**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 ...

**40**

votes

**4**answers

3k views

### The Arnold – Serre debate

I have read (but I cannot now find where) that Arnold & Serre had a public debate on the value of Bourbaki. Does anyone have more details, or remember or know what was said?

**2**

votes

**1**answer

160 views

### why the difference between terms and propositional variables?

Reading some old logic texts (written around 1930) I noticed that these texts make no difference between propositional variables and terms.
They do make difference between identity and truthvalue
...

**55**

votes

**14**answers

6k 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

191 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

178 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 ...

**-2**

votes

**2**answers

677 views

### Accidental, unplanned breakthroughs in Mathematics [closed]

In math/physics, or generally in science, there are many moments where the success and the triumph come from the accidental, unplanned attempts. Moreover, there are some cases that originally having ...

**45**

votes

**18**answers

7k 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 are ...

**8**

votes

**1**answer

315 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?

**7**

votes

**1**answer

452 views

### History of Jordan Canonical Form?

Can anyone suggest a reference that discusses the history of the Jordan canonical form? In particular, I am interested in:
When and how was it first stated? (I understand it was independently stated ...

**4**

votes

**2**answers

303 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 ...

**26**

votes

**1**answer

899 views

### Institutional response to “Esquisse d'un programme”

It is well-known that Grothendieck's "esquisse d'un programme" was submitted in 1984 as part as the author's application for a permanent position of "Directeur de Recherche" at the C.N.R.S. (the main ...

**20**

votes

**7**answers

1k views

### Was lattice theory central to mid-20th century mathematics?

Four years ago, I read a book on the history of mathematics up to 1970 or so. It was very interesting up until the end. The last few chapters, though, were on lattices. The author claimed that ...

**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 ...

**9**

votes

**1**answer

515 views

### Well founded induction attributed to Noether

What I know as well founded induction, namely the rule
$$ \big(\forall y.(\forall z.z\lt y\Rightarrow\phi z)\Rightarrow\phi y\big)\Longrightarrow\big(\forall x.\phi x\big), $$
whose validity is the ...

**14**

votes

**1**answer

2k 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

270 views

### History question: Roth's theorem on approximating algebraic numbers…before Roth

Roth's theorem has two universal quantifies, over irrational algebraic numbers $\alpha$ and over real $\epsilon>0$. Of course the theorem asserts in each instance that the inequality
...

**17**

votes

**1**answer

530 views

### What motivated Rademacher's contour along the Ford circles?

Apologies if this question isn't suitable for MathOverflow; I posted it on MSE here but it didn't get a response and it felt like it was on the cusp of being suitable for here.
After Ramanujan and ...

**12**

votes

**2**answers

843 views

### How did Gauss and contemporaries think of modular forms?

Accounts of modular forms say that they were studied in the early 19th century, but then define modular forms using terminology that didn't exist until the 20th century. How did the earliest ...

**5**

votes

**1**answer

328 views

### Influence of Yau's solution to the Calabi Conjecture on the field of PDEs

I remember reading a long time ago(I can't recall where, unfortunately) that Yau's solution of the Calabi-Yau conjecture introduced new techniques that were very important for the field of partial ...

**14**

votes

**1**answer

490 views

### History of Koszul complex

This is a question about history of commutative algebra. I'm curios why Koszul complex from commutative algebra is called Koszul complex? All Koszul's early papers are about Lie algebras and Lie ...

**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 ...

**7**

votes

**1**answer

254 views

### Analogy between Lagrange's Theorem and Rank-Nullity Theorem?

One can view view Lagrange's Theorem $$|G/H|=|G|/|H|$$ and the Rank-Nullity Theorem $$\dim(V/U)=\dim(V)-\dim(U)$$ as directly analogous. Does anyone know a high-level explanation of this analogy? I ...

**14**

votes

**2**answers

971 views

### Deligne Weil II

Deligne's Weil I has been published under the title "La conjecture de Weil: I" in 1974, and Weil II in 1980. So did Deligne know in 1974 that there would be a Weil II, and can one explain the period ...

**10**

votes

**5**answers

754 views

### What are good English-language sources for reading about the Luzin affair?

What are good English-language sources for reading about the Luzin affair?
I'm interested in the subject and am wondering about good historical sources.

**10**

votes

**1**answer

366 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

437 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, ...

**0**

votes

**1**answer

391 views

### What was the original/historical motivation for introducing Grothendieck (pre-)topologies

The title essentially explains it, but I'll give some background:
I'm giving a talk to some fellow grad students about the relative Picard functor which requires introducing Grothendieck ...

**9**

votes

**2**answers

492 views

### Origin of the Socle of a module

Where does the notation $\mbox{Soc}(M)$ (the sum of all simple submodules of a module $M$) first appear?

**6**

votes

**1**answer

438 views

### Where does the notation $\pi_1(X,x)$ for the fundamental group first appear?

I've spent the last half hour browsing Stillwell's translation of Poincaré's Analysis Situs and Dieudonné's History of Algebraic and Differential Topology, and I haven't found the source of this ...

**22**

votes

**3**answers

1k views

### What exactly does this diagram of Omar Khayyam represent?

Evidently Omar Khayyam (1048-1131) was quite the mathematician. He did groundbreaking work on finding geometric solutions to the cubic equation, which is all the more notable since he did not have a ...

**11**

votes

**2**answers

655 views

### Le Haut Commissariat qui surveille rigoureusement l'alignement de ses Grandes Pyramides

Yesterday I came across the following one-paragraph summary of the history of the Law of Quadratic Reciprocity in Roger Godement's Analyse mathématique, IV, p.313 (perhaps the only treatise on ...

**18**

votes

**14**answers

2k views

### Insightful books about elementary mathematics

What are some books that discuss elementary mathematical topics ('school mathematics'), like arithmetic, basic non-abstract algebra, plane & solid geometry, trigonometry, etc, in an insightful ...

**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 ...

**8**

votes

**0**answers

486 views

### Has anyone pursued Frege's idea of numbers as second-order concepts?

Gottlob Frege was a pivotal figure in the history of mathematical logic. He gave an analysis of numbers that proceeded along roughly the following lines, in his books "The Foundations of Arithmetic" ...

**18**

votes

**1**answer

1k 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 ...

**6**

votes

**4**answers

2k views

### Numerically computing $\int_0^1 \frac{1}{\sqrt{1-x^4}}dx$

In the book, "Pi and the AGM" by Borwein and Borwein, it is mentioned that Gauss computed the following integral to the eleventh decimal palce.
$\int_0^1 \frac{1}{\sqrt{1-x^4}}dx$
How did he do it? ...

**38**

votes

**18**answers

5k views

### What are some deep theorems, and why are they considered deep?

All mathematicians are used to thinking that certain theorems are deep, and we would probably all point to examples such as Dirichlet's theorem on primes in arithmetic progressions, the prime number ...

**4**

votes

**1**answer

382 views

### Where does the name “Reynolds operator” come from?

I always found it strange that, in the context of invariant and representation theory,
averaging over the group is called the "Reynolds operator". As far as I know the work of Reynolds was in fluid ...

**5**

votes

**2**answers

452 views

### When did the meaning of the term “metabelian” change?

I just realised that the meaning of the term "metabelian", when applied to groups, or Lie algebras, seems to have changed over years. (These days, it means that $[[G,G],[G,G]]$ is trivial, while in ...

**2**

votes

**3**answers

329 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

643 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 ...

**8**

votes

**1**answer

314 views

### historical antecedents of mathematical talks

Is there a general reference of how mathematical talks, say academic talks, evolve in history? Before the International Congress of mthematics, is there any antecedent of todays talks?

**1**

vote

**1**answer

242 views

### What is the name of the following theorem: dimension of complex irreducible representation divides order of group

Who proved it? When?
See also:
Irreducible Degrees and the Order of a Finite Group
http://planetmath.org/proofthatdimensionofcomplexirreduciblerepresentationdividesorderofgroup
Why would dim ...

**5**

votes

**1**answer

266 views

### Origins of Axiomatic Reasoning

Is there any evidence that axiomatic reasoning has been used prior to Thales of Milet (624-547BC), who is generally credited for the "invention" of axioms.
In this context I understand axioms in the ...

**24**

votes

**2**answers

774 views

### Origin and first uses of $\ell_p$ norms?

When exactly were $\ell_p$ norms first defined and used?
(Here is what I know, or think I know: Lebesgue and/or Riesz had something to do with them, but in some sense they go back to Minkowski, since ...

**12**

votes

**2**answers

554 views

### To what extent can fields be classified?

The study of algebraic geometry usually begins with the choice of a base field $k$. In practice, this is usually one of the prime fields $\mathbb{Q}$ or $\mathbb{F}_p$, or topological completions and ...

**2**

votes

**1**answer

166 views

### English translation of Steinitz 1910?

Does there exist an English translation of Steinitz' 1910 work "Algebraische Theorie der Körper"?
http://www.digizeitschriften.de/dms/img/?PPN=GDZPPN002167042

**12**

votes

**3**answers

927 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 ...

**11**

votes

**2**answers

932 views

### What might extraterrestrial mathematics look like? [closed]

In an extensive anthropological joint research project concerning the necessities in the development of life and civilisation my group is concerned with mathematics. This forum seems to be extremely ...