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

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3
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2answers
160 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
votes
0answers
38 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
votes
0answers
28 views

Cambridge Maths Tripos Papers

Does anyone know where I can find Cambridge Maths Tripos Papers for the 1980s?
1
vote
0answers
55 views

Mathematicians with hyphenated names [on hold]

I just found out that the Levi-Civita symbol is named after only a single person. Which other mathematical theorems or objects are named after mathematicians with hyphens in their names?
8
votes
0answers
67 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
votes
0answers
61 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
votes
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
votes
0answers
40 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
vote
1answer
52 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
vote
1answer
27 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
vote
1answer
25 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
105 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 ...
1
vote
3answers
107 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 ...
1
vote
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. ...
11
votes
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
votes
0answers
39 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
79 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 ...
0
votes
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 ...
0
votes
0answers
21 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
votes
1answer
129 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
votes
0answers
60 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
votes
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
votes
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 ...
1
vote
0answers
48 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. ...
0
votes
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
votes
2answers
105 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
votes
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: ...
1
vote
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 $x\frac{y}{z}=\frac{xz+y}{z}$?
8
votes
2answers
356 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. ...
5
votes
2answers
59 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
votes
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
votes
5answers
275 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
votes
1answer
95 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
votes
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
votes
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
votes
2answers
51 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
votes
1answer
108 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.)
7
votes
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 ...
1
vote
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
votes
2answers
84 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 ...
43
votes
7answers
5k views

What is the oldest open problem in geometry?

Geometry is one of the oldest branches of mathematics, and many famous problems have been proposed and solved in its long history. What I would like to know is: What is the oldest open problem in ...
6
votes
1answer
77 views

Who first discovered that some R.E. sets are not recursive?

Who first discovered that some recursively enumerable sets are not recursive, or equivalently that some semidecidable sets are undecidable? And in what context? Was the earliest formulation of this ...
10
votes
2answers
256 views

What meaning did Riemann assign to $dx$?

Detlef Laugwitz wrote a monumental biography of Riemann. The book was translated into English by Shenitzer. Laugwitz discusses Riemann's fundamental essay Uber die Hypothesen, welche der Geometrie ...
4
votes
1answer
88 views

Who are some blind or otherwise disabled mathematicians who have made important contributions to mathematics?

Two prominent mathematicians who were disabled in ways which would have made it difficult to work were Lev Pontryagin and Solomon Lefschetz. Pontryagin was blind as a result of a stove explosion at ...
3
votes
1answer
76 views

Ancient calculus or thorough observation

Integration. It's the simplest way on earth with which we can derive any formula like surface area or volume of symmetrical shapes and solids (square, circle, cube etc.). But what I've been hearing is ...
1
vote
1answer
52 views

Why is the argument of a complex number measured anticlockwise (from the positive real axis), rather than clockwise?

I was going through some basic examples of complex numbers (finding the argument and modulus) with my brother yesterday, and he asked Why is the argument measured anticlockwise rather than ...
9
votes
2answers
218 views

History of the matrix representation of complex numbers

It is well-known to many that $\mathbb{C}$ can be represented by matrices of the form $\left[ \begin{array}{cc} a & b \\ -b & a \end{array} \right]$. For example, see this question or this ...
1
vote
1answer
40 views

Origin of the Name 'Chernoff Sequence'

I discovered the Chernoff Sequence, $A006939$ while thinking about recreating the divisibility of $12$ and $360$. I was actually surprised to see that it already existed, and it caught my attention. ...