# Questions tagged [ho.history-overview]

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

1,207
questions

**1**

vote

**1**answer

114 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 ...

**3**

votes

**0**answers

87 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 ...

**14**

votes

**29**answers

4k views

### 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**

votes

**0**answers

214 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**

votes

**0**answers

63 views

### 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, ...

**20**

votes

**17**answers

3k views

### 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**

votes

**1**answer

1k views

### 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 ...

**10**

votes

**1**answer

439 views

### 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 ...

**8**

votes

**1**answer

636 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**

votes

**1**answer

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**

votes

**0**answers

243 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 ...

**13**

votes

**1**answer

685 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**

votes

**2**answers

1k views

### 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**

votes

**0**answers

125 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**

votes

**1**answer

193 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**

votes

**1**answer

2k views

### 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 (...

**2**

votes

**1**answer

157 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 ...

**33**

votes

**2**answers

4k views

### 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, ...

**-3**

votes

**1**answer

442 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?

**7**

votes

**1**answer

412 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 ...

**4**

votes

**0**answers

165 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**

votes

**1**answer

408 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**

votes

**1**answer

532 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**

votes

**3**answers

302 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 ...

**1**

vote

**0**answers

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 ...

**0**

votes

**0**answers

35 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 ...

**6**

votes

**1**answer

423 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**

votes

**4**answers

356 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 ...

**43**

votes

**11**answers

4k views

### 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**

votes

**1**answer

286 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**

votes

**2**answers

7k views

### 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**

votes

**1**answer

683 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**

votes

**0**answers

313 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 ...

**26**

votes

**5**answers

5k views

### Has any open/difficult problem in ordinary mathematics been solved only/mostly by appeal to set theory?

We know that many (if not all) mathematical notions can be reduced to the talk of sets and set-membership. But it nevertheless sounds like a grueling task (if at all possible) to actually get advanced ...

**7**

votes

**1**answer

376 views

### Abandoned notions in mathematics? [duplicate]

I'm looking for examples of abandoned or demised notions/concepts in mathematics, preferably (but not necessarily) after the age of foundations. To be clear: I'm not looking for abandoned ideas or ...

**15**

votes

**1**answer

807 views

### History of Study's Lemma?

The following theorem is usually attributed to Eduard Study:
Let $f(x,y)$ and $g(x,y)$ be polynomials in two variables over a field, with $f$ irreducible. If $f\nmid g$ then the curves $C_f:f=0$ and $...

**14**

votes

**1**answer

805 views

### Was Cantor aware of Lebesgue theory of integration?

Georg Cantor died in 1919, more than ten years after appearance of the Lebesgue theory of measure and integration at the beginning of the twentieth century. Lebesgue theory has a deep connection with ...

**5**

votes

**1**answer

371 views

### Proof that $x^2 + y^2 - z^2$ is universal

The (ternary) quadratic form $x^2 + y^2 - z^2$ is universal, meaning that any integer $n$ can be represented as $n = x^2 + y^2 - z^2$ for some integers $x, y, z$.
My question is this: who proved this ...

**31**

votes

**2**answers

1k views

### Wayback Machine for mathematics?

I have had a couple of experiences recently which have made me wonder whether the mathematics community should try to establish and maintain something like the Wayback Machine, but specifically ...

**48**

votes

**4**answers

7k views

### What are the main contributions to the mathematics of general relativity by Sir Roger Penrose, winner of the 2020 Nobel prize?

I received an email today about the award of the 2020 Nobel Prize in Physics to Roger Penrose, Reinhard Genzel and Andrea Ghez. Roger Penrose receives one-half of the prize "for the discovery ...

**5**

votes

**1**answer

171 views

### Skolem's method for checking truth-value assignments - a “cut-free proof procedure” for first-order logic?

In his intro to ( Skolem 1923a), Van Heijenoort (From Frege to Godel, p. 509) describes Skolem as giving “an alternative to the axiomatic approach” to proving a first-order formula. This is referring ...

**7**

votes

**0**answers

214 views

### Why are fundamental weights denoted by omega?

In my field (and many others, I believe) the absolutely standard notation for the fundamental weights of a root system is lowercase omega: $\omega$. Recently I was taken aback to receive a copyedited ...

**36**

votes

**9**answers

3k views

### Why is it still common to not motivate results in publications? [closed]

This is a question about practice and publication of research mathematics.
On the Wikipedia Page for Experimental Mathematics, I found the following quote:
Mathematicians have always practised ...

**11**

votes

**1**answer

410 views

### Source of infection on chessboard

I am looking for the original source of the following well known problem.
Seven unit cells of a 8×8-chessboard are infected. In one time unit, the cells with at least two infected neighbors (having a ...

**25**

votes

**0**answers

2k views

### What do you like in the mathematics of Vaughan Jones? And how Vaughan Jones liked mathematics to be? [closed]

Edit: Directed to mathematicians ,I think this is a suitable time to open this question to know more about the creative mathematician Vaughan Jones Probably his students are ready for getting answers ...

**3**

votes

**1**answer

173 views

### History of the notation for scalar product

What's the history of the development of the notation for (real or hermitian) scalar product? In particular,
Did "bra-ket" notations, such as $\langle u\mid v\rangle$ or $(u\mid v)$, first ...

**8**

votes

**0**answers

145 views

### History of the Lewis-Stegall theorem on factorization of representable operators

The following questions are about the history of a particular result in functional analysis, hence not "mathematical questions" per se; but I think they are relevant to the business of ...

**14**

votes

**3**answers

539 views

### What are some foundational authors/papers in dynamical systems?

I have just begun my first dynamical systems class, and I would like to try out the advice in the top answer here. To summarize, the answer suggests that when studying a new field, one should look at ...

**3**

votes

**1**answer

366 views

### What is the representation of the generators of the triangle group for the uniform (4 4 4) tiling of hyperbolic disk as Mobius transformations?

I wonder how can one describe the generators of the triangle group for the tesselation of Poincare unit disk by triangles with angles $\pi/4, \pi/4 , \pi/4 $ in terms of the action of the modular ...

**7**

votes

**1**answer

202 views

### Why is the Dyck language/Dyck paths named after von Dyck?

The Dyck language is defined as the language of balanced parenthesis expressions on the alphabet consisting of the symbols $($ and $)$. For example, $()$ and $()(()())$ are both elements of the Dyck ...