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

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3
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5answers
311 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
47 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
36 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
150 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
votes
2answers
232 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
62 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
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2answers
240 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
67 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
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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
100 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
16 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: ...
3
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2answers
132 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
votes
1answer
268 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 ...
2
votes
1answer
49 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?
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), ...
1
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0answers
55 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
66 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 ...
10
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1answer
80 views

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
137 views

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 ...
2
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3answers
93 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
171 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
65 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
votes
1answer
147 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 ...
84
votes
30answers
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 $G$ ...
4
votes
0answers
74 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 ...
3
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0answers
30 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 ...
2
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0answers
149 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
votes
1answer
142 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?
1
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1answer
144 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 ...
7
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0answers
98 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 ...
0
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0answers
33 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 ...
4
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0answers
97 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
169 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 ...
3
votes
0answers
113 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 ...
8
votes
2answers
171 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 ...
1
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0answers
52 views

Who invented the standard construction of finite fields (and field extensions)?

The title says it all, but just to be clear I mean the construction of taking $k[x]$ modulo an irreducible polynomial of suitable degree. Was it an open problem for any considerable amount of time, ...
4
votes
1answer
66 views

What is the history of this theorem about the finite sum of a polynomial?

I discovered and proved the following theorem back in high school, and have waited patiently to hear something about throughout my college career (which is nearing it's end, hope to have finished my ...
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5answers
326 views

who invented division and why we do division in those steps told?

i know how to divide but i dont quit understand why we use those steps told in schools. like for example ...
7
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6answers
345 views

Evaluating the reception of (epsilon, delta) definitions

There is much discussion both in the education community and the mathematics community concerning the challenge of (epsilon, delta) type definitions in real analysis and the student reception of it. ...
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0answers
35 views

The “enabler” of Maxwell's equations

Is it possible to point to a specific development in mathematics that allowed Maxwell's equations to happen? Similarly to Newton's laws of physics that depended on the invention of calculus? And ...
8
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0answers
178 views

How did Cohen invent forcing?

A couple of popular maths book, I forget which stated that Cohen invented Forcing. Now, generally I've noticed that there is a history which allows one in hindsight to show that how certain ...
3
votes
1answer
73 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 ...
5
votes
2answers
459 views

What fields (and operators acting on those fields) might form the basis of alien mathematics?

Addition and multiplication, according to most histories, arose in human civilizations out of a need to count a finite number of objects, and then later on especially, to measure land. What might be ...
12
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9answers
799 views

Why did we define the concept of continuity originally, and why it is defined the way it is?

The concept of continuity is a very important idea in topology. Though I am using it all the time, but indeed I don't know what is the original purpose for us to define this concept. And I also don't ...
3
votes
1answer
81 views

Why might one be inclined to think that polynomials of the form $\cos(n\arccos{x})$ would minimize error in Lagrange interpolation?

I was first introduced to Chebyshev polynomials (of the first kind) in the form $T_n(x)=\cos\left(n \operatorname{arccos}(x)\right)$. The usual recurrence relation was then derived from using trig ...
3
votes
1answer
320 views

sin(x) infinite product formula: how did Euler prove it?

I know that $\sin(x)$ can be expressed as an infinite product, and I've seen proofs of it (e.g. Infinite product of sine function). I found How was Euler able to create an infinite product for sinc by ...
2
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2answers
157 views

Which small area of mathematics had fully developed already and thus no more research in this area?

Which small area of mathematics had fully developed already and thus no more research in this area? For example, no more PHD research in Euclidean Geometry anymore.
2
votes
3answers
141 views

Mathematician's names in structures.

I would like to know how it is that mathematical objects come to receive the name of a mathematician. Do these mostly happen through the author's proposal, or is it a process that takes more time? ...