Biographies, philosophy of mathematics, mathematics education, recreational mathematics, communication of mathematics

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5
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1answer
308 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
1answer
427 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
1answer
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
1answer
241 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
2answers
900 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
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5answers
720 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
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1answer
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 ...
1
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0answers
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!
8
votes
1answer
411 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
1answer
363 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 ...
8
votes
2answers
457 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
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1answer
406 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
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3answers
934 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
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2answers
647 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 ...
16
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12answers
1k 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
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6answers
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 ...
7
votes
0answers
442 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" ...
16
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1answer
873 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
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4answers
990 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? ...
35
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17answers
4k 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
1answer
356 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
2answers
416 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
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3answers
298 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
1answer
621 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
1answer
302 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
1answer
231 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
1answer
253 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
2answers
756 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 ...
11
votes
2answers
477 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
1answer
155 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
3answers
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 ...
10
votes
2answers
841 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 ...
14
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3answers
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 ...
12
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2answers
724 views

An Euler-proof that cannot be repaired?

Ed Sandifer writes on Euler's wonderful work on prime numbers: The sum of the series of reciprocals of prime numbers $\frac{1}{2}+\frac{1}{3}+\frac{1}{5}+...$ is infinitely large, and is infinitely ...
14
votes
5answers
626 views

Historical use of figures in geometry

I was surprised to learn from John Stillwell's comment in answer to the question, "Can the unsolvability of quintics be seen in the geometry of the icosahedron?", that There is not a single ...
11
votes
2answers
501 views

Why did Voiculescu develop free probability?

I was recently asked why Voiculescu developed free probability theory. I am not very expert in this and the only answer I was able to provide is the classical one: he was challenging the isomorphism ...
1
vote
1answer
131 views

Understanding the rationale behind “batch means” estimation

Hello all, I am implementing an MCMC algorithm for my work, and I've come upon something in the literature which I just can't understand. Specifically, I am attempting to estimate the amount of ...
5
votes
1answer
141 views

How did Hankel determinants get the name Hankel-Hadamard?

My question concerns the name for determinants of Hankel-matrices $H = (s_{i+j})_{i,j = 0}^n$. In the classical textbook of Shohat and Tamarkin (1943) "The Problem of Moments", these determinants are ...
15
votes
2answers
924 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 ...
23
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0answers
736 views

Does a proof of Selberg's 3.2 inequality exist?

A well-known inequality of Montgomery and Vaughan (generalizing a result of Hilbert) states that $$ \left |\sum_{r \neq s} \frac{w_{r} \overline{w_{s}} }{\lambda_r - \lambda_s} \right| \leq \pi ...
7
votes
3answers
312 views

Meaning of historical fluxion notation

I've noticed that in 18th century English books on calculus writers would say that 'the fluxion of $ax$ is $a\dot{x}$' and 'the fluxion of $x^n$ is $n x^{n-1} \dot{x}$'. What does this extra ...
36
votes
4answers
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
2answers
986 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 $A\subset \mathbb{N}$ ...
6
votes
0answers
208 views

History of the characterization of commutative Artin rings

When it comes to the world of "classical" (pre-homological) Noetherian commutative algebra, I tend to think of most of the results (Krull's intersection theorem, the principal ideal theorem, etc.) as ...
4
votes
1answer
215 views

Historical precursor for Peano's axioms of a linear space?

Peano is typically credited with giving the first abstract definition of a vector space (1888): http://www-history.mcs.st-and.ac.uk/HistTopics/Abstract_linear_spaces.html Apparently, Peano credits ...
6
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7answers
930 views

famous papers/results by non professional mathematicians [duplicate]

Possible Duplicate: What recent discoveries have amateur mathematicians made? Dear overflowers Out of curiosity: do you know any famous papers and/or results by non professional ...
11
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0answers
395 views

Unpublished Lecture Notes

Hi, Overflowers There was a time (not so long ago) where lecture notes were not published, not commonly at least, and their reproduction was expensive. In my case, that was precisely the time when ...
19
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1answer
376 views

Biholomophic non-Algebraically Isomorphic Varieties

Recently, when writing a review for MathSciNet, the following question arose: Is it true that two smooth complex varieties that are biholomorphic are algebraically isomorphic? The converse is true ...
11
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0answers
498 views

Why did Bourbaki not use universal algebra?

I have seen a discussion about Bourbaki’s usage of categories before. So let me ask a different question: why did he not use universal algebra? Well, universal algebra is not much older than category ...
18
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5answers
2k views

Why did Bourbaki ignore the theory of categories? [closed]

QUESTION They had plenty of time to adopt the theory of categories. They had Eilenberg, then Cartan, then Grothendieck. Did they feel that they have established their approach already, that it's too ...