Questions tagged [ho.history-overview]
History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.
1,125
questions
4
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1answer
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history of geometric mechanics
I was thinking about the foundations of geometric mechanics and its precursors.
I wondered who was the first to realized the equivalence between Riemannian geometry and Lagrangian mechanics. In ...
4
votes
1answer
116 views
Is this elementary formula for the parabolic segment new?
Recently (May 2020) a formula for the area of the parabolic segment (i.e. the region enclosed by a parabola and a line), in terms of the coefficients of the Cartesian equations, has been published by ...
19
votes
1answer
571 views
Digitalized version of “Cours de topologie algébrique professé en captivité”
It is historically known that Jean Leray gave a course on algebraic topology while captive in the Officer's detention camp XVI in Edelbach, Austria during WW2. (References to this topic ...
28
votes
3answers
4k views
Why is this “the first elliptic curve in nature”?
The LMFDB describes the elliptic curve 11a3 (or 11.a3) as "The first elliptic curve in nature". It has minimal Weierstraß equation
$$
y^2 + y = x^3 - x^2.
$$
My guess is that there is some problem ...
6
votes
2answers
316 views
Unknown work of Nöbeling on topological/Hausdorff dimension
Let $\mathcal{H}^n$ denote the Hausdorff measure, $\dim_H X$ the Hausdorff dimension, and $\dim X$ the topological dimension of $X$.
A well known result of
Szpilrajn (He changed his name to ...
11
votes
0answers
149 views
Galois group of polynomials related to Fibonacci and Catalan numbers
Let $F_n$ be the Fibonacci and $C_n$ the Catalan numbers.
Define a polynomial by $F_n(x):=\sum\limits_{k=1}^{n}{F_k x^{n-k}}$.
For example $F_8(x)=x^7+x^6+2x^5+3x^4+5x^3+8x^2+13x+21$.
And another ...
6
votes
1answer
402 views
Origin of the term 'index of a subgroup'
The index of a subgroup $H$ in a group $G$ is the number of distinct cosets of $H$ in $G$.
Why did someone decide to call this an 'index'? What's the rationale for this?
31
votes
0answers
3k views
The origin(s) of the word “elliptic” [migrated]
The word elliptic appears quite often in mathematics; I will list a few occurrences below. For some of these, it is clear to me how they are related; for instance, elliptic functions (named after ...
18
votes
1answer
594 views
Why 'excedances' of permutations? [closed]
For a permutation $\pi=\pi_1\pi_2\cdots\pi_n$ written in one-line notation, an index $i$ for which $\pi_i > i$ is usually called an 'excedance.' To me, this seems like a mispelling of what should ...
6
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0answers
134 views
Two questions on history of symplectic geometry in the 80's
I have a question about the history of two important results from the eighties in symplectic geometry. In both cases it seems that important results were developed (almost) simultaneously by ...
2
votes
0answers
112 views
Why is faithful actions called faithful and who first called it faithful?
Sorry for this question. I asked this on MSE and hsm but no one answered and I decided to post it here that is full of experts.
I want to know why is faithful actions called faithful and who first ...
3
votes
0answers
91 views
Pyramids whose volume can be computed by simple cutting and glueing
Since this question remained without answers even after a bounty, I thought it might be time to ask it here.
For which pyramid can you compute the volume from simple cut-and-glue processes? The Dehn ...
14
votes
1answer
506 views
History of the notion of irreducible representation
I am looking for the earliest references where the study of irreducible representations appears. There has been many articles and books on the history of representation theory. A fundamental feature ...
6
votes
1answer
220 views
Why are orthogonal matrices so often denoted $Q$?
I apologize for the stupid question in the title. Of course, we can baptize a particular given matrix as we want but, for example, the QR-decomposition has a fixed meaning.
My humble guess is that ...
25
votes
3answers
1k views
What aspects of math olympiads do you find still useful in your math research?
I was rereading the book Littlewood's Miscellany and this passage struck me:
It used to be said that the discipline in 'manipulative skill' bore
later fruit in original work. I should deny this ...
28
votes
2answers
2k views
Who introduced direct limits?
The general notion of a direct limit of a commuting system of embeddings, indexed by pairs in a directed set, has seen heavy use in set theory. It is the same notion as in category theory. I was ...
4
votes
2answers
136 views
Function of moderate growth: history, motivation, and uses
I recently came across functions of moderate growth via this post and I was wondering, what are some concrete uses or applications of this space? Where does it appear and why was it introduced ...
54
votes
4answers
5k views
Bourbaki's definition of the number 1
According to a polemical article by Adrian Mathias, Robert Solovay showed that Bourbaki's definition of the number 1, written out using the formalism in the 1970 edition of Théorie des Ensembles, ...
13
votes
1answer
350 views
History of well founded relations
I have changed the title in the hope of attracting the attention of someone who knows about the history of set theory as well as intuitionistic logic:
Who was the first to state the definition of ...
203
votes
34answers
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Conway's lesser-known results
John Horton Conway is known for many achievements:
Life, the three sporadic groups in the "Conway constellation," surreal numbers, his "Look-and-Say" sequence analysis, the Conway-Schneeberger $15$-...
4
votes
2answers
380 views
Earliest use of deconvolution by Fourier transforms
From a previous discussion here Origin of the convolution theorem, it was shown that the property of convolution $y(t)$=$a$*$b$ becoming a multiplication after Fourier transform: $F$$(y(t))$= $F(a)F(b)...
6
votes
2answers
599 views
How did Hilbert prove the Nullstellensatz?
All of the many proofs of the Nullstellensatz I have seen use results from long after Hilbert’s time: Zariski’s lemma, Noether normalization, the Rabinowitch trick, model theory, etc. How did Hilbert’...
12
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1answer
496 views
Source of a quote by Ferdinand Rudio
I am looking for the source and context of this quote, found e.g. at St Andrews:
Only with the greatest difficulty is one able to follow the writings of any author preceding Euler, because it was ...
11
votes
1answer
330 views
Aleksandrov's proof of the second order differentiability of convex functions
Aleksandrov [A], proved a remarkable property of convex functions.
Theorem. If $f:\mathbb{R}^n\to\mathbb{R}$ is convex, then for almost every $x\in\mathbb{R}^n$ there is $Df(x)\in\mathbb{R}^n$ and ...
1
vote
0answers
175 views
Why is the exterior algebra symbol a Lambda? [closed]
My guess is that this is because the capital lambda looks like a wedge. In this case why is the symbol a wedge.
Does anyone have any sources for this?
3
votes
1answer
52 views
Uniqueness constraints for Delaunay triangulation
Commonly the assumption that is made on point sets that shall be Delaunay-triangulated is that no three are collinear and no four are cocircular.
Those assumptions are however too restrictive: if ...
2
votes
1answer
104 views
History- calculating convolution by tabular method
I often see a trick for calculating convolution of discrete data by a so-called Tabular method. There are a lot of Youtube videos and many Indian textbooks on Signal Processing [Books].1
Basically, ...
3
votes
0answers
125 views
Nascent formal group law
The formal group law (cf. Wikipedia, Ex. 1.6 of nLab, Hazewinkel) derived from an analytic function or formal series $f(x) = x + a_2 x^2 + a_3 x^3 + ...$ and its formal compositional inverse, perhaps ...
-2
votes
2answers
210 views
Early examples of proof appraisals [closed]
What are the earliest known examples for attributing proofs as 'deep', 'elegant' or 'beautiful' (or their equivalents in other languages)?
Gauß for example called one of his results 'remarkable' ...
4
votes
1answer
198 views
Earliest reference on the calculation of derivatives by Fourier transform
I was looking for an earliest reference or the name of the mathematician who showed calculating the derivatives is possible in the Fourier domain?
The Fourier transform of the derivative is (...
67
votes
9answers
17k views
Nontrivially fillable gaps in published proofs of major theorems
Prelude: In 1998, Robert Solovay wrote an email to John Nash to communicate an error that he detected in the proof of the Nash embedding theorem, as presented in Nash's well-known paper "The Imbedding ...
24
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5answers
3k views
Examples of incorrect arguments being fertilizer for good mathematics? [duplicate]
Sometimes (perhaps often?) vague or even outright incorrect arguments can sometimes be fruitful and eventually lead to important new ideas and correct arguments.
I'm looking for explicit examples ...
7
votes
0answers
125 views
Importance of textbooks in health of a sub-discipline
I am interested in published articles, and also more informal writing (blog posts, talk slides etc.) which discuss the importance of textbooks (where this word encompasses research monographs etc.) in ...
2
votes
0answers
152 views
What do you call an object constructed as part of a proof? (Terminology)
I find myself wanting to talk about parts of a proof, e.g. the role played by mathematical expressions within a proof.
When proving a theorem it is common to construct some kind of object and then ...
3
votes
1answer
336 views
Motivating the coefficient field of $\ell$-adic cohomology
It was already known to Weil that a sufficiently reasonable cohomology theory for algebraic varieties over $\mathbb{F}_p$ would allow for a possible solution to the Weil conjectures.
It was also ...
6
votes
0answers
144 views
Hahn's approach to Hilbert's 17th problem?
The Wikipedia article on Hahn Series mentions that these were studied by Hahn "in his approach to Hilbert's seventeenth problem".
Is this correct? If so, what was this approach, and where can I ...
53
votes
60answers
10k views
Mathematicians with both “very abstract” and “very applied” achievements
Gödel had a cosmological model. Hamel, primarily a mechanician, gave any vector space a basis. Plücker, best known for line geometry, spent years on magnetism. What other mathematicians had so distant ...
0
votes
0answers
53 views
First appearance of Euclidean algorithm with Euclidean divisions
When was first described the Euclidean algorithm using Euclidean divisions?
In Euclid's original presentation¹ in his Elements, each step consists in repeated subtractions, while the modern ...
7
votes
1answer
422 views
Why was the factor $\frac12$ introduced in the Riemann $\xi$ function?
The factor $\frac12$ in the Riemann $\xi$ function:
$$\xi(s)=\frac12 s(s-1)\,\pi^{-s/2}\,\Gamma(s/2)\,\zeta(s)$$
was introduced by Riemann, however appears to be redundant. Once he had arrived at:
...
26
votes
6answers
3k views
Any real contribution of functional analysis to quantum theory as a branch of physics?
In the last paragraph of this last paper of Klaas Landsman, you can read:
Finally, let me note that this was a winner's (or "whig") history, full of hero-worship: following in the footsteps of ...
4
votes
4answers
450 views
Reference request: Oldest books on logic with unsolved exercises?
Per the title, what are some of the oldest books on logic out there with unsolved exercises? Maybe there are some hidden gems from before the 20th century out there.
Update: Doesn't have to be ...
asked Dec 7 '19 at 4:35
Squid with Black Bean Sauce
1,1781 gold badge7 silver badges27 bronze badges
72
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10answers
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What are examples of (collections of) papers which “close” a field?
There is sometimes talk of fields of mathematics being "closed", "ended", or "completed" by a paper or collection of papers. It seems as though this could happen in two ways:
A total characterisation,...
3
votes
0answers
277 views
Understanding a part of Friedberg’s Priority Argument Paper
This is Richard Friedberg’s original 1957 proof of the Friedberg-Muchnik Theorem, the origin of the ground-breaking priority argument. (The result proven is that there are two recursively enumerable ...
19
votes
2answers
1k views
How did Riemann prove that the moduli space of compact Riemann surfaces of genus $g>1$ has dimension $3g-3$?
Consider the moduli space $M_g$ of compact Riemann surfaces (i.e., smooth complete algebraic curves over $\mathbb{C}$) of genus $g$ for some $g>1$. I'm interested in knowing how Riemann proved that ...
12
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2answers
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Origin of the noun “mathematician” [closed]
I have read that Pythagoras's fraternity had two kinds of members, the 'acousmaticians', who were allowed to attend the lectures, and the 'mathematicians', who had been initiated. Is this the origin ...
3
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0answers
83 views
Terminology for set systems: “trace” or “projection”?
Although the following question is not in itself mathematical, it is the expertise/breadth of the research community in mathematics that I wish to appeal to, beyond the filtered/trained search results ...
6
votes
0answers
223 views
Brief history of primality testing theory after 2002?
Its clear that there is about 15 years (2004-2019) after the publication of AKS primality testing in 2002 and its modifications in 2003-2004. AS result, is there any development happened in this ...
3
votes
1answer
572 views
Why Bourbaki's epsilon-calculus is not suitable for set theory?
Does anybody shed light on what is A. R. D. Mathias' idea that Bourbaki's $\tau$-calculus (Logically the same as Hilbert's $\varepsilon$-calculus) is not suitable for set theory, especially because of ...
30
votes
2answers
4k views
What is the meaning of Text inside of AMS logo [closed]
What is the meaning of the text inside this AMS logo?
The image is from here, and the logo seems to have been frequently used until the 80's. The text is
ΑΓΕΩΜΕΤΡΗΤΟΣ ΜΗ ΕΙΣΙΤΩ
but Google ...
43
votes
4answers
5k views
A historical mystery : Poincaré’s silence on Lebesgue integral and measure theory?
Lebesgue published his celebrated integral in 1901-1902. Poincaré passed away in 1912, at full mathematical power.
Of course, Lebesgue and Poincaré knew each other, they even met on several occasions ...
