Use this tag for questions concerning history of mathematics, historical primacies of results, and evolution of terminology, symbols, and notations.

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2
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1answer
110 views

Definition of the $\sec$ function

I am a postgraduate student of mathematics from Slovenia (central Europe) with quite some experience in mathematics. While answering questions on this site, I often encounter the function $\sec(x)$ ...
5
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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 ...
2
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2answers
74 views

Reason behind standard names of coefficients in long Weierstrass equation

A long Weierstrass equation is an equation of the form $$y^2+a_1xy+a_3y=x^3+a_2x^2+a_4x+a_6$$ Why are the coefficients named $a_1, a_2, a_3, a_4$ and $a_6$ in this manner, corresponding to $xy, x^2, ...
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4answers
495 views

What is the definition of a positive integer?

I am reading the book "The Number-System of Algebra (2nd edition)". At the starting of page-4 the author writes: A positive integer is a symbol for the number of things in a group of distinct ...
7
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4answers
207 views

“important” math concepts to pass on to next generation of creatures at some cataclysm [closed]

This may be somewhat silly to ask, but I couldn't resist the temptation. The idiosyncratic physicist Richard Feynman was once asked If, in some cataclysm, all of scientific knowledge were to be ...
7
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2answers
141 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
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2answers
206 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 ...
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0answers
18 views

Lebesgue - differentiation of monotone functions

I was wondering how Lebesgue himself proved the continuous case. Since my French is not good enough to read his own book, I was wondering if someone knows if there exists a translation ? (at least of ...
2
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1answer
75 views

History of the Enneper Surface

I was just wondering whether anyone could tell me more about the Enneper surface and its history (why it is important historically in the development of mathematics), or where to go in order to learn ...
2
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1answer
79 views

Soft Question: Algorithms: Will We (One Day) No Longer Need to Study Algorithms? [closed]

I'm just now getting into the study of algorithms and it seems like as computers get faster and faster the need to study algorithms may begin to diminish. How likely is it that in 50 years there ...
2
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1answer
56 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 ...
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3answers
160 views

Did the world experience a “mathematical drought” at any time in history?

Mathematics history goes back pretty far: the Greeks were studying it in 600BC, the Babylonians and Egyptians all the way back beyond 2000BC, and there's even some evidence of prehistoric mathematics. ...
2
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2answers
261 views

Are there still undiscovered simple/fundamental theorems? [closed]

Well, if it is undiscovered, then actually we cannot know whether it exists or not. But i am wondering if theorems/equalities like $Pythagorean$ $Theorem$ or maybe $Fermat's$ $Last$ $Theorem$ have ...
3
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5answers
316 views

Can mathematics be traced back to a fundamental system of truths?

I'm not sure exactly how to state this question, or even if it belongs here. Still, I hope you will consider it, as I find it very interesting: Most of the results I've seen in mathematics come from ...
1
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0answers
51 views

Historical study of dynamical system

I am currently doing a historical study on my school project 'study of ODE' which slowly shift to the study of dynamical system as I am interested in pursuing my study of ode from linear system, phase ...
4
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0answers
39 views

C. Neumann passage in Latin from *Annali di Matematica Pura ed Applicata*

Neumann, Carl. “Theoria nova phaenomenis electricis applicanda.” Annali di Matematica Pura ed Applicata 2, no. 1 (August 1868): 120–128. doi:10.1007/BF02419606. p. 121: Nova introducitur ...
3
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4answers
159 views

Soft question: Examples where implications derived from mathematical models failed to describe reality

I have always been fascinated by how well conclusions drawn from mathematical models could fit reality, so I wondered if there are any counter examples. In "Gödel, Escher, Bach" I could already find ...
7
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2answers
242 views

How to explain ✳43.3 and ✳43.31 in Whitehead and Russell's PM?

Take ✳43.3 for example, I presume $ P = R |Q $ where R is fixed. $ R| $ is the relation between $R|Q$ and $Q$, ie. $ R| = \hat{P} \hat{Q} \{ P = R|Q \} $ $Ɑ‘R|= \hat{Q}\{ E! R|‘Q \}$ Given that ...
2
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1answer
65 views

How did the Symmetric group and Alternating group come to be named as such?

The Dihedral group makes sense, "Di" means two, and "hedral" means.. shape I think (I've just realised how much of what I think words mean are guesses based on experience) like a "polygon" is a 2d ...
3
votes
2answers
323 views

How is it that treating Leibniz notation as a fraction is fundamentally incorrect but at the same time useful?

I have long struggled with the idea of Leibniz notation and the way it is used, especially in integration. These threads discuss why treating Leibniz notation as a fraction and cancelling ...
3
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0answers
70 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 ...
3
votes
1answer
70 views

A Concept Which Has Been 'Specialized' In the Course of History

There are so many concepts which have been generalized during history of mathematics - the concept of "number" may be the best examples. On the other hand, a concept may have been specialized ; the ...
2
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2answers
108 views

History Of Algebra

Did the Indians invent algebra which was taken by Arabs and introduced by them to Europe as their own invention? Or did the Arabs invent algebra?
2
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0answers
19 views

Borel's result on transcendence measure

In "Sur la nature arithmétique du nombre e" (Comptes rendus de l'Académie des Sciences 128 (1899), 596-9) Borel presented his result on transcendence measure for e. This can be restated as follows: ...
4
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2answers
136 views

Sources on Hamilton's Discovery of Quaternions

This is a strange question and I'm not sure where to put it; I'm currently writing an essay for a history of maths course, and I've chosen the topic of Hamilton's discovery of the quaternions. I ...
7
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1answer
279 views

Exactly who popularized the modern definition of domain and codomain of functions?

In Whitehead and Russell's Principia, domain is the referents of relation; converse domain is the relata. Modern function in mathematics is just one special case of relation whose referent is unique ...
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1answer
58 views

The Jacobi nome $q$

Does anyone know why $q = e^{-\pi K'/K} = e^{\pi i \tau}$ is called the nome? Is there a historical reason? Does the word nome mean something in Latin or German?
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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), ...
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0answers
56 views

How did Fourier find the formula for the fourier series coefficients?

The modern proof use the dot product but did he use that ?
2
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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
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1answer
71 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 ...
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1answer
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Cauchy gave 1st example of a Lie algebra in 1847 & exterior product in 1853‽

I read in PDF pg. 5 of this that Cauchy gave the first example of a Lie algebra in 1847: It also claims that he invented the exterior product in 1853. Does anyone have references for this?
3
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5answers
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Not pi - What if I used 3? Teaching pi discovery to K-6th grade

So, in ancient Mesopotamia they knew that they didn't really have the correct number (pi) to determine attributes of a circle. They rounded to 3. If you acted as though pi = 3, what shape would you ...
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3answers
104 views

Who was the first person to construct the real numbers by Cauchy sequences in $\mathbb{Q}$

Who was the first person to construct the real numbers by Cauchy sequences in $\mathbb{Q}$? Was it Cauchy himself?
2
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1answer
214 views

Famous deaf mathematicians?

There are some really inspiring examples of blind mathematicians. However in my experience I also think problems inside my head using words. So I was wondering if there are some examples of deaf ...
2
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0answers
66 views

Who proved Fundamental Theorem of algebra using Liouville's theorem?

One of the most famous proofs of the Fundamental Theorem of Algebra involves Liouville's theorom stating that a bounded entire function in constant. Who first came up to the idea of deriving FToA ...
5
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1answer
157 views

More unknown / underappreciated results of Euler

What are some of the more unknown and/or underappreciated things that Euler discovered? The man has done so much that there's bound to be notable results that most people aren't aware of. This could ...
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31answers
16k views

Examples of mathematical results discovered “late”

What are examples of mathematical results that were discovered surprisingly late in history? Maybe the result is a straightforward corollary of an established theorem, or maybe it's just so simple ...
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0answers
39 views

Indecomposable groups vs. indecomposable objects

An object $X$ in a category $\cal C$ with an initial object is called indecomposable if $X$ is not the initial object and $X$ is not isomorphic to a coproduct of two noninitial objects. A group $G$ ...
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0answers
77 views

Was the Weierstrass function constructed or discovered?

Reading Halmos' I want to be a mathematician, he mentions a continuous function without a tangent. Naturally, I was curious to see how such a function could possibly exist, and I imagined it to be ...
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0answers
32 views

History of Moment Generating Functions

I am beginning to appreciate how important Moment Generating Functions (MGFs) are regarding various common probability distributions and the ways their expectations/variances are calculated. My ...
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0answers
168 views

History of Mathematics Essay Feedback

A while ago I posted asking for advice on writing a History Essay for a University undergrad maths course: Tips on writing a History of Mathematics Essay The essay is below, if anyone would be ...
5
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1answer
151 views

Who invented the Riemann Sphere?

I have seen suggested that someone other than Riemann first came up with the Riemann Sphere. Is this correct? And if so, who did invent it?
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2answers
163 views

Have any definitions in mathematics been redefined

Based on certain intuitions and motivations we make certain definitions and then proceed to use these concepts in further developing our intuition. For example, we have an intuition that a line has ...
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0answers
103 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 ...
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0answers
36 views

Who proved Dirac's thoerem?

I was browsing wikipedia page on Paul Dirac and I found under things he is known for Dirac's theorem about Hamiltonian graphs. But while browsing this other article on Gabriel Andrew Dirac I found the ...
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0answers
100 views

Earliest precursor to category theory

In the Historical notes section of the Wikipedia article on category theory, it is mentioned that in 1942-1945, Samuel Eilenberg and Saunders Mac Lane, in the course of their work in algebraic ...
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1answer
218 views

Tips on writing a History of Mathematics Essay

I'm a third year maths undergrad currently taking a 'History and Development of Mathematics' module. As a maths student, you can probably guess my skills at writing an essay are a little (if not ...
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0answers
118 views

Why do Mathematicians use $u$ and $v$ as variables?

I'm sure this has happened to you as well: you are reading some hand-written work, the variables used are $u$ and $v$, and at some point the handwriting becomes unclear and you cannot distinguish the ...
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2answers
173 views

Are there examples that we know a number is a rational number but we do not know what is its numerator and denominator?

Are there examples that we know a number is a rational number but we do not know what is its numerator and denominator? In order to say clearly, this number should given by a certain formula, such as ...