6
votes
1answer
69 views

Who first proved the fundamental theorem of finitely generated (or finite) abelian groups?

The fundamental theorem of finitely generated abelian groups (or maybe just finite abelian groups) is well-known and can be found in just about any text on the theory of groups or abstract algebra. ...
4
votes
6answers
156 views

Interviews of famous modern mathematicians

I was wondering, are there any good collections of interviews of famous modern mathematicians? It can be text interviews, or audio or video recordings. I am not sure what exactly I mean by "modern". ...
2
votes
1answer
64 views

Descartes on imaginary unit.

I heard once that Descartes defining the imaginary unit had to talk about the imagining of rise of the spirit over the real numbers because definition based on square root of a negative number could ...
3
votes
1answer
81 views

History of $p$-adic numbers

I'm interested in learning about the historical motivation and development of $p$-adic numbers. I haven't been able to find any books on the topic. I'd appreciate any references, including to more ...
0
votes
1answer
53 views

About connection and topology

I'm looking for a good book (or article) about history of topology, and specially about the connection concept. I appreciate all your suggestions!!!
0
votes
1answer
40 views

Reference Request: Nicole Oresme history

It says on Wikipedia that [Nicole Oresme] also worked on fractional powers, and the notion of probability over infinite sequences, ideas which would not be further developed for the next three and ...
4
votes
5answers
394 views

How to defend Mathematics from “ignorant” people? [closed]

Some of my friends are blaming me to stop talking about and studying Math. But I love Math so much and I do Math almost everyday. The problem is that some of my friends told me "go and get a life". I ...
7
votes
2answers
624 views

History of notation: “!”

Does anyone know where the factorial "!" symbol came from? I can't decide if it is my favorite or least favorite notation in mathematics...
3
votes
1answer
40 views

Translation of Paolo Ruffini's work on Galois theory

Paolo Ruffini famously wrote a work providing the first proof of the unsolvability of the quintic with the extraordinary title "Teoria Generale delle Equazioni, in cui si dimostra impossibile la ...
2
votes
0answers
26 views

Which came first, energy minimization or pde?

I'm interested in a historical perspective on pde. I would like to know more about the original derivation of pde. It seems like d'Alembert was working on the one dimensional wave equation $$ ...
2
votes
1answer
101 views

Reference Request - Early Calculus Papers

Question: I am looking for good references on the early calculus papers. Optimally, I want emphasis on the mathematics itself and I want that mathematics to be translated into modern terminology and ...
1
vote
3answers
95 views

Mathematical logic and foundations of mathematics in the 20th century

I would like some references regarding the foundations of mathematics in the 20th century, and mathematical logic, e.g. (1) I want to understand what happened to the foundation, what originated the ...
9
votes
1answer
169 views

Ramanujan's personification of small positive integers

I dimly recall reading somewhere (perhaps in "The Man Who Knew Infinity"?) that Ramanujan associated personalities (perhaps it was mystical personalities, e.g. specific gods and goddesses?) with small ...
13
votes
1answer
274 views

l'Hopital's questionable premise?

Historians widely report that l'Hopital's 1696 book Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes contains a questionable premise expressed by an equation of type $x+dx=x$ ...
5
votes
1answer
65 views

eulers original derivation for the Euler–Maclaurin formula?

Please does someone know a good description of how Euler did derive his summation formula? Thank you!
12
votes
1answer
213 views

History of Lagrange Multipliers

How did Lagrange discover Lagrange multipliers? Also, was it related to his work on the calculus of variations? And how did he originally understand/implement the technique?
3
votes
1answer
159 views

Errors of Euler interpretation?

To complement the recent post on Euler's errors, I would pose the following question: what common errors of Euler interpetation appear in the literature? What errors are attributed to Euler's work in ...
23
votes
5answers
2k views

Euler's errors?

What mathematical errors is Leonhard Euler known to have made? PS: As I wrote in a comment below: "However, I would not consider proof to be an error merely because it's not a proof by present-day ...
7
votes
1answer
103 views

First usage of the symbol ∈

Concerning a book [1] I am reading the symbol $\in$ was first used by Giuseppe Peano and is the first letter $\epsilon$ (epsilon) of the word ἐστί (means "is"). Does anyone know in which work of Peano ...
2
votes
1answer
59 views

Enlightening books giving a guided tour of mathematics, in a style that Gian-Carlo Rota would not mind?

I am currently reading Gian-Carlo Rota's Indiscrete Thoughts. What more can I say apart from "the man can write"? (In other words, you should really read it if you are interested in mathematics.) I ...
1
vote
3answers
127 views

What is the “Principle of permanence”?

While reading the book "The Number-System of Algebra (2nd edition)." term "Principle of permanence" occurred to me. I remember I had read this in the book "Beginning algebra for college students.". I ...
5
votes
2answers
137 views

Why the $\log$ is so special?

When I first learn about the logarithm function $\log$ or $\ln$. My professor said that $\log x$ is a function that when we derive we get the inverse function $1/x$. This $\log$ becomes very popular ...
7
votes
2answers
125 views

History of Morse theory.

How can I get good references which give many information about history of Morse theory? Now I am interested in how and who found that Hessian have a lot of data. Thank you for your helping!!
4
votes
2answers
116 views

Works on Calculus by Newton and Leibniz (primary sources)

I'm trying to find PDFs or hard copies of the following works from the dawn of calculus. Does anyone know where I could find English translations of them? Newton - De analysi per aequationes numero ...
2
votes
1answer
55 views

Need help locating a paper

One of the references of the paper Paulo Régis C. Ruffino, A Criticism on "A Mathematician's Apology" by G. H. Hardy (arXiv:1112.4499 [math.HO]) is: Vershik, A. M. – A Dangerous Joke, The ...
3
votes
0answers
65 views

Grothendieck's manuscript on differential manifolds

I have a Japanese book on Grothendieck's life and his mathematical works. The author writes that Grothendieck wrote manuscripts(over 250 pages) on "the category of manifolds" and "differential ...
16
votes
1answer
7k views

Who discovered this number-guessing paradox?

In this math.se post I described in some detail a certain paradox, which I will summarize: $A$ writes two distinct numbers on slips of paper. $B$ selects one of the slips at random (equiprobably), ...
2
votes
0answers
30 views

Reference for Hilbert numbers

I've been studying a little bit of number theory, and during such studies I came across this interesting reference to Hilbert numbers, that is, numbers of the form $4n +1$. My question is a purely ...
0
votes
1answer
62 views

Reference on Infinite Dimensional Manifold

I am studying manifold. For comprehension, I read the site http://en.wikipedia.org/wiki/Manifold, and there is some information about infinite dimensional manifold. Now I have two questions or ...
7
votes
0answers
94 views

To whom is the proof that $A_n$ is simple for $n\geqslant 5$ due, in Rotman's book?

The proof in Rotman's book, Introduction to the Theory of Groups, that $A_n$ is simple consists of the observation that $A_n$ is generated by the $3$-cycles, and hence that if a normal subgroup $H\lhd ...
3
votes
1answer
72 views

Source request of axiom of Archimedes

I'm a little confused with axiom of Archimedes has a proof since it is an axiom. So I'm guessing there's a historical reason that this property of ordered field was given such a name. Is there any ...
6
votes
2answers
165 views

Popular Topics in mathematical analysis(Functional analysis)

I am writing a text(as a duty by my mentor) dealing with the recently popular topics(including open problems) in mathematical analysis. At first part, I briefly introduced the mathematical ...
1
vote
0answers
28 views

Is there a source linking Robinson's work in wing theory with his theory of infinitesimals?

Abraham Robinson worked in applied mathematics for several decades. MathSciNet lists 12 articles by Robinson in wing theory. His production included the book Robinson, A.; Laurmann, J. A. Wing ...
2
votes
0answers
56 views

The first proof for Poincare lemma in history

How can I get a reference about the first proof of Poincare lemma in history? I already know some methods of proof, but I do want to know the original approach. Thanks for your help!
0
votes
0answers
16 views

original reference for Gauss' integration formula

The Gauss $n$-point quadrature formula provides an approximation for an integral in terms of a weighted sum of $n$ function values and this approximation is exact for all polynomials of degree at most ...
3
votes
1answer
100 views

Recommendations for books that provide a good survey of the history of mathematics, and are meant to be read by mathematicians/mathematics students?

Preferably: The book should not be fixated upon the "standard/popular" accounts of the Greeks (which usually begin with Pythagoras, move on to Euclid and Aristotle, and end with Hypatia). The book ...
37
votes
0answers
1k views

Theorem that von Neumann proved in five minutes.

In "How To Solve It", George Pólya writes: "There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it ...
2
votes
0answers
192 views

Is there any English version of Récoltes et Semailles?

I felt like my question isn't appropriate for MO, so I though maybe I should post it here. I want to read Alexander Grothendieck's "Récoltes et Semailles", but I don't know any French. I can easily ...
1
vote
1answer
94 views

How can I find who discovered this integral?

I need to find the first paper/author to document this integral $$\int\log^nx\;\mathrm dx=(-1)^n\;\Gamma(n+1,-\log x)\quad n\in\Bbb N_0$$ To prevent this in the future, is there a service in which I ...
9
votes
1answer
115 views

The average of the roots of a polynomial equals the average of the roots of its derivative

Background: It's straightforward to check that the average (i.e. the mean) of the roots of a nonlinear polynomial equals the average of the roots of its derivative: if $$f(x) = x^n + a_{n-1} x^{n-1} ...
0
votes
2answers
453 views

Mathematics and slavery [closed]

I think that ancient Greek mathematics is a miracle. Think about Euclid. Developing mathematical arguments from a small set of axioms is incredibly modern. And their influence on modern mathematics is ...
0
votes
1answer
49 views

Who first described commutative algebraic theories explicitly?

Lately, I've been thinking that the concept of a commutative algebraic theory is really, really important. So I'm curious; who had the honor of first discovering this concept? In particular, I'd like ...
1
vote
2answers
148 views

Is there any surprising elementary probability problem that result in surprising solution like the Monty Hall problem?

For recreational purpose, i haven't seen a interesting elemetary probability question quite a while. Is there any surprising elementary probability problem that result in surprising solution like the ...
1
vote
1answer
112 views

Reform of math symbols for high school texts

I am looking for references to papers and resources related to reforming math symbols for introductory courses at middle or high school level. Pointers to other forums also welcome. Eidt: For ...
4
votes
0answers
69 views

The Leibniz rule in Euler's works

Does anyone know if the Leibniz rule (the method of differentiation under the integral sign), or a variation thereof, has ever appeared in any of Euler's papers? Any references would be appreciated. ...
1
vote
3answers
122 views

Golden ratio / Fibonacci which branch of math?

Friends, The Golden ratio / Fibonacci sequence are studied under which branch of math? Can you recommend some good textbooks on the subject? Thanks
4
votes
0answers
39 views

Reference? filler: IRS, Rhind Papyrus, High-school algebra

I believe something like this was included as a filler in one of the MAA journals many years ago. I am searching for the exact reference (for the filler, or an earlier source). Someone dies, and ...
1
vote
1answer
467 views

History of polynomial arithmetic

How did the notions of polynomial addition,multiplication and division develop historically? The fact that this correspondence with the integers exists seems to be of great importance and is not at ...
7
votes
2answers
134 views

Definition Topological Space

Consider the definition of a topological space: Topological Space: A topology on a set $X$ is a collection $\mathcal{T}$ of subsets of $X$ such that $\emptyset,X \in \mathcal{T}$. The union of ...
5
votes
5answers
242 views

Leisure reading for an undergraduate student

I am a freshman at a local university. I never really had much passion for math, but I always did well in math exams . I attribute this lack of passion to rote learning/emphasis on methods/formulas ...