# Tagged Questions

**2**

votes

**2**answers

129 views

### Euclid vs Eratosthenes

Very little is known about Euclid's life--much less than about other famous ancient Greek mathematicians, which is puzzling. It is also strange to me that Euclid didn't write about the Eratosthenes ...

**4**

votes

**1**answer

239 views

### History of the notation for substitution

One of the very common notations for syntactic substitution is $[\ /\ ]$.
There seems to be a large inconsistency in the literature about its use.
Many write $[t/x]$ for substitute $t$ for $x$ (e.g. ...

**4**

votes

**2**answers

704 views

### Unreasonable application of mathematics to the other areas [on hold]

What are some papers or talks on the philosophy of mathematics which contains some statements about the unnecessary and unreasonable application of mathematics in other areas of science?
I found ...

**2**

votes

**1**answer

159 views

### Cambridge Mathematical Tripos papers from late 19th century

Are the scanned images of Cambridge Mathematical Tripos papers from late 19th century available anywhere on Internet?

**19**

votes

**18**answers

8k views

### What are some applications of other fields to mathematics?

It is commonplace to consider applications of mathematics to other fields, especially the exact sciences. But what I would like to know about is the converse topic, namely:
What are some ...

**18**

votes

**6**answers

1k views

### Mathematics contests before 1800

Aside from well known examples of mathematics contests in 1535 and 1548, what are some other examples before 1800?
Background: In The History of Mathematics: an Introduction, 3rd edition (1995), ...

**59**

votes

**22**answers

9k views

### Examples of major theorems with very hard proofs that have NOT dramatically improved over time

This question complement a previous MO question: Examples of theorems with proofs that have dramatically improved over time.
I am looking for a list of
Major theorems in mathematics whose proofs ...

**5**

votes

**0**answers

158 views

+50

### Jets of sections of vector bundles expressed by symmetrized iterated covariant derivatives - who did it first?

The (non-unique) bundle isomorphism between the bundle $J^r E$ of $r$-th order jets of sections of a vector bundle $\pi:E\rightarrow M$ and the direct sum $$\bigoplus^r_{k=0}\vee^kT^*M\otimes E\...

**8**

votes

**1**answer

308 views

### Trinity College, Cambridge, circa 1896 maths scholarship papers [on hold]

I've been searching around looking for the (maths component) of the scholarship papers to Trinity College (Cambridge) from around 1890. Can anyone provide a link to a pdf scan of these papers?
Was ...

**13**

votes

**2**answers

2k views

### A certain mathematical competition in the UK

There is a foreword, written by professor Snow, to the book A mathematician's apology.
In the foreword, it is written some thing like the following:
"Hardy was opposed to a certain mathematical ...

**30**

votes

**3**answers

4k views

### Did Euler prove theorems by example?

In his 2014 book, Giovanni Ferraro writes at beginning of chapter 1, section 1 on page 7:
Capitolo I
Esempi e metodi dimostrativi
Introduzione
In The Calculus as Algebraic ...

**15**

votes

**3**answers

713 views

### History of the analytic class number formula

The (general) analytic class number formula gives a value for the residue of the Dedekind zeta function of a number field at the point $s=1$ (or, as I prefer, the leading Taylor coefficient at $s=0$). ...

**-2**

votes

**0**answers

85 views

### What are some of the most complete genealogies of mathematical subject areas? [closed]

Cross-posted from HSM:
I am interested in the way scientific and mathematical subject areas developed (and are still developing). One of the great visual tools that can help us gain insight in how ...

**35**

votes

**8**answers

4k views

### Motivation for and history of pseudo-differential operators

Suppose you start from partial differential equations and functional analysis (on $\mathbb R^n$ and on real manifolds). Which prominent example problems lead you to work with pseudo-differential ...

**7**

votes

**1**answer

368 views

### What was Gödel's Constitutional Problem? [closed]

It is well known that Kurt Gödel had doubts concerning the US constitution and believed that it somehow was inconsistent and opened up for a dictatorial grab.
What was he thinking?

**4**

votes

**0**answers

170 views

### Origin of the name ''momentum map''

Why is the momentum map in the differential geometry of symmetries called the ''momentum'' (or ''moment'') map?

**79**

votes

**23**answers

13k views

### Has philosophy ever clarified mathematics?

I've recently been reading some standard textbooks on the philosophy of mathematics, and I've become quite frustrated that (surely due to my own limitations) I don't seem to be gleaning any ...

**1**

vote

**0**answers

595 views

### Whether to posthumously honor Grothendieck's request to stop publishing his works? [closed]

Why did Grothendieck say stop publishing his works?
https://sbseminar.wordpress.com/2010/02/09/grothendiecks-letter/
Any edition or dissemination of such texts which have been made in the past ...

**18**

votes

**2**answers

1k views

### Felix Klein on mean value theorem and infinitesimals

This is a reference request prompted by some intriguing comments made by Felix Klein.
In 1908, Felix Klein formulated a criterion of what it would take for a theory of infinitesimals to be ...

**9**

votes

**2**answers

2k views

### Ramanujan's tau function

Why was Ramanujan interested in the his tau function before the advent of modular forms? The machinery of modular forms used by Mordel to solve the multiplicative property seems out of context until I ...

**5**

votes

**5**answers

547 views

### Important results with one or more than one proof [closed]

Can you give examples of deep, important results that have only one known proof, and not just because the first proof is fairly recent, or because not many people really cared to think about it? How ...

**3**

votes

**1**answer

187 views

### Does the collection of algebraic/number-theoretic methods applied to Euclidean Geometry have a name?

I am currently writing an essay on the history of geometry. To educate myself on the subject, I sometimes read the following Wikipedia article on the history of Euclidean Geometry. It seems to me that,...

**11**

votes

**3**answers

2k views

### Has Dedekind's proof of existence of infinite sets been analyzed by historians?

This pdf by David Joyce notes that in paragraph 66 of his famous essay, Dedekind claims to prove the existence of an infinite set.
The proof exploits the assumption that there exists a set $S$ of all ...

**35**

votes

**3**answers

2k views

### Definitive source about Dirichlet finally proving the Unit Theorem in the Sistine Chapel

(This question was posted on math.stackexchange a week ago at http://math.stackexchange.com/questions/187315/definitive-source-about-dirichlet-finally-proving-the-unit-theorem-in-the-sistinbut and ...

**144**

votes

**136**answers

31k views

### Fundamental Examples

It is not unusual that a single example or a very few shape an entire mathematical discipline. Can you give examples for such examples? (One example, or few, per post, please)
I'd love to learn about ...

**4**

votes

**2**answers

228 views

### Historical reference request on Nilpotent groups

From Wikipedia:
"Abelian groups were named after Norwegian mathematician Niels Henrik Abel by Camille Jordan because Abel found that the commutativity of the group of a polynomial implies that the ...

**20**

votes

**3**answers

801 views

### A historical question: Hurwitz, Luroth, Clebsch, and the connectedness of $\mathcal{M}_g$

The connectedness of the moduli space $\mathcal{M}_g$ of complex algebraic curves of genus $g$ can be proven by showing that it is dominated by a Hurwitz space of simply branched d-fold covers of the ...

**18**

votes

**2**answers

1k views

### Context for “Coronidis Loco” from Weil's Basic Number Theory

In Samuel James Patterson's article titled Gauss Sums in The Shaping of Arithmetic after C. F. Gauss’s Disquisitiones Arithmeticae, Patterson says
"Hecke [proved] a beautiful theorem on the different ...

**2**

votes

**2**answers

369 views

### What are the sense and reference of the propositions $R \notin R$, $R \in R$, where $R=\{x \mid x \notin x\}$ in Frege's Grundgesetze?

In the paper,
Aldo Antonelli and Robert May, Frege's new science, Notre Dame J. Form. Log. 41 (2000), no. 3, 242–-270, MR 1943495.
the authors give the following quote of Frege, from his paper "&...

**5**

votes

**2**answers

640 views

### Where does the definition of “Tower of Algebras” come from?

A tower of algebras is a sequence of algebras
$$A_0 \hookrightarrow A_1 \hookrightarrow \cdots \hookrightarrow A_n \hookrightarrow \cdots$$
with embeddings $A_n \otimes A_m \hookrightarrow A_{n+m}$ ...

**62**

votes

**15**answers

7k views

### Mathematical research published in the form of poems

The article
Friedrich Wille: Galerkins Lösungsnäherungen bei monotonen Abbildungen,
Math. Z. 127 (1972), no. 1, 10-16
is written in the form of a lengthy poem, in a style similar to that
of the ...

**55**

votes

**1**answer

3k views

### Did Bourbaki write a text on algebraic geometry?

Certainly Bourbaki never wrote an introduction to algebraic geometry: we would have heard about it, right?

**64**

votes

**59**answers

15k views

### Pseudonyms of famous mathematicians

Many mathematicians know that Lewis Carroll was quite a good mathematician, who wrote about logic (paradoxes) and determinants. He found an expansion formula, which bears his real name (Charles ...

**0**

votes

**0**answers

62 views

### Reference request: Uniformly totally bounded classes of compact metric spaces are Gromov-Hausdorff precompact

The following Theorem can be found for instance here (Theorem 7.4.15):
Theorem. (author ?) Any uniformly totally bounded class $\mathfrak X$ of compact metric spaces is pre-compact in the Gromov-...

**13**

votes

**2**answers

2k views

### What are examples of theorems which were once “valid”, then became “invalid” as standard definitions shifted?

That is, results established by correct proofs within some framework, yet the manner in which their author or the general mathematical community at the time would describe these results would, in ...

**2**

votes

**6**answers

2k views

### Looking for a source for Intended Interpretation

Hao Wang writes: "The originally intended, or standard, interpretation takes the ordinary nonnegative integers $\{0, 1, 2, \ldots \}$ as the domain, the symbols $0$ and $1$ as denoting zero and one, ...

**20**

votes

**2**answers

2k views

### Euler's mathematics in terms of modern theories?

Some aspects of Euler's work were formalized in terms of modern infinitesimal theories by Laugwitz, McKinzie, Tuckey, and others. Referring to the latter, G. Ferraro claims that "one can see in ...

**8**

votes

**3**answers

741 views

### English or French translation of Gauss' “Summatio Quarumdam Serierum Singularium”

I'm interested in looking at the details of Gauss' method of determining the sign of the Gauss sum in his "Summatio Quarumdam Serierum Singularium", and I was wondering if anyone knew if there was an ...

**24**

votes

**1**answer

2k views

### More on “Transalgebraic Theories” (a 19th century yoga)?

Among the talks at occasion of the Galois Bicentennial, one is about "Transalgebraic Theories". Unfortunately I found only this article describing that fascinating idea as " an extremely powerful '...

**-4**

votes

**1**answer

284 views

### Proof of formula for $\pi$ [closed]

The number $\pi$ can be expressed as $\pi=\lim_{n\to\infty} \frac{n\sqrt[n]{-1}-n}{\sqrt{-1}}$ or more poetically $\pi=\frac{\infty\sqrt[\infty]{-1}-\infty}{\sqrt{-1}}$. Here we choose the principal ...

**1**

vote

**0**answers

56 views

### History of Cauchy-Euler Equations

As I teach a class in ODE, and following this post and Rota's paper, I wandered what is the history of the research of -
$\sum\limits_{k=0}^n a_k x^k y^{(k)}(x) = g(x),\quad \forall k=0,\...

**42**

votes

**15**answers

6k views

### Abstract Thought vs Calculation

Jeremy Avigad and Erich Reck in their remarkable historical paper "Clarifying the nature of the infinite: the development of metamathematics and proof theory" claim that one of the factors of becoming ...

**10**

votes

**1**answer

503 views

### Why did Alonzo Church choose the letter $\lambda$ as the “binding operator”?

Is there any known reason why Alonzo Church chose Greek $\lambda$ as the "binding operator" for the Lambda Calculus?

**0**

votes

**1**answer

201 views

### Pasch axiom and Pythagorean field condition?

I am looking for a reference for the claim that the Pasch axiom is equivalent to the Pythagorean field condition, and with respect to what base theory this should be true.
Since posting the question, ...

**49**

votes

**9**answers

6k views

### When have we lost a body of mathematics because errors were found?

The history of mathematics over the last 200 years has many occasions when the fundamental assumptions of an area have been shown to be flawed, or even wrong. Yet I cannot think of any examples where, ...

**64**

votes

**10**answers

7k views

### Have you solved problems in your sleep?

I have hit upon major (for me—relative to my trivial accomplishments)
insights in my research
in various sleep-deprived altered states of consciousness,
e.g., long solo car-drives extending ...

**3**

votes

**1**answer

221 views

### Have there been any claims of mathematical breakthroughs while in altered states of consciousness?

This certainly is a related question:
Have you solved problems in your sleep?
Has anyone seriously attempted to make a similar claim for other altered states, besides dreaming?
I know the claim has ...

**11**

votes

**5**answers

1k views

### Texts on the General History of Contemporary Combinatorics

I am looking for some core texts (books, book chapters, papers) about the general history of contemporary combinatorics, starting, say, from the interwar period up to today.
Texts about the history ...

**14**

votes

**5**answers

2k views

### What are hypergroups and hyperrings good for?

I came across the concept of a hyperring in two recent papers by Connes and Consani (From monoids to hyperstructures: in search of an absolute arithmetic and The hyperring of adèle classes). It's a ...

**5**

votes

**0**answers

103 views

### Historical perspectives on CAT(0) spaces

Does there exist a survey on the early developments of CAT(k) spaces, with the first motivations and the first problems considered? I looked at Bridson and Haefliger's book On metric spaces of non-...