# Tagged Questions

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92 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 ? ...

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**1**answer

297 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, ...

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votes

**2**answers

448 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 ...

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votes

**2**answers

412 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 $M$) ...

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**1**answer

366 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 ...

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**3**answers

545 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 ...

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vote

**1**answer

94 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 ...

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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. ...

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793 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 $\widetilde D = \mathbb C \setminus D$
...

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**2**answers

365 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 ...

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**1**answer

481 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. ...

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600 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 ...

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**2**answers

480 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 ...

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**0**answers

239 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 ...

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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 ...

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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 ...

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**0**answers

174 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 ...

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167 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**

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**2**answers

278 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 ...

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votes

**8**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 ...

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**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 ...

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**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 ...

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**1**answer

312 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 ...

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167 views

### How to find old papers on Notices of AMS [duplicate]

I need some papers published on notices of AMS almost 40 years ago.
Does someone know if there is any online database that provide these papres? Thank you!

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**1**answer

409 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, ...

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**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 ...

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**1**answer

853 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 ...

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votes

**3**answers

295 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 ...

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**1**answer

619 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 ...

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897 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 ...

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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 ...

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**2**answers

911 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 ...

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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 ...

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**2**answers

973 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 $A\subset \mathbb{N}$ ...

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**0**answers

411 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 ...

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**1**answer

203 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 ...

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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* ...

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**0**answers

194 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 ...

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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 ...

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votes

**1**answer

575 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 ...

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256 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 ...

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votes

**1**answer

335 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 ...

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**1**answer

815 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

455 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
$$
...

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**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

524 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 ...

**3**

votes

**0**answers

237 views

### A Question Regarding Boolean-valued Models

What were the intuitions motivating the creation (or discovery, if you will) of Boolean-valued models? I have searched for the Scott-Solovay paper on the subject, but to no avail. There also seems to ...

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votes

**3**answers

432 views

### Origin of the theorem on the existence of the smallest field of definition of an affine variety

Weil proved the following theorem in his book Foundations of Algebraic Geometry, p.19.
The proof is somewhat involved.
I wonder if the theorem is his original.
Theorem
Let $K[X_1,\dots, X_n]$ be the ...

**16**

votes

**1**answer

1k views

### On a theorem of Galois

I am currently teaching Galois theory and this week, I mentioned the following theorem of Galois :
Let $P(x) \in \mathbf{Q}[x]$ be an irreducible polynomial of prime degree. Then $P$ is solvable by ...

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**1**answer

480 views

### Smallest dimension of nontrivial representation of a simple Lie algebra over `$\mathbb{C}$`

The question involved here is natural and very classical, but I'm unsure what has been formally stated and proved in the literature. The only approach I know involves assembling facts that apparently ...