# Questions tagged [ho.history-overview]

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

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### What was the first elementary proof that $\pi(x)=o(x)$?

Denote by $\pi(x)$ the number of primes $\leq x$. I'm interested in knowing who came up with the first elementary proof that $\pi(x)=o(x)$.
I know that Chebyshev demonstrated elementarily before ...

**11**

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**2**answers

1k views

### Where are Serre’s lectures at Collège de France to be found?

Having run into several references, at various places and occasions, to "Serre’s Course at Collège de France, 19xy-19xy+1" for various values of xy, I would genuinely like to know where these lectures ...

**17**

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**0**answers

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### Reference request for Grothendieck's work on “Integration with values in a topological group”

Disclaimer. This question was already asked in Mathematics Stack Exchange (see the link here). I wanted the question to be migrated here but I was told by a moderator that a question that old is ...

**24**

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**1**answer

1k views

### Have the Quantum Group Theorists taught the Group Theorists Anything?

I will start with the general before moving to the specific.
Consider for a moment the two (very) soft definitions.
An abstraction of an object $X$ is a category $\mathcal{C}_0$ such that $X$ ...

**2**

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**2**answers

456 views

### Who first discovered the concept corresponding to the symbol of class comprehension?

Who first discovered the concept corresponding to the symbol of class comprehension
{x/??}used today in set theory ?

**8**

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**1**answer

429 views

### Earliest use of the term “Galois extension”?

Does anyone know the earliest use of the term "Galois extension"? I thought it might be in Emil Artin's Notre Dame lectures but I couldn't find it there. (He does use the terms "normal" and "separable....

**14**

votes

**1**answer

323 views

### Carnot-Carathéodory metric

The metric in sub-Riemannian geometry is often called the Carnot-Carathéodory metric.
Question 1. What is the origin of this name? Who was the first to introduce it?
I believe that the "...

**4**

votes

**2**answers

552 views

### Hard implications that become easy with the right intermediate step

I’m interested in examples of theorems of the form “If $P$ then $Q$“ that were either unsolved or thought to require difficult arguments until someone came up with an $X$ for which “If $P$ then $X$” ...

**69**

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**15**answers

7k views

### Theorems that impeded progress

It may be that certain theorems, when proved true, counterintuitively retard
progress in certain domains. Lloyd Trefethen provides two examples:
Faber's Theorem on polynomial interpolation: ...

**5**

votes

**1**answer

181 views

### What does Rosenlicht mean by a “point”? By $k(v_1,v_2)$?

This is cross-posted from Math.SE at the recommendation of a commenter.
I'm reading M. Rosenlicht's 1956 paper, "Some Basic Theorems on Algebraic Groups" [link], and having trouble with some of the ...

**5**

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**0**answers

434 views

### Story of Grothendieck's Prime Number

I asked this question earlier, at hsm.stackexchange.com without much luck. Maybe somebody can answer it here.
There is a story about Alexander Grothendieck and the "Grothendieck Prime" 57, which ...

**10**

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**2**answers

730 views

### Gauss' Posthumous Publications?

I'm looking for any information about the posthumous publication of Gauss' mathematical correspondence and notebooks.
When did these become widely available, and how did it affect progress in ...

**2**

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**0**answers

61 views

### Accelerating convergence of a product by multiplying by zeta values: history?

Let $R(s_1,\dotsc,s_n) = \prod_p r(p^{-s_1},\dotsc,p^{-s_n})$, where
$r$ is a rational function on $n$ variables. Say we want to compute the value of $R(s_1,\dotsc,s_n)$ for some choice of $s_1,\dotsc,...

**6**

votes

**2**answers

576 views

### Books on the History of math research at European universities

Are there good books that cover the history of math and mathematical science (ex. physics, chemistry, computer science) PhD programs in the Occident? My primary motivation is to figure out how the PhD ...

**20**

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**1**answer

427 views

### Videos of Gian-Carlo Rota Lectures

I apologize if this is off topic.
I think most of his listeners would agree with me that Gian-Carlo Rota had a wonderful style of lecture delivery. I have heard him lecture, both as an undergraduate ...