, and complex numbers? And how were they solved?
I asked this question on MSE and comments suggested I should ask it here
I am currently reading Baby Rudin as my second analysis book (after Introduction to Real Analysis by Robert G. Bartle and ...
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Reference request: What were the problems of accepting zero, negative numbers, and complex numbers? And how were they solved? [duplicate]
I didn't know that can happen and since I already asked the question here I don't know what to do with this question should I delete it ?
I am currently reading Baby Rudin as my second analysis book (...
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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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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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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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Question about Leibniz's "characteristic numbers" and propositional logic
The Wikipedia article on Gottfried Wilhelm Leibniz mentions, in the chapter on symbolic thought, that:
Leibniz saw that the uniqueness of prime factorization suggests a central role for prime numbers ...
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What is the earliest use of the $\perp\!\!\!\!\perp$ symbol in statistics to denote statistical independence?
The symbol $\perp\!\!\!\!\perp$ in statistics is a way to denote statistical independence of a collection of random variables. I have seen two forms of it. The first is highly suitable in writing ...
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Attributed quote to Nikola Tesla
In many serious engineering and scientific publications including IEEE publications, we see a quote attributed to Nikola Tesla which goes like this
If you want to find the secrets of the universe, ...
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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.
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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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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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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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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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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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The Original Title of "Euclid's Elements"
What did Euclid originally call his treatise of thirteen books that we now refer to as "Euclid's Elements" ?
Was it "The Elements" ? Was it something else ? Does anyone know the ...
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Scientific articles discovered false and useless several years after their publication
I am looking for examples of important scientific articles that have been discovered to be false and useless several years after their publication. I mean:
they stated something interesting and ...
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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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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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Improvement to the classification and labeling in a list of mathematical references
I'm the maintainer of the Hyper-complex number List,
I am searching for some help in respect of the categorization, clasification regarding the List. I really like references in the line of the List, ...
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Is there any complete works of Abel, Lagrange, Jacobi and Gauss translated into English?
Is there any source which has the complete works of Abel, Lagrange, Jacobi and Gauss which has been translated into English? I'm asking for separate books for these mathematicians not necessarily a ...
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History of visualization in science and math - where may I read of it?
I am looking to inquire into the role of visualization in sciences and math and wish to read about the history of visualization in those fields and also wonder where I might read about the ...
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Reference explaining the history and motivation behind Heyting algebra?
I'm starting to have an interest in Heyting Algebras and their application in topological spaces. Is there any paper/reference which gives a history based exposition of it's ideas?
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Scientific discoveries that were made "late"
I'd like to ask a similar question from Math.SE for the natural sciences (physics, chemistry, biology and allied disciplines).
What are examples of scientific results that were discovered ...
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Provenance of mathematics quote from Robert Musil, 1913
The quote is as follows:
"Nur wenn man nicht auf den Nutzen nach aussen sieht, sondern in der Mathematik selbst auf das Verhältnis der unbenutzten Teile, bemerkt man das andere und eigentliche ...
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What's the name of P C Gilmore?
I have several times come across the name P C Gilmore, and even made use of a publication by her, or him, viz. "The consistency of partial set theory without extensionality", which was ...
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Early results on the Fourier transform
Published tables of Fourier transform pairs have been available for many years. One such example is the paper by George Campbell in the Bell Systems Technical Journal in 1928. Most such tables simply ...
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Where can I find the early proofs for the simplicity of $\text{PSL}(n,q)$?
I am doing a research project on the history of group theory, and want to know about the early developments on the subject. There are plenty of proofs about why the projective special linear group ...
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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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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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Reference request: modern assesement of J.H. Lambert's work on the "fluidity of sand"
While reading about different aspects of Johann Heinrich Lambert's life and work, I found many interesting side remarks about Lambert's work by different authors, though it is very hard to find modern ...
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The history and origin of the Argument Principle ( or Cauchy's argument principle)
I am looking for a book that discusses The history and origin of the Argument Principle ( or Cauchy's argument principle) Thanks!
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In which article/book chapter did Cantor, Hilbert, and Poincaré formally define or directly discusse the term “potential infinity”?
Some media sources say that "Cantor claimed that there would only be potential infinity, not actual infinity"
In addition, the following link claims that Hilbert, Poincaré, and Cantor were ...
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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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Reference Request: History of Chern-Simons Theory
Chern-Simons theory is a topological gauge field theory and play a prominent role in many brnaches of phyiscs and mathematics. On the physical side, it appears for example in three-dimensional ...
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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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Biographical details on Otto Zoll
Zoll's surfaces are a special kind of surfaces generalizing the spheres, in that all of their geodesics are closed and of the same length.
I've tried to gather some biographical details on Otto Zoll ...
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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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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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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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Historical proofs of the series expression for the Bessel function of the first kind
Introduction
The Bessel function of the first kind $J_n(x)$ ($n \in \mathbb{Z},\ x \in \mathbb{R}$) appeared early among other topics, in Celestial Mechanics, in the series expression of the true ...
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Original proof of the Schwarz lemma
The classical Schwarz lemma from one-variable complex analysis states that a holomorphic map $f : \Delta(r) \to \Delta(R)$ between two disks in the complex plane such that $f(0)=0$ satisfies $$|f(z)| \...
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Searching for book about non-Euclidean geometry that recapitulates the First Book of the Elements
I am looking for a specific book on non-Euclidean geometry that I read in my undergraduate years.
The unique characteristic of this book is that the first part of the book started by re-proving in ...
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Source of a Quote by M. Stone on Poincaré and Bourbaki
The quote in question is the following:
For Bourbaki, Poincaré was the devil incarnate. For students of chaos and fractals, Poincaré is of course God on Earth.
The common reference for this quote ...
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What major areas of mathematics have been abandoned?
It seems that the focus of mathematical research moves on every so often, and some areas are not proven wrong, but have just become uninteresting in the current mathematical culture. I was under the ...
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What is the origin of Arabic numerals
I was taught that the numerals {0,1,2,...,9} are from the Arabic alphabet. But they look completely different from today's Arabic letters. I wonder what is the origin of Arabic numerals?
Edit: The web ...
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Fibonacci and straightedge and compass constructions
In "Mathematical Thought from Ancient to Modern Times" Morris Kline claims (on page 209) that Leonardo da Pisa (Fibonacci) "showed that the roots of $x^3+2x^2+10x=20$ are not ...
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When and where was Legendre's Conjecture first published?
When and where did Legendre first publish or write about his conjecture that there is a prime between consecutive square numbers?
$$n^2 < p < (n+1)^2$$
I have looked through edition 1 and 2 of ...
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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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