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

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6
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2answers
112 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
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 ...
4
votes
5answers
377 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
125 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
135 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
56 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
81 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
votes
0answers
306 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
94 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
307 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
623 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
116 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 ...
2
votes
1answer
110 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
votes
2answers
298 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
76 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
votes
4answers
318 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
votes
2answers
288 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
903 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
147 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
140 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
325 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
899 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
182 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
113 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
196 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
104 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% ...
4
votes
0answers
2k 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
211 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
168 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
votes
1answer
59 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
219 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
votes
7answers
592 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
votes
1answer
105 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
votes
3answers
805 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 ...
3
votes
2answers
153 views

What is the intutive explanation of why the notation of matrices is as it is?

If I want to solve a system of linear equations, like 2x-y=1 x+2y=4 Then the matrix notation for the same would be: $$ \begin{bmatrix} 2 & -1 \\ 1 & 2 \\ \end{bmatrix} \begin{bmatrix} X\\ ...
2
votes
1answer
121 views

Why didn't Frege succeed in his attempts to reduce mathematics to logic?

My background: Sophomore-level understanding of mathematics and philosophical logic. All the explanations I have found online so far are either far too technical or too simplistic. Thanks in advance ...
1
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1answer
73 views

Why we can't define more mathematical constant?

I would like to know how many mathematical constant are there? I saw this link and I know the names. Who can define a mathematical constant? Someone can say that ...
0
votes
2answers
81 views

What is the meaning of calculating sine of a number?

When we calculate sine/cos/tan etc. of a number what exactly are we doing in terms of elementary mathematical concept, please try to explain in an intuitive and theoretical manner and as much as ...
7
votes
1answer
147 views

Who first proved the fundamental theorem of finitely generated (or finite) abelian groups?

The fundamental theorem of finitely generated abelian groups (or maybe just finite abelian groups) is well-known and can be found in just about any text on the theory of groups or abstract algebra. ...
10
votes
7answers
769 views

Interviews of famous modern mathematicians

I was wondering, are there any good collections of interviews of famous modern mathematicians? It can be text interviews, or audio or video recordings. I am not sure what exactly I mean by "modern". ...
2
votes
0answers
29 views

Cayley on “trivial transformations”

In his 1854 paper, "Deuxième mémoire sur les fonctions doublement périodiques" ("Second memoir on doubly periodic functions"), Cayley discusses (what we would today describe as) a certain class of ...
15
votes
2answers
744 views

History of Algebraic Geometry: Motivation behind definition of schemes

I am trying to read an article by Jean Dieudonne which talks about development of Algebraic Geometry. The article was being published in the journal "Advances in Mathematics" Volume 3, Issue 3, Pages ...
3
votes
1answer
105 views

Coincidence about nabla?

I was surprised to notice that gradient of function and Levi-Civita connection have the same notation, i.e. nabla sign $\nabla$. Moreover, extending any connection on tensors, one let it be ...
2
votes
1answer
95 views

Descartes on imaginary unit.

I heard once that Descartes defining the imaginary unit had to talk about the imagining of rise of the spirit over the real numbers because definition based on square root of a negative number could ...