Questions tagged [ho.history-overview]
History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.
1,407
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Taking a theorem as a definition and proving the original definition as a theorem
Gian-Carlo Rota's famous 1991 essay, "The pernicious influence of mathematics upon philosophy" contains the following passage:
Perform the following thought experiment. Suppose that you are ...
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1
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Known and fixed gaps in the proof of the CFSG
As the "second-generation" proof of the Classification of Finite Simple Groups is being written up in the volumes by Gorenstein, Lyons, Aschbacher, Smith, Solomon, and others (see e.g. this ...
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Can the theory of elliptic functions developed from purely geometric considerations?
I always had this question, but was unable to get a definitive answer to it.
There is the theorem of division of the arc length of the lemniscate with ruler and compass. So I always wondered, is it ...
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When did Grothendieck join Bourbaki? [closed]
Bourbaki listed Grothendieck as a third-generation member. Nevertheless, it does not provide details on when he joined and when he left.
Concerning his departure, there is a
Letter from October 9, ...
9
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1
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Duhamel's formula
Formula (12) in the paper
Bauer, M., Chetrite, R., Ebrahimi-Fard, K., & Patras, F. (2013).
Time-ordering and a generalized Magnus expansion. Letters in
Mathematical Physics, 103(3), 331-350.
...
11
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Jouanolou thesis on l-adic cohomology
Does someone have a copy of the Jean-Pierre Jouanolou's thesis:
Catégories dérivées et cohomologie l-adique
or has the ability to make a digitalization? The thesis was done at Université de Paris 1969....
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3
answers
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John von Neumann's remark on entropy
According to Claude Shannon, von Neumann gave him very useful advice on what to call his measure of information content [1]:
My greatest concern was what to call it. I thought of calling it '...
5
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0
answers
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Relation between Bott-Samelson theorem and James reduced product
I asked this question on the homotopy theory chat, but I haven't got any answer - thus I decided to post it as a question here.
The question is rather historical. Let $X$ be a connected topological ...
2
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0
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Does Arnold say that Hardy is responsible for Ramanujan's untimely death? [closed]
Vladimir Arnold in his book Yesterday and Long Ago, Springer (2007) writes:
When I resided at Cambridge as a senior fellow of Trinity College,
Indian colleagues told me some details of Ramanujan'...
8
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0
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Bounding eigenvalues by taking high powers of matrices: history?
Let $A$ be real symmetric matrix. It is a well-known observation that we can bound any eigenvalue $\lambda$ of $A$ by using the fact that
$$\lambda^{2 k} \leq \textrm{Tr} A^{2 k}$$
for any $k\geq 1$. ...
1
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0
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Polynomial Splines vs Whittacker-Shannon Interpolation for uniform data
Question:
(why) are polynomial splines preferred over Whittacker-Shannon interpolation?
Is it for genuine mathematical reasons like numeric stability and/or precision, or for other reasons?
Having ...
2
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1
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Explanation of two interrelated identities of Gauss about cubic and biquadratic periods
On p.112-113 of volume 10-1 of Gauss's werke, which contain an unpublished fragment dated to 1805, Gauss states some results on cubic and biquadratic "Gaussian periods" in a trigonometric ...
2
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0
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Historical question about tangent lines to disjoint circles
It is pretty well known that two disjoint circles have 4 different lines that are simultaneously tangent to both circles. There are constructions with ruler and compass available in many books, but I ...
4
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0
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Tangent coalgebras and hyperalgebras
Takeuchi's On coverings and hyperalgebras of affine algebraic groups references Tangent coalgebras and hyperalgebras. I and II, with II being listed as submitted to MAMS. On coverings and ...
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0
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History of simplicial complex
It is easy to find the definition of a simplicial complex:
https://en.wikipedia.org/wiki/Simplicial_complex
I am interested in the history and first occurrences of the concept.
When did people start ...
25
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5
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Why are distributions "tempered"?
Google N-Gram shows that both "tempered distribution" and "temperate distribution" are used in English, but the first version significantly prevails, and usage of the second term ...
6
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1
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How did Euler calculate $i^i$?
There is a well-know quotation of Euler in a letter from 1746 to Goldbach:
Letztens habe ich gefunden, dass diese expressio $\sqrt{-1}^{\sqrt{-1}}$ einen valorem realem habe, welcher in fractionibus ...
5
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0
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Schröder and graphical logic?
I was actually surprised by a comment by John Baez over at the n-Category Cafe about his surprise that Ernst Schröder, a mathematician of whom he had known through Schröder's work on mathematical ...
15
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Why is the thing dual to a "meridian" called a "longitude"?
A pair of distinguished generators of the fundamental group $\pi_1(\partial(S^3 \setminus K))$ of the boundary torus of a knot complement are usually called the "meridian" and "...
2
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1
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Mistake in Karl Pearson's 1900 paper introducing the chi-squared distribution
Background
I'm reading Karl Pearson's 1900 paper titled:
On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be ...
5
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1
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387
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Origin of Laguerre geometry?
Laguerre geometry is described as either the geometry of oriented lines and circles in the Euclidean plane, equipped with a certain unusual symmetry group (see https://en.wikipedia.org/wiki/...
6
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The history and original paper of the Rosser–Iwaniec sieve
I'm trying to find Rosser's original paper where he introduces his eponymous sieve. I've already found https://arxiv.org/pdf/math/0505521 (where the reference isn't given, but where it is indicated ...
7
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0
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Were algebraic theories and abstract clones defined independently?
Algebraic theories (by which I mean the formalism based on bijective-on-objects functors) and abstract clones both capture universal algebraic structure, and are well-known to be equivalent. Algebraic ...
8
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6
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Papers on history and philosophy of mathematics suitable for master's students
In the fall, I will give a course called "Perspectives in Mathematics". This is a mandatory course at our master's program in mathematics (including applied mathematics and statistics). The ...
9
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2
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Egyptian number theory
Might there be a good historical reference on Egyptian number theory ($ \sim 2000$ B.C.)? The following online reference by a professor at the UCLA indicates that they were aware of the Pythagorean ...
11
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1
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Explanation of several unpublished remarks of Gauss on representations of a given number as sums of two, three and four squares
Remark 1: On p.384 of volume 3 of Gauss's Werke, which is a part of an unpublished treatise on the arithmetic geometric mean, Gauss makes the following remark:
On the theory of the division of ...
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0
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Initiatives to systematically archive researchers' notes
Are there ongoing initiatives to systematically archive all notes of mathematicians? If not, what body (the IMU? the AMS? The Clay fundation?...) should I contact to make that case?
Of course in the ...
13
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2
answers
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Prehistory of Gromov-hyperbolic spaces/groups
When speaking about hyperbolic groups/spaces, one usually refers to Gromov's monograph Hyperbolic groups for their introduction. However, coarse notions of hyperbolicity can be found in some of his ...
25
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1
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Looking for source: "How not to be a graduate student"
I remember having read, about 15 years ago, a transcript of a lecture given by Richard K. Guy, titled "How not to be a graduate student". He gave lots of advice, mostly humorous, concealing ...
6
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3
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Anomalous phenomena [closed]
What are examples of strikingly anomalous phenomena in mathematics, where just one or a rather small number of cases stand out because they don't fit a general pattern?
This is most interesting when ...
0
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0
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Why the name 'regular' space?
It is well known that a regular space is a topological space $X$ with these two properties:
1)All one point sets are closed.
2)For every $x\in X$ and every closed set $B$ (such that $x\notin B$), ...
17
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Question about the theory behind an important footnote to entry 109 in Gauss's diary
Entry 109 in Gauss's diary (and the related material in Gauss's Nachlass) is the main subject of David Cox's famous article "The Arithmetic-Geometric mean of Gauss". This entry deals with ...
5
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Origin of the term "singular integral" in the circle method
Ever since I learned about the circle method, I have implicitly held the following beliefs about the topic in the title:
The terms "singular integral" and "singular series" were ...
33
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2
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First use of term "Hilbert's Nullstellensatz"
The post below first appeared on hsm.stackexchange over a week ago and has received no answers there yet, so by now I think it is okay to ask it here.
This year (2021) marks the 100th anniversary of ...
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Nicely motivated papers or book chapters on the formula for the sum of the $k$-th powers of the first natural numbers [closed]
Do you know of a text where I can find a nicely motivated proof of the formula for $1^{k}+2^{k}+\cdots+n^{k}$?
At the very beginning of page 68 of Professor H. S. Wilf's generatingfunctionology, one ...
10
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2
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Publishing solution but temporarily holding back solution method
https://www.quantamagazine.org/mathematician-disproves-group-algebra-unit-conjecture-20210412/
Above is an article about a researcher disproving an open conjecture in algebra (Kaplansky's unit ...
15
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1
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$\mathbb{R}^3$ as the union of disjoint circles
In the question Covering the space by disjoint unit circles
the following result is attributed to Sierpinski.
Theorem. The Euclidean space $\mathbb{R}^3$ is a union of nondegenerate disjoint circles....
7
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1
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Reference request: Who first proved that right adjoints preserve limits?
One of the most famous and unifying theorems in category theory is that right adjoints preserve limits. I wonder: Who was the first one to prove this fact?
The notion of adjoint functors is, of course,...
7
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0
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Who is Claude Morlet?
[Please delete if off-topic.]
I would be curious to find out more about the life and mathematical achievements of the French topologist Claude Morlet.
The internet told me he got his PhD in 1968 with ...
13
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1
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Various authors of the Bourbaki's books
As far as I understand, each chapter of the Bourbaki's collection was written by one (or two?) specific authors. The book itself was reviewed, corrected and after all approved by the whole Bourbaki ...
5
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1
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Ramanujan and his influence on others
A few years ago I saw a paper where a few important researchers were asked which theorem of Ramanujan impressed them most.
I don't remember details, but I would like to see this paper again.
Details, ...
0
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0
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Expansion around a singular point of a multivalued meromorphic function (due to Riemann/Cauchy)
In Riemann's publication about Abelian functions
'Theorie der Abelschen Functionen' (Here the original paper in german)
at the end of Chapter 4, part 2 is clamed that for every Riemann
surface $T$ and ...
8
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2
answers
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The Einstein minus convention, lost
In his milestone paper on general relativity, Einstein not only introduces the Einstein summation convention, but also (formula (45) in [1]) abbreviates a minus at the Christoffel symbols away by ...
28
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2
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Who was H. Vogt?
In Chapter I.9 of Chandler-Magnus "The History of Combinatorial Group Theory", a number of important mathematicians in the early history of the development of group theory and sources for ...
18
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Who started the "-oid" suffix fashion in math?
There are lots of structures which have name suffixed by "oid". Off the top of my head, matroid, greedoid, perfectoid, causaloid...
Who started this? AFAIK, "matroid", by Whitney, ...
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4
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The first female algebraist in US/Britain?
Recently I dug up some biographical details of Lindsay Burch, of Hilbert-Burch Theorem fame, whose few papers have had quite an impact on commutative algebra. This made me curious about the first ...
3
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0
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Reference for the Netto's theorem on the permutation groups which was mentioned in the paper of Frobenius
I'm trying to read 'Uber die Charaktere der mehrfach transitiven Gruppen' written by Frobenius.
There he mentioned some theorems of Netto.
I'm depending on the Google translator. and the translation ...
55
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9
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Proofs of theorems that proved more or deeper results than what was first supposed or stated as the corresponding theorem
Recently, I figured out that a colleague of mine has had published during recent years a proof of a theorem in which he was actually proving a deeper result which we both thought to be still open. ...
5
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2
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First time appearance of Lie crossed module (crossed module of Lie groups) in literature
Can someone point me to a reference where the notion of "Lie crossed module" appeared for the first time?
I see many papers "recall" the definition of the Lie crossed module but, I ...
2
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1
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Origin of the term relaxation method in numerical analysis for iteratively solving linear equations
In the iterative methods for solving a system of linear equations, a term called relaxation method is often appears along with Jacobi and Gauss Seidel methods. As per the Earliest Known Uses website,
...