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

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Historical motivation for Hilbert's Third problem

What was the historical motivation for Hilbert's third problem? Why did Hilbert feel it was worthy of including on his published list? Hilbert's Third problem: Say that two polyhedra are scissors ...
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0answers
22 views

$A(x+p)²-B(x-p)²=y$, historical/math reference

I'm trying to build a reminder of all that I found about the quadratic function over the years. Here I came across this form of quadratic equation that I did not know: A(x+p)²-B(x-p)²=y I have no ...
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2answers
73 views

Does axiom of foundation/regularity protect against Russell-like paradoxes?

In ZF set theory the axiom of regularity (also called axiom of foundation) says that: In all nonempty sets x there is an element y such that x∩y=∅ As I been told that the intention of the axiom ...
7
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1answer
40 views

Geometry and land

The word "geometry" in Greek means "measurement of Earth/land". This may imply that geometry was originally invented in order to solve problems related to land. Are there historical accounts of ...
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0answers
43 views

Mathematics department e-mail addresses [closed]

I have noticed that many mathematics departments (a little over half of the public and private Group I departments) follow the name@math.univ.edu format. Does anyone know of a reference to a ...
10
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2answers
89 views

What is a good book, or article, that explains the history of fourier analysis?

What is a good book on the history of Fourier Analysis? I'm looking for a book which explains how it came to be and what the mathematicians (or physicists) were thinking when they came up with it. If ...
8
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4answers
110 views

Which was defined first to represent $\underbrace{a+a+a+\cdots+a+a+a}_{n \text{ terms}}$? $n\times a$ or $a \times n$?

When we are talking about multiplication, we often use it without knowing which one was defined first and which one was defined because of its commutative property. Here I want to know which one was ...
0
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1answer
53 views

How did Newton calculate 3x7 by 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 ...
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0answers
57 views

Hard-to-put-together but easy-to-prove results

What are the most important examples of theorems and definitions which are post factum obvious, i.e., hard to put together but easy to understand and use (and prove, in the case of theorems) once you ...
3
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2answers
167 views

What does it mean by acta?

There are a lot math journals with title "acta" includes, for instance, Acta Mathematica, acta arithmetica, etc. Would you explain what "acta" means?
2
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0answers
39 views

Where do divisors on curves come from?

I've been learning about Riemann surfaces and the Riemann-Roch theorem, and I've been able to experience some of its great power. However, I'm curious as to what the history behind divisors on curves ...
3
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0answers
32 views

Cambridge Maths Tripos Papers

Does anyone know where I can find Cambridge Maths Tripos Papers for the 1980s?
8
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0answers
75 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 ...
4
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0answers
62 views

math historian who don't belong to academia

Is there examples of math historian who don't belong to academia? Is it possible for professionally non-academician to perform good work in the field of the history of mathematics and publish? Does ...
0
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0answers
49 views

When do two points coincide in euclidean geometry?

The 4° common notion in the Elements of Euclid says: "Things which coincide with one another equal one another". Many authors have interpreted this sentence as a principle of superposition that could ...
6
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0answers
45 views

Who did first use the concept of “supremum”?

Is there one specific person, who first defined the concept of "supremum"? If so: In which work? In my textbooks or by a quick search on the internet, I did not find an answer to my question.
1
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1answer
55 views

In Whitehead&Russell's PM's ✳210, how can the product of $\lambda$ be not a member of $\lambda$?

Take ✳210.23 for example: Assuming $\kappa$ is a classes of classes such that, of any two, one is contained in the other, i.e. $\alpha, \beta \in \kappa .\supset_{\alpha, \beta} : \alpha \subset ...
1
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1answer
28 views

Etymology of the word “function” in mathematics

What is the etymology of the word "function" (i.e. a map) in mathematics. How does (historically) the etymology of the word function relate to the mathematical definition and the mathematical concept ...
1
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1answer
26 views

In Whitehead&Russell's PM, What is $\max_p$'s converse domain?

Here is the definition of upper limit. If I'm not mistaken, $\max_P$'s converse domain is the universal set $V$. The definition appears to be limiting the converse domain of $\operatorname{seq}_P$ ...
3
votes
2answers
108 views

Motivating mathematics(particularly algebraic number theory) through historical problems.

Most mathematical textbooks start a subject by going backwards, historically. They will define the terms that were invented to solve a problem in their polished form and then use these definitions and ...
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3answers
109 views

History of category theory

I am searching some information about the origins of the category theory. Anyone know where can I read about those topics? Thanks!
1
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0answers
33 views

first example of backwards induction?

In Mathematics Magazine 28(1954/55), 21-46, Richard Bellman presents a proof for the theorem which says that the geometric mean of $n$ numbers is always not greater than the arithmetic mean: the proof ...
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0answers
32 views

recommend me some texts on the history of the non-western mathematics

I would like to self study the detailed history of the non-western mathematics. I have started the literature of Barton (7th Ed.) but it primarily concentrated on Western and American Mathematics. ...
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5answers
1k views

What is the meaning of set-theoretic notation {}=0 and {{}}=1?

I'm told by very intelligent set-theorists that 0={} and 1={{}}. First and foremost I'm not saying that this is false, I'm just a pretty dumb and stupid fellow who can't handle this concept in his ...
0
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0answers
40 views

Determinant - derivation of the general formula and its history [duplicate]

I know the formula for calculating matrix determinant. What's I'm wondering is where did that general formula come from? And why determinants are so important? Obviously they are useful in finding ...
4
votes
1answer
82 views

Origin and usage of $\therefore$ and $\because$

I've recently read a book which used the sign $\therefore$ (for "therefore"). It was more or less clear from the context what was meant, but I looked it up among the AMS LaTeX symbols just to be ...
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0answers
29 views

Areas of Nice Shapes known to Greeks

The Greeks had known how to find the areas of a triangle, rectangle, circle etc., and possibly, Archimedes invented these formulas. Recently, I read that given a parabola in a plane and a line ...
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0answers
22 views

How has the definition of a tensor changed since Tullio Levi-Civita's definition?

To get a good grounding in tensors, I'm reading the book *The Absolute Differential Calculus (Calculus of Tensors) (Dover Books on Mathematics) Paperback by Tullio Levi-Civita. I'll then move on to a ...
7
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1answer
134 views

Which hot math research fields became insignificant later on?

In history (for last 150 years), which math research fields were hot (popular) at their time , but whose results became insignificant (almost useless) later on? The reason I ask this question is ...
2
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0answers
61 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: ...
18
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4answers
3k views

Why is an image called an “image”?

Given a function $f : A \to B$, the image, denoted by $\operatorname{Im}f$ is the set of all $f(x)$ where $x \in A$. Why do we call this set the image? When was it first used, and what motivated its ...
22
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2answers
2k views

Math symbol in German thesis from 1963

I have the following math symbol in a German thesis written in 1963. Is it anything more than just a function name? It is used in the following context and then goes on to state that "If the ...
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0answers
50 views

In Whitehead and Russell's PM, are homogenous relations the only ones that have relation numbers?

Given the definition of ordinal similarity: ✳151.01 $P \overline{smor} Q = \hat{S}\{ S\in 1\rightarrow 1. C‘Q=ConverseD‘S. P=S^;Q\}$ Df. $Q$ has to be homogeneous, otherwise $C‘Q$ is meaningless. ...
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1answer
49 views

History of Mathematical Formulas

I just wondered why in calculating something for example Variance we square the difference of the value and its Arithmetic Mean and do not take the absolute value of the difference? Are there books or ...
18
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6answers
2k views

What is the motivation for quaternions?

I know imaginary numbers solve $x^2 +1=0$, but what is the motivation for quaternions?
2
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2answers
107 views

Example of a proof using the axiom of commensurability

I'm teaching our intro to proofs course (well, one of them) and one of the classic illustrations of an overturned "axiom" is the Greek axiom of commensurability, which stated in geometric terms the ...
2
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2answers
58 views

Hilbert's construction of multiplication of two numbers

I am now reading Hilbert's "Foundations of Geometry", section 15, where he describes there a geometric way to construct, given two segments of length $a$ and $b$, a segment of length $ab$ (in short: ...
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1answer
82 views

Why $1\frac{1}{2}\ne \frac{1}{2}$?

Why mathematicians have chosen notation such that in algebra $1\frac{1}{2}=\frac{3}{2}$ but $x\frac{y}{z}=\frac{xy}{z}$, instead of $x\frac{y}{z}=\frac{xz+y}{z}$?
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2answers
359 views

What is the history behind the development of the term “coefficient”? [closed]

Why are coefficients called "coefficients"? For example I learned that squaring a number is called "squaring" because it actually refers to "making a square". That's how it was developed. ...
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2answers
61 views

Spherical geometry as an example of non euclidean geometry

I have recently been learning some hyperbolic geometry and the professor briefly mentioned spherical geometry. From a modern, naive point of view, it seems quite easy to show that spherical geometry ...
3
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0answers
79 views

What's so special about binomial coefficients that someone decided to organize them in a triangle?

I know that binomial coefficients are related to figurate numbers (which were studied by Greeks a loooong time ago, because of its connections to geometry). I also understand how the Pascal's triangle ...
5
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5answers
279 views

Examples of advancement in mathematics due to war

It's not a lie that, in most sciences, some of their advancement comes from war. A couple examples would be the Haber process in chemistry and none other than the Manhattan Project in both physics and ...
9
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1answer
96 views

Any book on major (recent) math discovery (results) in an easy understanding way?

All: Can anyone recommend a book which illustrate major (recent) math discoveries (results) in an easy understanding way ? For "recent discoveries", I meaning something discovered in last 50 years. ...
3
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1answer
56 views

Why are normal subgroups called “Normal”?

Why are normal subgroups called "Normal"? Who is credited with naming them, and why are they named such?
3
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1answer
46 views

Who first proved that every triangle has a circumscribed circle?

Wikipedia only mentions that it follows from the Cartesian equation for a circle: $\left(x - a \right)^2 + \left( y - b \right)^2=r^2$ https://en.wikipedia.org/wiki/Circumscribed_circle#cite_note-1 ...
5
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2answers
54 views

How is Cartesian coordinate system related to his philosophy

In 1637, Rene Descartes published his famous monograph about philosophy "Discourse on the Method of reasoning well and Seeking Truth in the Sciences", and analytic method of geometry has been come up ...
4
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1answer
109 views

Who first studied semilattices?

Historically, who first studied semilattices, as opposed to lattices or Boolean algebras? (With or without identity, I do not mind.)
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0answers
62 views

Decoding Gauss' Easter Algorithm

In 1800, Gauss published this algorithm for computing the date of Easter in a given year $year$: $a = year \mod 19$ $b = year \mod 4$ $c = year \mod 7$ $k = \lfloor year/100 \rfloor$ $p ...
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0answers
77 views

Why nobel prize is not for mathematicians [closed]

I have heard from many people that nobel prize is not given to mthematicians.Waht is the reason behind this?I also heard that a women rejected the nobel because of some famous mathematician.Is this ...
3
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2answers
91 views

Prove withoui calculus: the integral of 1/x is logarithmic

It was known in the 17th century that the function $$ t \mapsto \int_{1}^{t} \frac{dx}{x} $$ is logarithmic: a geometric sequence in the domain produces an arithmetic sequence in the codomain. This ...