Questions tagged [ho.history-overview]

History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.

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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 ...
40 votes
1 answer
2k views

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 ...
Carl-Fredrik Nyberg Brodda's user avatar
8 votes
2 answers
578 views

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 ...
Kuga's user avatar
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4 answers
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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, ...
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9 votes
1 answer
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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. ...
Arnold Neumaier's user avatar
11 votes
1 answer
964 views

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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30 votes
3 answers
5k views

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 '...
Aidan Rocke's user avatar
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5 votes
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 ...
Igor Sikora's user avatar
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2 votes
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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'...
Tyrell's user avatar
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8 votes
0 answers
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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 $k\geq 1$. ...
H A Helfgott's user avatar
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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 ...
Manfred Weis's user avatar
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2 votes
1 answer
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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 ...
user2554's user avatar
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2 votes
0 answers
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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 ...
Federico Castillo's user avatar
4 votes
0 answers
91 views

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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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 ...
Till's user avatar
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25 votes
5 answers
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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 ...
Alexandre Eremenko's user avatar
6 votes
1 answer
700 views

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 ...
Jochen Wengenroth's user avatar
5 votes
0 answers
225 views

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 ...
Tom Copeland's user avatar
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15 votes
2 answers
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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 "...
Calvin McPhail-Snyder's user avatar
2 votes
1 answer
416 views

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 ...
Kimmel's user avatar
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1 answer
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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/...
wlad's user avatar
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6 votes
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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 ...
Cloudscape's user avatar
7 votes
0 answers
185 views

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 ...
varkor's user avatar
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8 votes
6 answers
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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 votes
2 answers
665 views

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 ...
Aidan Rocke's user avatar
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11 votes
1 answer
471 views

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 ...
user2554's user avatar
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1 vote
0 answers
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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 ...
Archie's user avatar
  • 883
13 votes
2 answers
752 views

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 ...
AGenevois's user avatar
  • 7,481
25 votes
1 answer
786 views

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 ...
grok's user avatar
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6 votes
3 answers
548 views

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 votes
0 answers
123 views

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 $x\notin B$), ...
mahdi meisami's user avatar
17 votes
1 answer
1k views

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 ...
user2554's user avatar
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5 votes
0 answers
218 views

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 ...
Christian Bernert's user avatar
33 votes
2 answers
2k views

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 ...
KConrad's user avatar
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0 votes
1 answer
123 views

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 ...
Jamai-Con's user avatar
10 votes
2 answers
638 views

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 ...
none's user avatar
  • 1,117
15 votes
1 answer
769 views

$\mathbb{R}^3$ 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....
Alexey Ustinov's user avatar
7 votes
1 answer
1k views

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,...
user907616's user avatar
7 votes
0 answers
486 views

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 ...
Jens Reinhold's user avatar
13 votes
1 answer
2k views

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 ...
Libli's user avatar
  • 7,210
5 votes
1 answer
299 views

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, ...
Helmut Prodinger's user avatar
0 votes
0 answers
195 views

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 ...
user267839's user avatar
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8 votes
2 answers
971 views

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 ...
Martin Gisser's user avatar
28 votes
2 answers
4k views

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 votes
2 answers
4k views

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, ...
Arnaldo Mandel's user avatar
21 votes
4 answers
2k views

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 ...
Hailong Dao's user avatar
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3 votes
0 answers
107 views

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 ...
gualterio's user avatar
  • 1,043
55 votes
9 answers
6k views

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 votes
2 answers
271 views

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 ...
Praphulla Koushik's user avatar
2 votes
1 answer
691 views

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, ...
AChem's user avatar
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