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

learn more… | top users | synonyms (1)

4
votes
2answers
79 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?
5
votes
1answer
119 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!
10
votes
3answers
178 views

Why do people prefer cosine to sine when speaking of harmonic oscillation?

In almost all of the physics textbooks I have ever read, the author will write the oscillating function as $$x(t)=\cos\left(\omega t+\phi\right)$$ My question is that, is there any practical or ...
7
votes
0answers
224 views

Did Guinness Book of Records screw this up? [closed]

Crossposted on HSM See Guinness Book of Records. Did they screw this up? It says that Fermat's Last Theorem was the longest open problem - with only 365 years. However, there are Greek problems that ...
1
vote
2answers
53 views

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

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.
0
votes
0answers
38 views

What are the levels of math? [closed]

I'm in geometry and I want to know what are the next levels of it. I was in algebra and then geometry. So does that mean. Algebra 2 comes after the geometry?
16
votes
1answer
242 views

$\sin$ vs. $sin$ - history and usage

One thing newcomers to TeX or MathJax often get wrong is that they write something like $sin(x)$ instead of $\sin(x)$ - the point being that common mathematical functions with names consisting of ...
19
votes
2answers
644 views

Approximation for $\pi$

I just stumbled upon $$ \pi \approx \sqrt{ \frac{9}{5} } + \frac{9}{5} = 3.141640786 $$ which is $\delta = 0.0000481330$ different from $\pi$. Although this is a rather crude approximation I ...
0
votes
1answer
71 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 ...
532
votes
16answers
49k views

Is $\frac{\textrm{d}y}{\textrm{d}x}$ not a ratio?

In the book Thomas's Calculus (11th edition) it is mentioned (Section 3.8 pg 225) that the derivative $\frac{\textrm{d}y}{\textrm{d}x}$ is not a ratio. Couldn't it be interpreted as a ratio, because ...
2
votes
0answers
45 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
votes
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 ...
1
vote
0answers
22 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 ...
15
votes
3answers
1k views

When the trig functions moved from the right triangle to the unit circle?

I have to write a paper about the unit circle and I'm trying to uncover some of its origins. Also, when the trig functions were expanded to angles greater than 90° and what was the rationale behind ...
0
votes
0answers
19 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
votes
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 ...
8
votes
2answers
503 views

Unpublished Discoveries by Gauss that Were Later Rediscovered and Attributed to Other Mathematicians

Karl Friedrich Gauss made many discoveries that he did not publish and that remained unknown until later mathematicians (re)discovered them. When Gauss's personal notebooks were later examined, it ...
0
votes
0answers
24 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?
6
votes
3answers
168 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 ...
98
votes
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 ...
41
votes
14answers
4k views

Examples of famous problems resolved easily

Have there been examples of seemingly long standing hard problems, answered quite easily possibly with tools existing at the time the problems were made? More modern examples would be nice. An example ...
20
votes
0answers
328 views

Why is $J$ often used to denote $\mathbb{N}$ or $\mathbb{Z}$ in older texts?

In older books, I've noticed that authors tended to use $J$ to denote (usually) the natural numbers and (less commonly) the integers. Does anyone have any idea why that might've been? A few examples ...
1
vote
0answers
47 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
vote
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
vote
1answer
54 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
votes
1answer
57 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
vote
0answers
74 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 ...
0
votes
2answers
142 views

How to calculate 3x7 by using logarithm?

This is a story about Newton I read once when I was a child. Now that book is lost and I can only tell you what I remember. When Newton was young, he had been already famous in curiosity and ...
6
votes
1answer
343 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 ...
2
votes
10answers
857 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, ...
1
vote
0answers
83 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
votes
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
votes
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: ...
27
votes
4answers
2k views

Is mathematical history written by the victors?

The question is the title of a recent piece in the Notices of the American Mathematical Society, by twelve authors (of which I am one). The contention is that traditional history of mathematics is ...
22
votes
0answers
841 views

Irrationality of $e$

I have a question about the irrationality of $e$: In proving the irrationality of $e$, one can prove the irrationality of $e^{-1}$ by using the series $$e^x = 1+x+\frac{x^2}{2!} + \cdots + ...
0
votes
1answer
42 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 ...
18
votes
1answer
655 views

A curious theorem by Peano

Let $f$ be defined on $[a,b]$ and there differentiable. Show that for every $ \epsilon>0 $ there exists a partition $\, a=a_0<a_1<...<a_n=b \,$ of $ \,[a,b] \,$ so that $$\left|\frac ...
4
votes
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 ...
3
votes
0answers
274 views

There is some intuitive idea of Pascal's 's theorem in Projective Geometry?

In projective geometry, Pascal's theorem (formulated by Blaise Pascal when he was 16 years old) determines that a hexagon inscribed in a conic, the lines that contain the opposite sides intersect in ...
1
vote
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 ...
10
votes
5answers
471 views

When can ZFC be said to have been “born”?

The "History" section of the Wikipedia article on ZFC isn't particularly helpful. The only thing I have understood from it is that ZFC had appeared after 1922. In what book or paper was ZFC first ...
2
votes
0answers
50 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 ...
8
votes
2answers
210 views

The 'abelian group' custom

This is just a question for fun: As far as I know, frequently it is considered to be customary to denote an additive commutative group as 'abelian group' in lowercase, although the term is named ...
2
votes
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 ...
15
votes
4answers
635 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 ...
4
votes
1answer
85 views

What was babylonians estimation for square root 3?

We see a lot of papers and talk about ancient Babylonians exactness of calculating the value of square root of 2. For example: ...
4
votes
1answer
163 views

Pell's Equation and the Pigeon Hole Principle

David Speyer gave a beautiful application of the pigeon hole principle here to show that Pell's equation $$x^2-Dy^2=1$$ has infinitely many integral solutions. I was wondering if anybody knows the ...
7
votes
1answer
117 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 ...
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 ...
83
votes
6answers
3k views

Why does mathematical convention deal so ineptly with multisets?

Many statements of mathematics are phrased most naturally in terms of multisets. For example: Every positive integer can be uniquely expressed as the product of a multiset of primes. But this ...