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

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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
34 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
25 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 ...
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1answer
179 views
+50

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

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 - ...
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0answers
35 views

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

It seems odd that something that looks so much like a join would get given "the wrong symbol". It's even worse when you dualise it and get something called (quite reasonably) the "meet product", but ...
0
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0answers
52 views

Learning outcomes of reading textbooks [closed]

So I've densely mined this site for the scholarly materials I need most. And have prudently written many of them down, so I can sort them if I see fit. But, are the books always the preferred method ...
5
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1answer
130 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!
1
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2answers
53 views

What is the remainder produced when the integer 2099^(2017^13164589) is divided by $99$? [closed]

I'am looking for the remainder produced when the integer $2099^{2017^{13164589}}$ is divided by $99$ ? The goal reached is to avoid large integers.
3
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1answer
69 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
84 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
75 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
46 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
25 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
23 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
22 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
26 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
21 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 ...
1
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0answers
49 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
55 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
58 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 ...
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0answers
75 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
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1answer
346 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 ...
1
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0answers
84 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 ...
0
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0answers
29 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
169 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
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1answer
43 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
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2answers
47 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 ...
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0answers
63 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 ...
2
votes
10answers
868 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 ...
3
votes
2answers
100 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 ...
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4answers
641 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
64 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 ...
4
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0answers
67 views

Unclear on why Meissel's approach to counting primes works

I am reading through the Wikipedia article on prime counting. The following is presented to describe Meissel's approach: Let $p_1, p_2, \dots, p_n$ be the first $n$ primes. Let $\Phi(m,n)$ be the ...
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0answers
38 views

Deriving the wave equation in 3 dimensions and the history of it

I'm trying to find how the wave equation was derived in 3 dimensions. Surprisingly, there isn't much information available on this apart from wikipedia of all places ...
7
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0answers
100 views

Who is “R. Drabek”?

The book "Algebra für Einsteiger" bei Bewersdorff (I think the English edition is called "Galois Theory for Beginners") starts with a nice quotation: Math is like love; a simple idea, but it can ...
6
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0answers
49 views

Proofs of Simplicity of $A_n$

There are different proofs of simplicity of the group $A_n$, and one can get at least two proofs by choosing randomly 10 books of the subject, so I will not go into what are these proofs? Rather, I ...
2
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0answers
51 views

Separability and second countability is the same thing to Halmos

I was browsing through Paul Halmos' classic book on measure theory, when I came by the following definition of separability on page $3$ in the chapter on prerequisites: Today a separable space is ...
3
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0answers
31 views

Characterizations of Nilpotent Groups

There are several characterizations of finite nilpotent groups (they are, as in wiki): $G$ is (finite) nilpotent group. Normalizer of every proper subgroup is bigger than the subgroup. Every ...
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0answers
22 views

History of graph minor concept

I can't find the correct reference to the first introduction of graph minor. There are plenty of strong results on minors (Kuratowski theorem, well-quasi-ordering by Robertson and Seymour, ...) and ...
7
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1answer
118 views

Serendipitous mathematical discoveries in recent times

As of today, most important results in mathematics are conjectured long before they are proven. Are there any examples of (important) mathematical discoveries that were proven by chance rather than ...
98
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19answers
4k views

Past open problems with sudden and easy-to-understand solutions

What are some examples of mathematical facts that had once been open problems for a significant amount of time and thought hard or unsolvable by contemporary methods, but were then unexpectedly solved ...
14
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3answers
607 views

Why is the word associative used to represent the concept of the associative property?

For the commutative property ... According to wikipedia: The word "commutative" is a combination of the French word commuter meaning "to substitute or switch" and the suffix -ative meaning ...
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0answers
23 views

What is the origin of the distinction between assignable and inassignable number?

Leibniz described his infinitesimals as being inassignable numbers in a number of texts, e.g., in his Cum Produisset that was analyzed in detail by H. Bos in a seminal text dating from the 1970s. The ...
3
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0answers
25 views

Reference on the history of ergodic theory

I'm looking for some good books on the history of ergodic theory. I'm a Ph.D student in the field, and I am taking Steven Weinberg's advice to learn about the history of my field: ...
0
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0answers
32 views

Why do we define a limit/continuous function/vector space etc. the way we do?

I am looking for any material dealing with the evolution of what now are standard mathematical definitions. One example what I am looking for: Let $(a_n)_{n\in\mathbb N}$ be a sequence with ...
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0answers
60 views

Proportion and disproportion in the Pythagorean theorem.

Is there any accepted explanation about why the square areas of the Pythagorean theorem are proportionated if the referential lengths of the legs and the hypothenuse are disproportionated? I think ...
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0answers
57 views

On the History of the Concept of Module

I am interested in knowing a little bit more about the history of the concept of module. As far as I know, there are two primary meanings of the word in mathematics, namely, modules as derived from ...