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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0answers
75 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
54 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
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1answer
61 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 ...
19
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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
175 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
96 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
102 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 $x\frac{y}{z}=\frac{xz+y}{z}$?
9
votes
2answers
490 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. ...
6
votes
2answers
108 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
89 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
368 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
122 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. ...
4
votes
1answer
131 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
55 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
78 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
122 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
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0answers
281 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 ...
3
votes
2answers
112 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 ...
50
votes
8answers
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
93 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 ...
12
votes
2answers
301 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 ...
21
votes
5answers
588 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
110 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
102 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 ...
10
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2answers
290 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
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1answer
68 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. ...
6
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4answers
317 views

A question regarding ❋166.44 in Whitehead & Russell's Principia Mathematica

In the first step of Dem, I wonder how $\Sigma ‘\times P^{;}Q$ is transformed into $\Sigma‘ \Sigma^;(P \overset{\downarrow}{.,})\dagger^; Q$. Thanks,
7
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2answers
263 views

History of the power of a point with respect to a circle

There is a concept of a "power of a point with respect to a circle". If one has a point which is distance $d$ away from the centre of some circle and that circle has radius $r$ then the power of this ...
8
votes
1answer
781 views

Where does the “Visual Multiplication” technique originate from?

There is a geometric technique to perform multiplication of numbers. But as the internet goes, it is hard to figure out who deserves the credit. What I've heard is A mayan technique From Vedic ...
1
vote
1answer
38 views

Source for original article by Euler

I am looking for Euler's article E19, namely E19 De progressionibus transcendentibus, seu quarum termini generales algebraice dari nequeunt. Auct. L. Eulero. The terms of the sequence given by ux = ...
8
votes
3answers
144 views

Why does the sign $\times$ vanish in mathematical expressions?

I just would like to know whether or not there exists an historical reason to prefer the expression $a b$ to $a \times b$. Why does the sign $\times$ vanish (whereas $+$ stays)? I thought that ...
1
vote
5answers
122 views

What is the reason to introduce and study logarithmic functions?

I don't understand why logarithms exist when we have exponential functions. Exponential functions seem to be an easier and less convoluted way to write something. Why invent logarithms to do something ...
1
vote
5answers
287 views

Mathematical proof for order of operations

I was watching this YouTube video and at around 40:40 the speaker himself states that he does not know why we have the order of operations we have today. This got me thinking and I realize that I ...
14
votes
5answers
887 views

In what ways has physics spurred the invention of new mathematical tools?

I came across this comment: Mathematical rigor is not a criterion that physicists have for evaluating their theories. From a mathematical perspective, the non-rigorous theories are far more ...
1
vote
4answers
177 views

Why didn't Fermat provide proofs of his theorems?

Apparently Fermat stated but didn't provide proofs of various theorems named after him, including Fermat's little theorem, Fermat's theorem on sums of two squares, Fertmat's polygonal number theorem, ...
5
votes
1answer
110 views

How would Johann Bernoulli have tutored Euler?

Early in Euler's life (when he was still a child/teenager), the Euler family friend Johann Bernoulli would tutor Euler in mathematics. Do we know how Johann Bernoulli would have tutored the young ...
7
votes
0answers
193 views

How do mathematicians know what is known?

How do mathematicians know that what they are researching has not been already know for 200 years? Obviously if they are researching something that is cutting edge it is not a problem, but if one is ...
32
votes
5answers
3k views

Examples of “Non-Logical Theorems” Proven by Logic

I am still an undergraduate student, and so perhaps I just haven't seen enough of the mathematical world. Question: What are some examples of mathematical logic solving open problem outside of ...
2
votes
1answer
103 views

Did the ancient Sumerians calculate the square root of two?

This post makes the claim: Not bad you might think, but compare it to the Summerian Kù of 51.85cm of the copper of Nippur and its derived unit SAR of 3600 Kù being 1866.6 meter being only 0.77% ...
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0answers
1k views

What is the origin of “how the Japanese multiply” / line multiplication?

A few months ago I made a video about a way to multiply numbers using lines (here) and it got really popular. I had heard about this trick before and I wanted to trace its origins. It seems to me to ...
6
votes
1answer
177 views

How did Le Verrier calculate Neptune's position?

In the Wikipdia article on Neptune the discovery is described as a mathematical achievement: Subsequent observations revealed substantial deviations from the tables, leading Bouvard to ...
4
votes
2answers
166 views

Who invented or used very first the double lined symbols $\mathbb{R},\mathbb{Q},\mathbb{N}$ etc

Who invented or used very first the double lined symbols $\mathbb{R},\mathbb{Q},\mathbb{N}$ etc. to represent the real number system, rational number system, natural number system respectively?
2
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1answer
57 views

Origin of Slater's condition

I've been looking all over the internet to answer this question: Slater's condition is a commonly used to certify that strong duality holds in a convex optimization problem. Although used in many ...
3
votes
1answer
218 views

What is this myth/legend and origin of related ideas?

There is a story I recently heard but the story teller (who read about it someone on the Internet) have forgotten the majority of the story, so there is little I can work on: my search attempts went ...
15
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7answers
589 views
0
votes
1answer
55 views

Sophie Germain primes

Why did Germain come up with her Germain primes? I am intrigued to know why Sophie came across these primes. Do they have any applications?
0
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1answer
94 views

Understanding the difference between relations and functions.

$R=\{(1,2),(1,3)\}$ is a relation but not function. The logic for this is that if the first element of every ordered pair must remain different, then it is said to be function. Otherwise, it's just ...
22
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3answers
785 views

Who named “Quotient groups”?

Who decided to call quotient groups quotient groups, and why did they choose that name? A lot of identities such as $$\frac{G/A}{B/A}\cong \frac{G}{B}$$ suggest that whoever invented the notation ...