# Tagged Questions

Use this tag for questions concerning history of mathematics, historical primacies of results, and evolution of terminology, symbols, and notations. Consider if History of Science and Mathematics Stack Exchange is a better place to ask your question.

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### Ignoring the lack of rigor, is this a fair argument to make when considering if 0^0 should be equivalent to 1? [closed]

The Professor of Mathematics argued that 0^0 is undefined because the limits $0^x$ and $x^0$ as x approaches 0 don't agree. That seemed logical to me, but then Scott pointed out in the comments that ...
37 views

### Looking for in depth material on a formal propositional calculus using only the NAND connective

I am looking for secondary literature on a formal propositional calculus which has the NAND connective as its sole connective. I am coming upon many pages which briefly state that Nicod had shown ...
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### Why is a $\sigma$-algebra defined as such?

We know that a $\sigma$-algebra is a collection of sets closed under countable set operations. My question is: how was it determined that this is the right collection? i.e., how was it determined ...
45 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 ...
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### 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 ...
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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 ...
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 ...
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### 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?
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### 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 +...
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### 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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### 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 spaces&...
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### 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 ...
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### 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 ...
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### 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?
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### 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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### 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 ...
576 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 ...
112 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 ...
174 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 ...
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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 ...
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### 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.
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### 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 ...
655 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 - ...
118 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 (...
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### 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!
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### 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 ...
106 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?
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### 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 ...
56 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 ...
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### 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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### 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 ...
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### 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 these ...
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 "...
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### Explanation of the term rings [duplicate]

why do we call rings rings ? Is it random name or is it because of some structural property?
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### 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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### 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 "peaks")?...
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### 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 use?...
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### 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 it'...
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### 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 ...
379 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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### 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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### 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: math/...
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### 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 ...
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### 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 non-...
59 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 ...
990 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, ...
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 ...
135 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 ...