3
votes
0answers
28 views

Cambridge Maths Tripos Papers

Does anyone know where I can find Cambridge Maths Tripos Papers for the 1980s?
6
votes
0answers
40 views

Who did first use the concept of “supremum”?

Is there one specific person, who first defined the concept of "supremum"? If so: In which work? In my textbooks or by a quick search on the internet, I did not find an answer to my question.
3
votes
2answers
105 views

Motivating mathematics(particularly algebraic number theory) through historical problems.

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 ...
1
vote
3answers
107 views

History of category theory

I am searching some information about the origins of the category theory. Anyone know where can I read about those topics? Thanks!
1
vote
0answers
32 views

recommend me some texts on the history of the non-western mathematics

I would like to self study the detailed history of the non-western mathematics. I have started the literature of Barton (7th Ed.) but it primarily concentrated on Western and American Mathematics. ...
0
votes
0answers
29 views

Areas of Nice Shapes known to Greeks

The Greeks had known how to find the areas of a triangle, rectangle, circle etc., and possibly, Archimedes invented these formulas. Recently, I read that given a parabola in a plane and a line ...
7
votes
1answer
129 views

Which hot math research fields became insignificant later on?

In history (for last 150 years), which math research fields were hot (popular) at their time , but whose results became insignificant (almost useless) later on? The reason I ask this question is ...
2
votes
2answers
105 views

Example of a proof using the axiom of commensurability

I'm teaching our intro to proofs course (well, one of them) and one of the classic illustrations of an overturned "axiom" is the Greek axiom of commensurability, which stated in geometric terms the ...
9
votes
1answer
95 views

Any book on major (recent) math discovery (results) in an easy understanding way?

All: Can anyone recommend a book which illustrate major (recent) math discoveries (results) in an easy understanding way ? For "recent discoveries", I meaning something discovered in last 50 years. ...
10
votes
2answers
256 views

What meaning did Riemann assign to $dx$?

Detlef Laugwitz wrote a monumental biography of Riemann. The book was translated into English by Shenitzer. Laugwitz discusses Riemann's fundamental essay Uber die Hypothesen, welche der Geometrie ...
9
votes
2answers
218 views

History of the matrix representation of complex numbers

It is well-known to many that $\mathbb{C}$ can be represented by matrices of the form $\left[ \begin{array}{cc} a & b \\ -b & a \end{array} \right]$. For example, see this question or this ...
0
votes
1answer
25 views

Source for original article by Euler

I am looking for Euler's article E19, namely E19 De progressionibus transcendentibus, seu quarum termini generales algebraice dari nequeunt. Auct. L. Eulero. The terms of the sequence given by ux = ...
2
votes
1answer
43 views

Origin of Slater's condition

I've been looking all over the internet to answer this question: Slater's condition is a commonly used to certify that strong duality holds in a convex optimization problem. Although used in many ...
3
votes
1answer
179 views

What is this myth/legend and origin of related ideas?

There is a story I recently heard but the story teller (who read about it someone on the Internet) have forgotten the majority of the story, so there is little I can work on: my search attempts went ...
7
votes
1answer
87 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. ...
6
votes
6answers
296 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
73 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
110 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
55 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
41 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
420 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 ...
11
votes
3answers
711 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
49 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
38 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
108 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
99 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
184 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
288 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
74 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!
13
votes
1answer
272 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
163 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 ...
8
votes
1answer
115 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 ...
3
votes
1answer
61 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
162 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
138 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
136 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
169 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
68 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
33 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
67 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
99 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
76 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
175 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
32 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
60 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
17 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
121 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 ...