# Questions tagged [ho.history-overview]

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

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### history of geometric mechanics

I was thinking about the foundations of geometric mechanics and its precursors. I wondered who was the first to realized the equivalence between Riemannian geometry and Lagrangian mechanics. In ...
116 views

### Is this elementary formula for the parabolic segment new?

Recently (May 2020) a formula for the area of the parabolic segment (i.e. the region enclosed by a parabola and a line), in terms of the coefficients of the Cartesian equations, has been published by ...
571 views

### Digitalized version of “Cours de topologie algébrique professé en captivité”

It is historically known that Jean Leray gave a course on algebraic topology while captive in the Officer's detention camp XVI in Edelbach, Austria during WW2. (References to this topic ...
4k views

### Why is this “the first elliptic curve in nature”?

The LMFDB describes the elliptic curve 11a3 (or 11.a3) as "The first elliptic curve in nature". It has minimal Weierstraß equation $$y^2 + y = x^3 - x^2.$$ My guess is that there is some problem ...
316 views

### Unknown work of Nöbeling on topological/Hausdorff dimension

Let $\mathcal{H}^n$ denote the Hausdorff measure, $\dim_H X$ the Hausdorff dimension, and $\dim X$ the topological dimension of $X$. A well known result of Szpilrajn (He changed his name to ...
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### Galois group of polynomials related to Fibonacci and Catalan numbers

Let $F_n$ be the Fibonacci and $C_n$ the Catalan numbers. Define a polynomial by $F_n(x):=\sum\limits_{k=1}^{n}{F_k x^{n-k}}$. For example $F_8(x)=x^7+x^6+2x^5+3x^4+5x^3+8x^2+13x+21$. And another ...
402 views

### Origin of the term 'index of a subgroup'

The index of a subgroup $H$ in a group $G$ is the number of distinct cosets of $H$ in $G$. Why did someone decide to call this an 'index'? What's the rationale for this?
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### The origin(s) of the word “elliptic” [migrated]

The word elliptic appears quite often in mathematics; I will list a few occurrences below. For some of these, it is clear to me how they are related; for instance, elliptic functions (named after ...
594 views

### Why 'excedances' of permutations? [closed]

For a permutation $\pi=\pi_1\pi_2\cdots\pi_n$ written in one-line notation, an index $i$ for which $\pi_i > i$ is usually called an 'excedance.' To me, this seems like a mispelling of what should ...
134 views

### Two questions on history of symplectic geometry in the 80's

I have a question about the history of two important results from the eighties in symplectic geometry. In both cases it seems that important results were developed (almost) simultaneously by ...
112 views

### Why is faithful actions called faithful and who first called it faithful?

Sorry for this question. I asked this on MSE and hsm but no one answered and I decided to post it here that is full of experts. I want to know why is faithful actions called faithful and who first ...
91 views

### Pyramids whose volume can be computed by simple cutting and glueing

Since this question remained without answers even after a bounty, I thought it might be time to ask it here. For which pyramid can you compute the volume from simple cut-and-glue processes? The Dehn ...
506 views

### History of the notion of irreducible representation

I am looking for the earliest references where the study of irreducible representations appears. There has been many articles and books on the history of representation theory. A fundamental feature ...
220 views

### Why are orthogonal matrices so often denoted $Q$?

I apologize for the stupid question in the title. Of course, we can baptize a particular given matrix as we want but, for example, the QR-decomposition has a fixed meaning. My humble guess is that ...
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### What aspects of math olympiads do you find still useful in your math research?

I was rereading the book Littlewood's Miscellany and this passage struck me: It used to be said that the discipline in 'manipulative skill' bore later fruit in original work. I should deny this ...
2k views

### Who introduced direct limits?

The general notion of a direct limit of a commuting system of embeddings, indexed by pairs in a directed set, has seen heavy use in set theory. It is the same notion as in category theory. I was ...
136 views

### Function of moderate growth: history, motivation, and uses

I recently came across functions of moderate growth via this post and I was wondering, what are some concrete uses or applications of this space? Where does it appear and why was it introduced ...
5k views

### Bourbaki's definition of the number 1

According to a polemical article by Adrian Mathias, Robert Solovay showed that Bourbaki's definition of the number 1, written out using the formalism in the 1970 edition of Théorie des Ensembles, ...
350 views

### History of well founded relations

I have changed the title in the hope of attracting the attention of someone who knows about the history of set theory as well as intuitionistic logic: Who was the first to state the definition of ...
27k views

### Conway's lesser-known results

John Horton Conway is known for many achievements: Life, the three sporadic groups in the "Conway constellation," surreal numbers, his "Look-and-Say" sequence analysis, the Conway-Schneeberger $15$-...
380 views