All Questions
Tagged with history or ho.history-overview
1,456 questions
6
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0
answers
272
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The history of Riemann-Roch theorem [closed]
I became interested in the history of the Riemann-Roch theorem, so I searched various materials.
So, I read Über die Wechselwirkungen zwischen der französischen Schule, Riemann und Weierstraß. Eine ...
- 245
3
votes
1
answer
324
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About Grothendieck and special cases
I was recently reminded of a quote about (not by!) Alexander Grothendieck that I had read many years ago, I think in the 1990s or 2000s.
The quote was about the way in which Grothendieck solved ...
- 857
4
votes
0
answers
275
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Derek the Differentiable Dinosaur
I’ve come across several fond references to some semi-published lecture notes from Warwick in the 80s, by Bill Breckon (and, in some mentions, I. Harrison), Differentiating functions of lots of ...
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12
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0
answers
267
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What is known about G. A. Croes
G. A. Croes is the author of the first description of the 2-opt moves heuristic for improving non-optimal traveling salesman tours:
Croes, G. A. “A Method for Solving Traveling-Salesman Problems.” ...
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5
votes
2
answers
665
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Recent breakthroughs with applied origins
Historically, the boundary between pure mathematics and its applications was much less defined. However, with the increasing complexity of modern mathematics and the resulting need for specialization, ...
3
votes
0
answers
97
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Historical appearance of using $\operatorname{SO}_3$-representation theory for spherical harmonics
$\DeclareMathOperator\SO{SO}$The spherical Laplace equation and the spherical harmonics are a beautiful example of a differential equation dominated by the representation theory of the Lie group of ...
- 1,846
1
vote
4
answers
799
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Examples of long running and consecutively numbered international meetings [closed]
I just saw a poster at the next office's door announcing the
95th Annual Meeting of the International Association of Applied Mathematics and Mechanics.
Here is another example of a meeting I will ...
0
votes
0
answers
69
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Evaluating the coprimality in a bivariate polynomial equation
Given a prime $p>2$, let $x$ and $y$ be real numbers such that $x>y>0$ and
$$ \begin{equation} x^p-y^p=(x-y)^p+pxy(x-y)R \tag{1} \label{eq:one} \end{equation} $$
where $R$ is a bivariate ...
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45
votes
10
answers
10k
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Has the mathematics research community ever been led astray by a dumb mistake?
This is a highly subjective question, but here goes.
Has anyone ever published a result that was "taken seriously" by the research community, but was then discovered to be incorrect because ...
18
votes
2
answers
2k
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When did the distinction between "pure" and "applied" mathematics become common?
Some ages ago, there was no difference between chemistry, physics, mathematics, and perhaps even philosophy. These were not further distinguished and largely practiced by the same people.
Obviously, ...
- 5,327
7
votes
0
answers
265
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Herbrand's consistency proof
Jacques Herbrand's thesis "Investigations in proof theory: The properties of true propositions" (or in the original French "Recherches sur la théorie de la démonstration", with the ...
- 161
0
votes
1
answer
790
views
What is John Charles Martin Nash known for? [closed]
John Nash and his wife Alicia tragically passed away in 2015. According to Sylvia Nasar's book "A Beautiful Mind", their son is apparently a good mathematician. What works is he known for?
user538849
37
votes
6
answers
6k
views
What is the oldest open math problem outside of number theory?
The question of "What is the oldest open problem in mathematics?" comes up from time to time, and there seems to be consensus that the answer is "Are there any odd perfect numbers?"...
- 12.9k
7
votes
0
answers
312
views
Did Lebesgue like non-measurable set or not?
I was surprised by the following paragraph in Bressoud's A radical approach to Lebesgue's theory of integration, quoted by Caicedo's in his comment to this question:
Vitali's nonmeasurable set, ...
- 865
6
votes
2
answers
607
views
Whence “uniform distribution”?
The “Earliest Uses” site suggests that the expression “uniform distribution” first appeared in Uspensky (1937), and “uniformly distributed” in Sakamoto (1943). Is that true?
- 31.5k
12
votes
3
answers
793
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The orders of the exceptional Weyl groups
Who first calculated the orders of the Weyl groups $E_6$, $E_7$, $E_8$, $F_4$, and $G_2$? How were these orders calculated?
- 421
6
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0
answers
141
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Historical background of finding the roots of cubic equations using continued fractions
I came across an algebra problem book written in 1899 for students of Dar al-Fonun ([dɒːɾolfʊˈnuːn], meaning, "polytechnic college",) the only modern educational institute in Iran at the ...
- 2,437
7
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0
answers
335
views
Gauss, Cantor, and infinite confusion
There is an interesting comment by Gauss on "infinite magnitude as a
complete thing" that has invited varying interpretations. In a
well-known passage, Gauss criticized the use of infinity ...
- 16.6k
9
votes
1
answer
435
views
On the origin of a fundamental theorem of additive number theory
Given $a, b \in \mathbb Z$, set $[\![a,b]\!] := \{x \in \mathbb Z: a \le x \le b\}$. A basic result in additive number theory goes as follows:
If $A$ is a finite subset of $\mathbb N$ with $0 \in A$ ...
- 10.5k
5
votes
1
answer
588
views
Was homology influenced by Euler's polyhedron formula?
First of all, Alama - Formal proofs and refutations contains information about Euler's Polyhedron Formula. If you look at pp. 47–49, you will see that Poincaré proved Euler's Polyhedron Formula, and ...
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60
votes
1
answer
3k
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Eisenstein's last theorem
Hopefully the following is appropriate for MathOverflow; it's possible the question (of a somewhat historical nature) is unanswerable, but I think there's some hope it can be answered, as I'll explain ...
- 23k
18
votes
2
answers
888
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Serre’s comment on Hurwitz: connecting FLT to points of finite order on elliptic curves
In the paper Sur les représentations modulaire de degré 2 de Gal$(\overline{\mathbb{Q}}/\mathbb{Q})$, Serre makes the following comment:
Remarque. La relation existant entre "solutions de l'...
- 6,734
7
votes
0
answers
77
views
Earliest historical work on Cauchy's infinitesimal delta functions?
As early as 1981, Hans Freudenthal briefly mentioned Cauchy's work on "singular integrals (i.e., integrals of infinitely large functions over infinitely small paths [$\delta$ functions])" on ...
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0
votes
0
answers
75
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Logan's theorem in compressed sensing
In some research papers in the nuclear magnetic resonance field Ref:, Logan's theorem is used to provide a justification for randomized sampling of free induction decay curves which are converted to ...
- 879
12
votes
1
answer
597
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Fermat last theorem : proof of a criterion by Cauchy
In 13 Lectures on Fermat's Last Theorem, Ribenboim states the following theorem (on page 7) attributed to Cauchy:
If the first case of Fermat's theorem fails for the exponent $p$, then the sum:
$$ 1^{...
- 121
2
votes
3
answers
1k
views
Concrete works by Alexandre Grothendieck, other than Dessin d'Enfants?
For me "Dessin d'Enfants" by Alexandre Grothendieck is the more concrete research work he has done. I would like to know if there are others.
When he was teaching at Montpellier University (...
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14
votes
1
answer
295
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When were Allegories first introduced?
I’m doing some bibliographic work for my PhD and I’m struggling to find the earliest resources on Allegories.
They were surely made famous by the 90s book “Categories, Allegories” by Freyd and Scedrov....
- 249
2
votes
1
answer
260
views
Usage and origin of the terms dictionary and atom in compressed sensing
In compressed sensing two terms or perhaps fancy word are frequently encountered. One is the dictionary and the other is atom. The dictionary is the matrix and its columns are called "atoms" ...
- 879
4
votes
1
answer
684
views
Who and when proved Artin's Theorem on alternative rings?
I am interested in the history of the proof of Artin's Theorem (on the diassociativity of alternative rings).
Question. When has Artin proved this theorem and where was it published for the first ...
- 41.8k
10
votes
1
answer
521
views
About Friedrichs historical contribution to QFT cited in Reed and Simon
In the Reed and Simon book, Appendix X.7, they mention that Friedrichs provided the first examples of inequivalent representations of the canonical commutation relations via the Weyl relations in the ...
- 424
8
votes
1
answer
2k
views
Mathematical emails
How should one archive mathematical emails (especially keeping in mind that one may move from one institution to another, or may forget precise wording later on so that searching becomes difficult)?
...
10
votes
1
answer
513
views
Earliest proof of Solovay's theorem for successor cardinals
Solovay's partition theorem states that a stationary set over a regular cardinal $\kappa$ can be partitioned into $\kappa$-many disjoint stationary sets. The full theorem was proven by Solovay in 1971 ...
- 576
2
votes
0
answers
336
views
Who contributed [GT13] to "Computers and Intractability"?
This is a followup to my question How does the complexity of calculating the Permanent imply the NP completeness of directed 3-cycle cover?
Question:
who contributed problem [GT13] PARTITION INTO ...
- 13.2k
13
votes
0
answers
2k
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Is there any correspondence between Gödel and Kreisel that supports Kreisel's observation that Gödel changed his mind about his 1938 set theory note?
At a conference in 1965 there were some interesting comments made by Kreisel and Mostowski asserting that Gödel later changed his mind regarding his1938 note on his set theory results (see Problems in ...
- 481
4
votes
1
answer
143
views
On the history of cone-3-manifolds
A cone-3-manifold (of constant curvature) is a geometric 3-manifold locally modelled either on the Euclidean/hyperbolic/spherical 3-space or on the respective metric cones over spherical cone-surfaces ...
- 353
2
votes
0
answers
114
views
Robinson's views on Heyting's work?
Abraham Robinson and Arend Heyting had mutual respect (though holding differing philosophical views on the nature of mathematics). Heyting repeatedly expressed admiration for Robinson's work; see for ...
- 16.6k
4
votes
0
answers
205
views
Who first considered "Pascal Triangle"? [closed]
Arnold was used saying in his talks,
"Pascal’s triangle, so called, because it was by Chinese discovered"!
How much is he right?
- 85
7
votes
1
answer
1k
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An unpublished calculation of Gauss and the icosahedral group
According to p. 68 of Paul Stackel's essay "Gauss as geometer" (which deals with "complex quantities with more than two units") , Gauss calculated the coordinates of the vertices ...
- 2,099
3
votes
1
answer
234
views
Independence of CH and permutation models?
Can independence of $\sf CH$ from $\sf ZFCA$ be established using $\sf FM $ permutation models? And if so, then historically did this came first or Cohen's forcing?
- 11.3k
2
votes
0
answers
207
views
History of bump functions
When were the standard bump function examples such as $e^{-1/(1-x^2)}$ first understood, and what was the context or motivation at the time?
As an upper bound I would guess that they must have been ...
- 2,247
15
votes
1
answer
1k
views
A cipher proposed by Littlewood
In J. E. Littlewood's, "A Mathematicians Miscellany" there is the following passage about ciphers. I found it interesting for a couple of reasons.
First of all the "legend that every ...
12
votes
1
answer
449
views
Did Gödel possess a proof of the independence of $\mathsf{AC}$?
We all know Gödel proved the consistency of the Axiom of Choice with $\mathsf{ZF}$ using his constructible universe, and Cohen proved the consistency of $\neg \mathsf{AC}$ using his new method of ...
- 1,322
4
votes
2
answers
275
views
Diagrammatic representation of sets as irregular plane figures
I am trying to find the earliest use of plane diagrams of various shapes for representing sets. For example, this is snapshot is from the book called Some Modern Mathematics for Physicists and Other ...
- 879
19
votes
2
answers
949
views
Etymology of “real numbers"
I would like to know why the real numbers are called “the real numbers.” I would also like to know the meaning of “real” in the phrase “real number.”
Further questions and clarifications:
I’d like to ...
- 319
5
votes
1
answer
560
views
Hilbert's and Gödel's expanded definition of "Recursive Function"
There is a very interesting comment in this post:
I must also make one terminological caveat: Hilbert, and later Godel, used the phrase "recursive function" in a way very different from the ...
- 4,897
9
votes
0
answers
260
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Who was the first to prove that the automorphism group of a finite field is cyclic and is generated by the Frobenius automorphism?
$\DeclareMathOperator\Aut{Aut}$It is well-known that the automorphism group $\Aut(F)$ of a finite field $F$ of characteristic $p$ is cyclic of order $n$ where $|F|=p^n$. Moreover, the cyclic group $\...
- 41.8k
4
votes
0
answers
133
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Curiosity about "conditional trig identities"
Perhaps this should be cross-posted on Math Stackexchange, but it came up in the context of some research mathematics (quaternion orders, etc.) In this context, I have three angles $\alpha, \beta, \...
- 13.3k
12
votes
2
answers
402
views
Is there something I am missing about the computation of the $p$-part of the class groups of cyclotomic fields?
Well, the answer of the question in the title in certainly Yes, many things in fact, but let me be more precise.
In 1958, Serre gave a Bourbaki talk on the recent works of Iwasawa on class groups in ...
- 10.9k
18
votes
3
answers
3k
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What's the earliest result (outside of logic) that cannot be proven constructively?
Although mathematicians usually do not work in constructive mathematics per se, their results often are constructively valid (even if the original proof isn't).
An obvious counter-example is the law ...
- 6,353
1
vote
1
answer
125
views
History of knot enumeration tables
There is much arbitraryness in the Rolfsen (and later) tables.
Of course anyone would name $7_1$ to be the first knot with
$n=7$ crossings, but already my own "natural" ordering attempt
(...
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