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
40 views

Kempe's proof of the four colour theorem

What exactly was Kempe's error in his proof of the four colour theorem? What I understand of his general idea is by the following case: Suppose an uncoloured "country" is surrounded by countries of ...
2
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2answers
74 views

Ideas for a history of math paper (with an emphasis on the mathematics), having to do with 19/20th century logic?

So I'm currently taking a history of math course and I need to write a 15 page paper in place of my final. It's a 400 level course (high undergrad) so the paper needs to have emphasis on the ...
0
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1answer
75 views

Seemingly contradictory results [duplicate]

The following infinite sums produce remarkable results. $1+2+3+4+...=-\frac{1}{12}$ $1-2+3-4 +...=\frac{1}{4}$ So how are these results compatible with the statement; that integers are closed ...
54
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17answers
3k views

Good “history of mathematical ideas” book?

All too often, mathematical history books include far too much material on the private lives of the personalities involved and not enough information on the actual ideas. Mathematics is a living ...
0
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0answers
17 views

Cartesian coordinates conventions

Is there any historical account of how did the Cartesian coordinate system get its current conventions of orientation and representation? Are there any mathematical reasons for these conventions?
0
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0answers
18 views

Weiertrass equation of an elliptic curve.

We know that every elliptic curve is a non-singular $\textbf{cubic}$ projective curve (curve of genus 1), but we can transform this in the Weiertrass form $$y^2 + a_1xy + a_3y = x^3 + a_2x^2 +a_4x ...
1
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0answers
41 views

Hermite's identity for sum of floor function

In Hermite's 1884 paper "Sur quelques conséquences arithmétiques des formules de la théorie des fonctions elliptiques", volume 5 of Acta Mathematica, pages 310-315, he proves what is often called ...
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0answers
24 views

On the origin of the notion of polynomial between Banach spaces

I have already asked here a few questions about polynomials in Banach spaces (Counterexample of polynomials in infinite dimensional Banach spaces, Mujica's "Complex analysis in Banach ...
7
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2answers
164 views

How did Leibniz prove that $\sin (x)$ is not an algebraic function of $x$?

In the Wikipedia article about transcendental numbers we can read the following: The name "transcendental" comes from Leibniz in his 1682 paper where he proved that sin(x) is not an algebraic ...
8
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2answers
74 views

Any surviving contemporary manuscripts by ancient mathematicians?

As I understand it, most of what we know about ancient mathematics comes from copies, quotations, and summaries by later scribes and scholars. Medieval Arab mathematicians in particular are given ...
-3
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1answer
60 views

Why are there two different notations for negation in boolean logic?

For the boolean variable $x$, there are two notations for its negation: $\neg x$ and $\bar x$. So why are there two different notations?
5
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2answers
61 views

Original usage of 'Bénabou cosmos'

A (Bénabou) cosmos is a bicomplete closed symmetric monoidal category (see, for example, the $n$Lab). However, I can't find the paper where Bénabou first uses this term - googling turns up nothing. ...
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0answers
35 views

Who extended the Euler Product Formula to all real $s>1$?

I believe Euler discovered this identity but only wrote them for particular values of $s$, then Chebychev extended to real $s>1$. However, I read in the book Riemann's Zeta Function, H.M. Edwards ...
10
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2answers
550 views

What does “Mathematics of Computation” mean?

I visited this link: http://www.ams.org/journals/mcom/1950-04-030/S0025-5718-50-99474-9/ And I a bit confused by its title "Mathematics of Computation". I am not a native English speaker. Could ...
0
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0answers
27 views

need information about the history of the Hotelling and Bodewig method.

I need information about Hotelling and Bodewig, who they were and why the developed this method. anything will help, references to articles, links, or any other information. link to the method: ...
2
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1answer
97 views

Origin of delta

Why does delta mean change? What is the origin of delta? I understand that upper-cased delta is used in this way and that delta is the fourth letter of the Greek alphabet. I also read that delta is ...
8
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0answers
157 views

Fréchet L-Spaces

According to the paper The emergence of open sets, closed sets, and limit points in analysis and topology famous mathematician Maurice Fréchet who introduced the concept of metric spaces has also ...
4
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2answers
64 views

Looking for details on historical math anecdote

My memory is very sketchy here so bear with me. A fairly prominent 19th or 20th century mathematician was captured by a military force, probably invaders. He claimed that he was just a civilian, a ...
6
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1answer
41 views

Epicycles as precursors of Fourier series

How convincing an argument can be formulated to claim that the Ptolemaic epicycles were actually an early precursor of Fourier series? Ptolemy lived ~200AD, and so well pre-dates Fourier ~1800.
1
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1answer
40 views

Which are the most used and correct nomenclature for gradient, divergence, curl and Laplace operator in differents contexts?

I used to write these operator in this way: $\vec{\nabla}$ for divergence and gradient and for Laplace operator $\vec{\nabla}^2$. But I have noticed that in some books and website divergence is ...
0
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2answers
635 views

Is it to the students' advantage to learn the language of infinitesimals? [closed]

A colleague of mine asked an interesting question reproduced below with his permission. It is reasonable to ask whether it is to the students' advantage to learn the language of infinitesimals - ...
6
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0answers
117 views

Why is the symbol for the exterior product a meet rather than a join?

I've moved this over to HSM. It seems odd that something that looks so much like a join [see below] would get given "the wrong symbol". It's even worse when you dualise it and get something called ...
4
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1answer
157 views

Why is $s$ used for arc length?

Why is $s$ used for arc length? I looked around online, but I can't find a definite answer. Thank you!
3
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1answer
77 views

Circle is similar to a polygon with infinite number of sides

It is know from the time of Euclid, that a circle is similar to a polygon with infinite number of sides. But this ^^ is informal. Do you know any formalization where it appears that a circle is a ...
6
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2answers
100 views

Why was $\aleph$ (aleph) chosen for infinities?

Why did Cantor choose a letter from the Hebrew alphabet to represent infinities, rather than using some Greek letter?
0
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1answer
81 views

Can we build mathematics without studying it?

This is one question that I can never get the answer of, because I am too young at this moment. My question is that can a common person like me, not a genius, just a normal person, build mathematics ...
2
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0answers
52 views

A Taylor Expansion before Taylor

Taylor expansion was introduced in its currently well known form by Brook Taylor. Though the concept as this page says, has been formulated by James Gregory. Among his other works, Gregory established ...
0
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0answers
30 views

Konig's theorem and perfect graphs

I want to understand why perfect graphs are so named and why are they relevant. Consider the following statement from wikipedia's article on Konig's theorem. A graph is perfect if and only if its ...
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0answers
26 views

Where does the name of the hypergeometric distribution come from?

I understand what it does and how to get there, but why is it called hypergeometric? All the other distributions I know of have rather self-explanatory names like "binomial" or "exponential", or are ...
0
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0answers
26 views

Rooms and Passages Domains

I'm currently looking into Dirichlet Laplacian and Neumann Laplacian boundary conditions on the rectangle and came across the Rooms and Passages domains, I was just wondering if anyone knew why ...
24
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4answers
1k views

Were “real numbers” used before things like Dedekind cuts, Cauchy sequences, etc. appeared?

Just the question in the title, I'm trying to understand how something like analysis could be developed without formal constructions of the real numbers. I'm also very interested, if the answer is ...
0
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0answers
28 views

Explanation of the term rings [duplicate]

why do we call rings rings ? Is it random name or is it because of some structural property?
1
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0answers
23 views

Wiener's construction of the Wiener Measure

I am writing an essay about Norbert Wiener and I already have sufficient info about him in general and his history, but now I would like to know how he constructed the Wiener measure. I found some ...
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0answers
54 views

what is the origin of the proof via peaks?

What is the history of the proof of the existence of a monotone subsequence via peaks as found for example here as well as in problem 6, page 4 here (where they are called "giants" instead of ...
1
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1answer
57 views

History of Norbert Wiener

I have to write an essay about Norbert Wiener. A bit about him in general, but mostly about his contribution to stochastic processes. Does anyone have any suggestions concerning materials I should ...
3
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1answer
59 views

Evolution of Definitions

I try to understand how the definitions of mathematics have evolved (or formulated)... I'll use the epsilon-delta continuity definition as an example to ask my question... It may seem trivial, but ...
1
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0answers
81 views

Why are $\pi$ and $e$ simply referred to as “pi” and “e”?

I'm aware of the names "Archimedes' constant" and "Euler's number" for $\pi$ and $e$ respectively, but these don't seem to be used very commonly. Even in school I remember $\pi$ and $e$ being almost ...
6
votes
1answer
362 views

Generalizing complex numbers: Is there a mathematical system isomorphic to 3 dimensional space?

As I understand it, complex numbers: $ax+i$ are isomorphic to two-dimensional space. Quaternions consist of $4$ dimensions. Is that right? Wikipedia says "quaternions form a four-dimensional ...
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0answers
90 views

On publication regarding right ideals of a ring and the sublanguages of science [closed]

As some of you may know (or may experience by searching some of my threads), I have been working on the applications of right ideals of a ring to the study of language (in particular, to the so-called ...
0
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0answers
17 views

Prime Counting: In truncation rule #2 mentioned in an AMS.org article, I'm unclear how “special leaves” work?

I'm reading through an AMS.org article on prime counting. The article covers the history of prime counting and focuses on improvements to the Meissel-Lehmer method. It is the improvement on page ...
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0answers
34 views

Did Ackermann produce a finitary consistency proof of second-order $PRA$?

In Wilhelm Ackermann's Doctoral Thesis (it is claimed, by Richard Zach, for one, in his paper "The Practice of Finitism: Epsilon Calculus and Consistency Proofs in Hilbert's Program", arXiv: ...
6
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3answers
184 views

What are the disadvantages of non-standard analysis?

Most students are first taught standard analysis, and the might learn about NSA later on. However, what has kept NSA from becoming the standard? At least from what I've been told, it is much more ...
0
votes
1answer
52 views

What is the origin of the name Hermitian and Unitary matrix?

A matrix $H$ is Hermitian if $H ^\dagger = H$. A matrix $U$ is Unitary if $U^\dagger=U^{-1}$. My question is: Why do we name matrices of such properties Hermitian and Unitary? These names are ...
4
votes
2answers
58 views

Where do hash functions come from?

I have some basic understanding of how hash functions work, however, I have no idea of how mathematicians created them. Were them a byproduct of a non cryptografics related research or were them a ...
1
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0answers
65 views

Theorems in math that have lead to significant development in other areas of mathematics? [closed]

Several theorems in mathematics are guided by a sheer curiosity, but at times, certain tools are created out of necessity. Are there any theorems in mathematics, that although bear, have no ...
1
vote
10answers
953 views

What's an example of an infinitesimal?

If you want to use infinitesimals to teach calculus, what kind of example of an infinitesimal can you give them? What I am asking for are specific techniques for explaining infinitesimals to students, ...
2
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0answers
31 views

Trying to understand how Lehmer's method represents a simplification of Meissel's method for counting primes

My question stems from a wikipedia article on prime counting. The details on Meissel's method can be found in the wikipedia article. As I understand, Meissel proposed two formulas which I asked ...
4
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2answers
126 views

Peano Arithmetic before Gödel

If I understand correctly, Gödel was the one to discover how to encode finite sequences of integers in Peano Arithmetic, with his Chinese Remainder Theorem trick (his "beta function"). As a ...
15
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4answers
679 views

What did Whitehead and Russell's “Principia Mathematica” achieve?

In philosophical contexts, the Principia Mathematica is sometimes held in high regard as a demonstration of a logical system. But what did Whitehead and Russell's Principia Mathematica achieve for ...
3
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1answer
65 views

Why Frobenis concerned the groups which today called “Frobenius Group”?

From their work, it seems that the Ancient mathematicians were investigating a mathematical object not as a fun, but to solve some problem occurred in earlier work of someone. Lagrange, Galois, Abel ...