# Tagged Questions

**4**

votes

**2**answers

418 views

### Who first defined quantum integers?

Who first gave the defintion of quantum integers
$$ [m]_q = \frac{1 - q^m}{1 - q} $$ and addition as
$$ [m]_q \oplus_q [n]_q = [m]_q + q^m [n]_q $$ and multiplication as
$$ [m]_q \otimes_q [n]_q = ...

**5**

votes

**3**answers

257 views

### A. Markov's papers?

A. Markov published several papers on his chains, starting in 1906, so it is written, in the journal:
(1) Извѣстія Физико-математического общества при Казанском университете
I am surprised by the ...

**1**

vote

**0**answers

136 views

### Motivating mathematics(particularly algebraic number theory) through historical problems [closed]

Most mathematical textbooks start a subject by going backwards, historically. They will define the terms that were invented to solve a problem in their polished form and then use these definitions and ...

**6**

votes

**1**answer

341 views

### Different approaches to forcing

There are many different approaches to the forcing method, and I am looking for all known such approaches. So my question is:
Question 1. Which different approaches to set theoretic forcing are ...

**6**

votes

**0**answers

223 views

### Silver's unpublished work on reverse Easton iteration

Silver was the first person who used the method of reverse Easton iterations in connection with large cardinals, and used it to force the failure of $GCH$ at some measurable cardinal.
At most papers ...

**1**

vote

**0**answers

107 views

### First Description of how to Remove Radicals from Equations

Who first described the technique of removing radicals as indicated in the answers to questions Tools for Removing Radicals from Equations and Rewrite sum of radicals equation as polynomial equation ? ...

**10**

votes

**1**answer

302 views

### Elements of the method of forcing in some papers of N. N. Luzin

In the paper
Eléments de la méthode de forcing dans quelques travaux de N. N. Lousin. (French) [Elements of the method of forcing in some papers of N. N. Luzin] Amphora, 469–479, Birkhäuser, ...

**7**

votes

**2**answers

475 views

### Survey of the history of calculus?

Boyer 1939 is a nice readable survey of the history of the calculus, but it's showing its age. Discussing the notion of instantaneous velocity, he has:
Mathematics knows no minimum interval of ...

**9**

votes

**2**answers

432 views

### Origin of the term “generic” in set theory

In set theory, in particular the context of forcing, if $M$ is a model of $\sf ZFC$ and $P\in M$ is a partial order, we say that $G\subseteq P$ is a generic filter (or $M$-generic or generic over $M$) ...

**3**

votes

**1**answer

373 views

### Levi's book on Leibnizian calculus

Raphael Levi learned from Leibniz at a late stage in Leibniz's career. This might be a definite advantage for understanding Leibniz. Leibniz did not elaborate some of the philosophical principles ...

**2**

votes

**3**answers

569 views

### The Hidden Aspect of Set Theory [closed]

This question is inspired by a similar question at the beginning of Kunen's new book, "Set Theory".
Many mathematicians believe they are exploring a "real" universe. In such a Platonic point of ...

**1**

vote

**1**answer

96 views

### Original sources for two theorems by Bass, Matlis and Papp

It is an interesting fact that a commutative ring $R$ is noetherian if and only if direct sums of injective $R$-modules are injective, and if and only if every injective $R$-module is a direct sum of ...

**22**

votes

**2**answers

1k views

### Was Vinogradov's 1937 proof of the three-prime theorem effective?

Was Vinogradov's first proof of the three-prime theorem effective?
Reasons for my question: Vinogradov presented his proof in 1937 in a monograph; the English translation by K.F. Roth and A. ...

**13**

votes

**2**answers

814 views

### Who first defined _simply connected_, reference?

The following definition is due to Donald J. Newman:
A connected open subset $D$ of the plane $\mathbb C$
is simply connected
if and only if its complement $\widetilde D = \mathbb C \setminus D$
...

**9**

votes

**2**answers

379 views

### Historical quotation search: Equations/formulae in (Latin?) prose, before modern symbolic notation

I have been trying, without success, to find a vaguely-remembered quotation: the quadratic equation (or perhaps the quadratic formula), given in (Latin?) prose, along lines like “Consider that ...

**4**

votes

**1**answer

488 views

### Origin of “Woodin cardinal”

Sorry if this is a completely stupid question (I'm a not a set-theorist, though I've been doing some reading in the subject), but I was wondering, specifically, about the exact provenance of the name. ...

**16**

votes

**2**answers

611 views

### Felix Klein on 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 ...

**11**

votes

**2**answers

487 views

### Riemann's quote cited by Lakatos: what is the context?

"If only I had the theorems! Then I should find the proofs easily enough."
This quote is generally attributed to Bernhard Riemann. In particular,
on page 9 in Proofs and refutations by Imre ...

**8**

votes

**0**answers

244 views

### From Frege to Gödel - German equivalent?

I know this question does not quite fit here, but I felt it could best be answered here. I recently stumbled upon the book From Frege to Gödel, which is a sourcebook containing some of the most ...

**18**

votes

**2**answers

2k views

### Where are Georg Cantor's Original Manuscripts?

Georg Cantor is famous for introducing transfinite numbers and set theory.
A main part of his mathematical point of view about this new type of "numbers" and this new "realm of mathematics" cannot be ...

**54**

votes

**14**answers

5k 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 ...

**7**

votes

**0**answers

178 views

### Reference Request: Topological h-cobordism theorem in higher dimensions

I think this question on math.stackexchange is more appropriate on mathoverflow. Correct me, if you don't think so.
The h-cobordism theorem is true in the topological and in the smooth category in ...

**2**

votes

**0**answers

169 views

### Does anyone know what is the right reference for the following simple lemma from harmonic analysis?

The lemma says that given $\lambda\geq 1$, $p\geq 1$, $a_j\geq 0$, for a collection of balls $\{B_j\}_{j\in\mathbb{N}}$ in $\mathbb{R}^n$, it holds
$$\|\sum_j a_j\chi_{\lambda B_j}\|_p\leq ...

**4**

votes

**2**answers

283 views

### Who first used the cross-ratio to describe shapes in hyperbolic geometry?

I was reading this Wikipedia article today:https://en.wikipedia.org/wiki/Shape#Similarity_classes
and I realized that it strongly resembles the use of coss-ratios as "shape parameters" in hyperbolic ...

**25**

votes

**9**answers

2k views

### Are there some other notions of “curvature” which measure how space curves?

I am learning differential geometry and have a few questions on curvature. -- Background:
Gauss invented "Gauss curvature" to measure how surface curves.
Riemann gives an ingenious generalization ...

**12**

votes

**1**answer

1k views

### Fourier transform of the unit sphere

The Fourier transform of the volume form of the (n-1)-sphere in $\mathbf R^n$ is given by the well-known formula
$$
\int_{S^{n-1}}e^{i\langle\mathbf a,\mathbf u\rangle}d\sigma(\mathbf u) = (2\pi)^{\nu ...

**8**

votes

**1**answer

2k views

### What is the source of this E̶r̶d̶ő̶s̶ quote?

Namely, the following one
"All problems appeared once in the [American Mathematical] Monthly."
I remember reading it several years ago... When I first posed the question, I believed that I had ...

**10**

votes

**1**answer

319 views

### Who is Petrov of the Petrov-Galerkin method?

I was not able to find the origin of the name Petrov in the Petrov-Galerkin method for the numerical approximation of PDEs.
Wikipedia refers to a certain Alexander G. Petrov, but it is still not ...

**8**

votes

**1**answer

419 views

### “'Category' was defined in order to define 'functor', which was defined in order to define 'natural transformation'”

I am looking for the source (and original version) of the above oft-repeated quotation. Mac Lane mentions it in Categories for the Working Mathematician, attributing it to Eilenberg-Mac Lane; however, ...

**12**

votes

**6**answers

1k views

### The origins of forcing in mathematical logic and other branches of mathematics

As everyone knows, forcing was created by Cohen to answer questions in set theory.
Question 1. What are the first applications of set theoretic forcing in other branches of mathematical logic, like ...

**16**

votes

**1**answer

890 views

### Arnold on Newton's anagram

Arnold, in his paper
The underestimated Poincaré, in Russian Math. Surveys 61 (2006), no. 1, 1–18
wrote the following:
``...Puiseux series, the theory which Newton, hundreds of years before ...

**2**

votes

**3**answers

300 views

### Good Books on the history of Zero

I am looking for books that discuss the origins of the zero, specifically the differences in the use and concept of the zero number among different civilizations (considering also the Mesoamerican ...

**6**

votes

**1**answer

624 views

### What are current trends/questions in algebraic logic?

What are current trends/questions in algebraic logic? I mean the research developed by Paul Halmos.
Could anyone give some references for the overview of its history? Any overview of its application ...

**12**

votes

**3**answers

904 views

### When was the continuum hypothesis born?

The question Solutions to the Continuum Hypothesis states that the continuum hypothesis was posed by Cantor in 1890. In http://en.wikipedia.org/wiki/Continuum_hypothesis the year 1878 is quoted ...

**14**

votes

**3**answers

1k views

### Who introduced the terms “equivalence relation” and “equivalence class”?

Consider that the question does not concern the origin of the ideas of equivalence relation and equivalence class. It exactly concerns the origin of the terms "equivalence relation" and "equivalence ...

**15**

votes

**2**answers

941 views

### Where did Sophus Lie write the group commutator for two one parameter groups

If $X,Y$ are vector fields and $\def\Fl{\operatorname{Fl}}\Fl^X_t$ and $\Fl^Y_t$ their local flows, let $[\Fl^X_t,\Fl^Y_t]:= \Fl^Y_{-t}\Fl^X_{-t}\Fl^Y_t\Fl^X_t$ denote the group commutator of the ...

**36**

votes

**4**answers

3k views

### What is the source of this famous Grothendieck quote?

I've seen the following quote many times on the internet, and have used it myself. It is usually attributed to Grothendieck.
It is better to have a good category with bad objects than a bad category ...

**21**

votes

**2**answers

1k views

### The Erdős-Turán conjecture or the Erdős' conjecture?

This has been bothering me for a while, and I can't seem to find any definitive answer. The following conjecture is well known in additive combinatorics:
Conjecture: If $A\subset \mathbb{N}$ ...

**8**

votes

**0**answers

425 views

### Reference/quote request: “All of combinatorics is the representation theory of $S_n$”

I think I remember reading somewhere a glib (or is it deep?) quote, perhaps due to Rota?, which was something like
"All of combinatorics is essentially [or can be reduced to?] the representation ...

**11**

votes

**1**answer

216 views

### What is flexible about flexible algebras?

A possibly non-associative algebra is flexible if it satisfies the identity $$(xy)x=x(yx).$$ This is clearly a very weak form of associativity —and obviously an associative algebra is flexible— but it ...

**3**

votes

**0**answers

121 views

### Citation for subset complement result

Let $S=\lbrace s_1,\ldots,s_n \rbrace \subset \lbrace1,\ldots,2n\rbrace$. Consider two operations on $S$: the complement $C(S)=\lbrace 1,\ldots,2n \rbrace \setminus S$ and a reflection* ...

**3**

votes

**0**answers

201 views

### Where was the arithmetic zeta function of a scheme first defined?

Let $X$ be an arithmetic scheme, that is, a scheme of finite type over the integers. We denote the set of closed points of $X$ by $|X|$. For every $x\in|X|$, write $N(x)$ for the cardinality of the ...

**21**

votes

**2**answers

1k views

### Similarities between Post's Problem and Cohen's Forcing

Remark: I have since learned that G.H. Moore addresses this question in the third reference listed at the end of this post, beginning on p. 157 in which he cites a letter from Kreisel to Gödel dated ...

**4**

votes

**1**answer

611 views

### Ancient method to study Archimedean spiral

It is well-known the properties of Archimedean spiral ($\rho = k\phi$) which is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant ...

**5**

votes

**0**answers

259 views

### Sophus Lie on the symplectic foliation theorem

Given a Poisson manifold $(P,\{\cdot,\cdot\})$, its characteristic distribution $\mathcal C$ is the singular tangent distribution on $M$ generated by the Hamiltonian vector fields,i.e.
$$\mathcal ...

**6**

votes

**1**answer

342 views

### Where do the Kähler Identities first appear?

The Kähler identities (sometimes known as the Hodge identities) are an important collection of relationships between operators on the exterior algebra of a Kähler manifold. These relationships ...

**6**

votes

**1**answer

845 views

### Deligne's letter to Looijenga from 1974

Hello,
I wonder if anyone has a copy of Deligne's letter to Looijenga from 1974 mentioned as reference [26] in Bessis' paper Finite complex reflection arrangements are $K(\pi,1)$ from 2006, see ...

**15**

votes

**1**answer

466 views

### The Riemann zeros and the heat equation

The Riemann xi function $\Xi(x)$ is defined, with $s=1/2+ix$, as
$$
\Xi(x)=\frac12 s(s-1)\pi^{-s/2}\Gamma(s/2)\zeta(s)=2\int_0^\infty \Phi(u)\cos(ux) \, du,
$$
where $\Phi(u)$ is defined as
$$
...

**11**

votes

**7**answers

2k views

### What are some Applications of Teichmüller Theory?

I'm trying to collect some specific examples of applications of Teichmüller Theory. Here are some things I have collected thus far:
No-wandering-domain Theorem (Sullivan)
Theorems of Thurston ...

**8**

votes

**1**answer

535 views

### Who was Hermann Künneth?

Question as in the title:
Who was Hermann Künneth? Where can I find some biographical information beyond what is available on Wikipedia?
The well-known Künneth formula, for example in the form of ...