Questions tagged [ho.history-overview]

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

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31
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2answers
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 ...
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1answer
101 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 ...
8
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2answers
535 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 ...
15
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1answer
536 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....
7
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1answer
847 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,...
6
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375 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 ...
13
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1answer
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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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1answer
219 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, ...
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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 ...
7
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2answers
799 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 ...
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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 ...
14
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2answers
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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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4answers
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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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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 ...
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9answers
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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. ...
4
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2answers
214 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 ...
2
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1answer
65 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, ...
1
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1answer
130 views

Reference request for some fragments of Gauss with dubious origin

Gauss's results on the interconnection between the different values of the arithmetic-geometric mean of two complex numbers as recorded in his private notebooks led him to introduce foundational ...
7
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151 views

On the “Collected Works” of Charles Bradfield Morrey, Jr

Why Charles Bradfield Morrey, Jr.'s "Collected works" haven't been published yet? I've been thinking of this question for a while, at least from the first time I started to improve the ...
12
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29answers
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Which great mathematicians had great political commitments? [closed]

Some mathematicians claim that their field has nothing to do with political concerns; others are deeply involved in political life. Are there many great mathematicians with great political commitments?...
3
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0answers
228 views

Groups with “just not” a property

There seems to be a standard trick in group theory which is to show that a group has a quotient group which "just not" has some property. To make things clear: let $\mathcal{P}$ be a group ...
3
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0answers
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Proving interpolation results through amalgamation

Notice: this is a cross-posting, I have asked essentially the same question on MSE (https://math.stackexchange.com/questions/4012960) but received no answers, and as this problem, although very basic, ...
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17answers
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Which great mathematicians were also historians of mathematics?

As the question title suggests, which great mathematicians were also historians of mathematics? We all know plenty of great mathematicians, but not many historians of mathematics. Not to mention that ...
17
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1answer
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Did André Bloch or any other mathematician receive the Becquerel Prize?

On this biography page of André Bloch, it is said that The Académie des Sciences awarded him the Becquerel Prize just before his death. This claim is also repeated in PlanetMath, Wikiversity and ...
12
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2answers
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Several questions about Gauss's mathematical conception of braids

I'm trying to figure out several things about Gauss's thoughts concerning a certain four-strand braid. The reference my questions are based on is mainly Moritz Epple's excellent article "orbits ...
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1answer
683 views

Translation of “The joy of learning” by Hironaka

According to this Quanta article about June Huh, there exists a memoir by Heisuke Hironaka called The Joy of Learning. It seems to be this short article: Heisuke Hironaka, The joy of learning, ...
4
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1answer
51 views

Singularities on null capacity sets are removable — Wiener or Bouligand?

A classical theorem on harmonic functions states that singularities of bounded harmonic functions are removable if the singular set is of null capacity. This theorem is sometimes attributed to ...
5
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0answers
250 views

Earliest reference for infinitesimal neighborhoods of the diagonal

Where was $I_x/I_x^2$ first introduced? (DG or AG) asks about the algebraic cotangent space. The paper First neighborhood of the diagonal and geometric distributions by Kock claims Grothendieck ...
15
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1answer
948 views

What are some of the earliest examples of analytic continuation?

I'm wondering how Riemann knew that $\zeta(z)$ could be extended to a larger domain. In particular, who was the first person to explicitly extend the domain of a complex valued function and what was ...
14
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2answers
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Year of birth of Craige Schensted

For a paper I am writing related to the history of combinatorics, I am looking for the year of birth of Craige Eugene Schensted, the eponym for the Schensted correspondence. According to this site, a ...
5
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0answers
137 views

Are there any neusis-hard/neusis-complete problems?

I have lately been enjoying Richeson's Tales of Impossibility (see MAA review), an accessible book on the famous problems of Euclidean geometry including angle trisection/cube doubling/heptagon ...
3
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1answer
210 views

Origin of the Liouville theorem for harmonic functions

What is the paper where the Liouville theorem for harmonic function was first stated? Did it come before or after (or in the same paper) as the Liouville theorem in complex analysis?
10
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1answer
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Did human computers use floating-point arithmetics?

Before the proliferation of computers in the 1950s, did human computers use floating-point formats for their computations? Floating-point calculation was reportedly implemented already in the 1910s (...
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1answer
159 views

Leibniz habilitation dissertation in philosophy

Gottfried Leibniz completed his habilitation dissertation (as part of his book De Arte Combinatoria) in philosophy somewhere in the mid-1660s. Prior to that, he had acquired his master’s degree; what ...
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2answers
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Euler's Master's Thesis

At the age of 16, Leonhard Euler defended his Master's Thesis, where he discussed and compared Descartes' and Newton's approaches to planet motion. I don't know anything else about it. In particular, ...
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1answer
481 views

When and where did Gauss say this [closed]

This quote is often attributed to Gauss: ``Die Mathematik ist die Königin der Wissenschaften, und die Arithmetik ist die Königin der Mathematik". Where and when did he say that?
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1answer
417 views

Origin of phrase 'natural number'

This is a simple historical question about the origins of the English phrase 'natural numbers', and ancestor phrases in other languages containing words similar to 'natural'. My curiosity just stems ...
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0answers
166 views

Ideals with certain properties

I recently isolated the following definition, which I believe it should have appeared somewhere. Let $\kappa$ be a cardinal, and let $X$ be a set with $\kappa^+\leq |X|$. Definition: An ideal $\...
10
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1answer
413 views

Chebyshev's other inequality

It is a simple fact, the granddaddy of correlation inequalities that if $f,g$ are monotone functions on $[0,1]$ then $$\int_0^1 f(x)g(x) dx \ge \int_0^1 f(x) dx \int_0^1 g(x) dx.$$ In their famous ...
8
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1answer
540 views

Origin of the symbol for the tensor product

I have recently realised that the Paleo-Hebrew (and Phoenician) graph for the Hebrew letter ט (Teth) is $\otimes$. This made me wonder if there is any relation between the choice of the symbol and the ...
3
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3answers
316 views

Motivations for the term “jet” in the context of viscosity solutions for fully nonlinear PDE

My question is very direct: What are the motivations for the name "jet"(subjet, superjet) in the context of viscosity solutions for second order fully nonlinear elliptic PDE? The ...
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0answers
71 views

The earliest discrete optimization problem

What is the earliest example of anything that could be considered a discrete optimization problem? I can find plenty of examples of ancient continuous optimization problems (e.g. Dido's isoperimetric ...
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0answers
37 views

First upper bound on model size for the decidability of monadic first-order logic

Lowenheim (1915) is credited with the first proof of the decidability of semantic validity over the monadic fragment of first-order predicate logic. However, I find no reference in his proof to an ...
9
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1answer
540 views

Gödel on pure mathematics and medieval theology

I was watching this youtube video recently where Gregory Chaitin paraphrases something from one of Gödel's unpublished essays (apparently published now). It is at the 4:48 mark of the video Gregory ...
11
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4answers
364 views

Autobiographies and correspondences of mathematicians [duplicate]

Lately I have enjoyed reading several autobiographies and correspondences of mathematicians. I'd like to find more, so I thought I'd ask here which others you have come across and enjoyed. P.S. I have ...
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11answers
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Reference request: Examples of research on a set with interesting properties which turned out to be the empty set

I've seen internet jokes (at least more than 1) between mathematicians like this one here about someone studying a set with interesting properties. And then, after a lot of research (presumably after ...
8
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1answer
292 views

Reference request: Origins of differential homological algebra

Differential homological algebra in its initial formulation is due to Eilenberg and Moore, who published the homological version of the Eilenberg–Moore spectral sequence in 1965 (and the cohomological ...
60
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2answers
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Who is the “young student” André Weil is referring to in his letter from the prison?

I am reading a nice booklet (in Italian) containing the exchange of letters that André and Simone Weil had in 1940, when André was in Rouen prison for having refused to accomplish his military duties. ...
10
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1answer
689 views

History of Sylvester's resultant?

Suppose that we have two polynomials that split: $$\begin{align*} f(x)=\sum_{k=0}^d a_{d-k}x^k&=\prod_{i=1}^d (x-\lambda_i),\\ g(x)=\sum_{k=0}^e b_{e-k}x^k&=\prod_{j=1}^e (x-\mu_j).\\ \end{...
3
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0answers
324 views

Is the study of additive functions dead?

I am learning more about the theory of additive functions ($f(nm)=f(m)+f(n)$) and I am struck by how powerful the theorems given are. For example, we have a complete characterization of not only what ...

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