Questions tagged [mathematics]

For questions about the quantitative study of topics such as numbers, structure, space, and change, carried out by investigating patterns.

Filter by
Sorted by
Tagged with
1
vote
1answer
63 views

How did Hagoromo Fulltouch chalk gain so much popularity among mathematicians in the West?

I recently read Hagoromo, the 'Rolls Royce of chalk,' continues writing its legacy in South Korea article recently, and was fascinated by the huge amount of attention this specific chalk is getting. ...
3
votes
1answer
73 views

Origin of the “law of quadratic reciprocity”

Today, "reciprocity" is the standard mathematical word used for quadratic reciprocity and its generalizations. I found that the name dates back to no later than 1832, when a paper of Dirichlet (...
0
votes
1answer
43 views

Did Isaac Barrow also discover the other thing about the inverse relation between area and tangent?

Barrow surely discovered that the tangent to the area curve of a function at a point equals the value of the function at that point. Also, I’ve seen geometric proofs of this. But did he also discover ...
6
votes
1answer
130 views

What is the origin of the Chinese Stick Multiplication method?

A while back I came across an interesting method to do multiplication. I don't know what it's called and am interested in when (and who) developed this method. I don't know if it's a mathematical ...
5
votes
2answers
154 views

Reference Request: Did Descartes leave solving the quintic as an exercise to his readers?

In this document by Jim Brown it is claimed (on Section 3, pg 5) that: [Descartes] believed that all polynomials of degree $>4$ could be solved with the same methods as had been applied to the ...
2
votes
0answers
52 views

On Trigonometric Methods Available to Aristarchus

Approximately 2300 years ago, Aristarchus proposed a method for determining the relative distances of the sun and the moon in relation to the earth. Specifically, he asserted that when the moon is in ...
3
votes
0answers
167 views

How was this equation for pi derived by Ramanujan?

Have we figured out how this series was derived by Ramanjuan? $$\frac{1}{\pi}=\frac{\sqrt{8}}{9801}\sum_{n=0}^{\infty}\frac{(4n)!}{(n!)^4}\frac{26390n+1103}{396^{4n}}$$
2
votes
1answer
67 views

Why was Indicial equations named so?

In ODE, in Frobenius method, there's an equation called "Indicial Equation." Is there any particular contextual/historical reason that it is named so?
6
votes
1answer
91 views

Who invented the gradient descent algorithm?

In connection to the question "Who invented the gradient?", I want to know who invented the gradient descent algorithm?
7
votes
2answers
565 views

On the history of Haar measure

Haar measure is a well-known concept in measure theory. Many books are perfectly dedicated to present its existence and uniqueness such as measure theory for D. Cohn. I am looking for a good ...
0
votes
3answers
78 views

Does Heliocentrism predate Copernicus?

I have seen this mentioned on the interwebs a few times. people have mentioned that some Greek thinkers and Islamic astronomers came up with heliocentrism before Copernicus and that Copernicus copied ...
0
votes
1answer
58 views

Was there a more intuitive early proof of the generalized mean value theorem?

I am interested in the early proofs of the theorem. It is often called Cauchy mean value theorem, so perhaps Cauchy proved it first. In all the proofs that I have seen we construct a contrived ...
4
votes
1answer
132 views

What was the problem that led to Calculus discovery

As far as I remember, Calculus was invented/discover/founded by Newton. But what he was trying to achieve that made him find the limit of of difference approaching zero. how far did he get into ...
3
votes
1answer
121 views

Were people aware of the “mistakes” in Euclid's Elements before the start of the formalization of Mathematics?

For example, in proposition 1, Euclid assumes that the instersection of the two circles exist, when he shouldn't have. This, among many other things, was corrected quite recently (by Hilbert and ...
2
votes
1answer
154 views

Were ancients really so bad at computations before Arab numerals?

It is often said that Romans (see below) had a terrible number system, which made a computations a mess. I do believe this, but I'm really suspicious of the claim that nobody had better ways to do ...
0
votes
0answers
30 views

On the Origin of the Concept of Aliasing & the Discrete Fourier Transform Frequency Axis

The development of fast Fourier transform is attributed to Cooley & Tukey, both have written a lot about it is historical development. However, I am searching early publications which showed how ...
0
votes
1answer
60 views

Logarithm tables vs multiplication tables

When John Napier and Joost Burgi developed logarithms in the 16th century, they succeeded in replacing long, tedious, error-prone multiplications with table-look-up and addition, giving other ...
5
votes
2answers
117 views

Why are “join” and “meet” named as they are?

In the context of partially ordered sets, why are the words for supremum and infimum "join" and "meet"? I find the nomenclature puzzling, especially since the English words "join" and "meet" are ...
2
votes
0answers
110 views

What was Havil's source for the statement that G.H. Hardy would offer his Savillian chair to whoever could prove irrational?

In Havil's 2003 book Gamma he states that Hardy offered up his chair in Oxford to whoever could prove that the Euler-Mascheroni constant $\gamma$ is irrational. I'm almost positive I had heard a ...
5
votes
1answer
166 views

What are some of the unsolved mathematical problems posed and stated clearly prior to the year 1900?

I chose year 1900 because of: "Hilbert's problems are twenty-three problems in mathematics published by German mathematician David Hilbert in 1900. The problems were all unsolved at the time, and ...
3
votes
1answer
591 views

Who came up with the convolution theorem?

I am looking for the earliest reference which proposed the convolution theorem which is often utilized in signal processing (i.e., convolution becomes a multiplication in the Fourier domain). The ...
4
votes
0answers
169 views

Entry in Gauss' Mathematisches Tagebuch (Mathematical Diary)

Does someone have a reference or further explanation on Gauß' entry from May 24, 1796 in his mathematical diary (Mathematisches Tagebuch, full scan available via https://gdz.sub.uni-goettingen.de/id/...
7
votes
2answers
2k views

What triggered jesuits' ban on infinitesimals in 1632?

... since the very idea of infinitesimal was foreshadowed by Cavalieri ( "limit") in 1635, then put forward in an indirect way by John Wallis ($1/\infty$) in 1655, and then formalized by Newton ( "$o$...
8
votes
2answers
122 views

The relationship between solvability of ruler and compass problems and solvability of algebraic equations by radicals

Galois obtained necessary and sufficient conditions for an algebraic equation (in one variable) to be solvable by extraction of a chain of square roots. A beautiful application of this is to the ...
3
votes
4answers
162 views

Are there any sources of mathematicians talking about their research methods?

I recall reading this article that was written to explain how Descartes read philosophy effectively. I am wondering if such analogous tips have been made by past mathematicians?
3
votes
1answer
75 views

Who coined the term random variable?

Who is the first person defined the concept of a random variable?
4
votes
3answers
635 views

Were tables of square roots ever in use?

Before the advent of calculators they had useful ready made tables for the main functions:sines,cosines logs etc..., do you know if tables of square roots were ever produced or in use? I never heard ...
7
votes
0answers
149 views

Who first defined polynomials as sequences?

Question 1. When did the modern definition of a polynomial (as a sequence of coefficients, with multiplication defined by $\left(ab\right)_n = \sum\limits_{k=0}^n a_k b_{n-k}$) emerge? Let me clarify:...
2
votes
0answers
68 views

I am searching for a book of this form and content, is there any?

I would like to know is there a book that is both a history of mathematics and a collection of open problems? I know that there exist many books that cover either larger or smaller periods of the ...
-5
votes
2answers
122 views

What are the great works of Richard Phillips Feynman? [closed]

What are the prerequisites to read his book? Why Richard Phillips Feynman is so famous? What are great works of Richard Phillips Feynman?
0
votes
1answer
85 views

When did trigonometry move away from treating chord as primitive?

I remember reading that in a couple of places that ancient trigonometry, particularly Ancient Greek trigonometry, used the chord as the primitive concept instead of sine and cosine. I can't tell ...
6
votes
1answer
95 views

Euler's Derivation of Euler's Method for ODEs

I am looking for an English translation of Euler's derivation of Euler's method for ODEs, namely the update $$ y_{n+1} = y_n + h f(y_n, t_n) $$ What motivated Euler to consider this problem, and how ...
2
votes
0answers
78 views

Who first “depressed” the cubic equation?

In his Ars Magna Cardano specifies procedures to "depress" a cubic - a means to convert an equation such as $x^3+6x^2=100$ to $y^3=84+12y$, eliminating the $x^2$ term. Was he the one who discovered ...
1
vote
1answer
98 views

Why is Robinson arithmetic “Q”?

I see Peano arithmetic so often abbreviated as "P" or "PA". Why is Robinson Arithmetic "Q"? Following the obvious pattern, I would have expected R" or "RA".
6
votes
3answers
103 views

Usage of reverse side of circular slide rule

I have a circular slide rule, but I can't figure out what the markings on the back are used for. The front face has two logarithmic scales, the outer one runs from $1$ to $100$ (exclusive), and the ...
1
vote
1answer
30 views

Where can I find sources for Gergonne's research on the fundamental relations among classes?

Alfred Tarski writes The whole of the old traditional logic...can almost entirely be reduced to the theory of the fundamental relations among classes, that is, to a small fragment of the entire ...
10
votes
3answers
1k views

What was the notion of limit that Newton used?

I have read that the notion of limit became rigorous two centuries after the discover of calculus What Newton had in his mind regarding the notion of limit?
8
votes
2answers
2k views

What is the status of the three crises in the history of mathematics?

I have seen a claim in some literature that there are three crises in the history of mathematics. The first is the discovery of $\sqrt2$ being irrational in Greek time which shook the belief that ...
3
votes
3answers
129 views

When was 4D space “conceived of”?

In Measurement by Paul Lockhart (Harvard Press), he says (p.351): the classical geometers (as far as I know) never even conceived of four-dimensional space, whereas adding another variable is ...
3
votes
0answers
110 views

Why is the representation of the direction of the x and y axes in two dimensions different than in three dimensions?

So I apologize if this question seems a bit nit-picky, but it has bothered me for a while. Usually when a coordinate system is represented in two-dimensions, the x-axis is pointing towards what might ...
10
votes
1answer
125 views

How is the word kernel associated with distributions?

I am trying to rationalize the meaning of the term kernel, especially when it is associated with distributions. The English and German etymology all show that the literal meaning is corn (English) and ...
1
vote
1answer
83 views

What were the typical ways students were taught the elements when it remained the prime textbook of mathematics?

In modern textbooks, students are greeted with plenty of exercises. Usually they are also organized in such a way that you have examples and pointers to what concepts are most important. The elements ...
7
votes
1answer
254 views

How did the obelus ÷ come to stand for division?

The obelus ÷ represents division on calculator keyboards, and sometimes in elementary education. It has a long non-mathematical history starting before 200 BC. Its ...
4
votes
1answer
65 views

Influence of Poincaré on Julia and Fatou

Poincaré was one of the major precursors of the modern theory of dynamical systems, notably through his famous memoir on the 3 body problem, and subsequent discovery of homoclinic intersections and ...
23
votes
1answer
4k views

How was Lagrange appointed professor of mathematics so early?

It is well-known that in 1755 Lagrange was appointed Professor of Mathematics at the Royal Artillery School in Turin. He was 19. His work up until then involves correspondence with Euler. Was he ...
3
votes
1answer
85 views

Mellin's original paper on his transform

There is no link on wikipedia to his work. This is really a nice transform. There is coherent theory behind. I am curious what motivated him to invent this transform.
1
vote
0answers
51 views

What are some good books on history of mathematical thought? [closed]

And if possible books that could be downloaded for free
2
votes
1answer
105 views

The convention for speakers to refer to themselves at the board with a single initial

I found an interesting question on Math SE asked by @KCd, but it is over four years old without a clear answer. Since it seems to be more on topic here than on Math SE, I thought to post it here in ...
13
votes
2answers
2k views

When were vectors invented?

Encyclopedia Britannica says, In their modern form, vectors appeared late in the 19th century when Josiah Willard Gibbs and Oliver Heaviside (...) independently developed vector analysis to express ...
2
votes
0answers
84 views

Were notable physicists great at math or computing? [closed]

Were famous or popular physicists like Galileo, Newton, Einstein, Feynman predominantly mathematicians or scientists (computing, experimenting, engineering, etc.)? I am curious if people like the ...