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Questions tagged [mathematics]

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

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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 ( "$o$...
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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 ...
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4answers
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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?
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Who coined the term random variable?

Who is the first person defined the concept of a random variable?
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601 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 ...
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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:...
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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 ...
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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?
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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 ...
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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 ...
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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 ...
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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".
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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 ...
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1answer
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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 ...
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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?
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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 ...
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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 ...
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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 ...
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121 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 ...
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1answer
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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 ...
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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 ...
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1answer
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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 ...
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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 ...
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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.
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What are some good books on history of mathematical thought? [closed]

And if possible books that could be downloaded for free
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1answer
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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 ...
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2answers
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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 ...
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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 ...
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When did the term “order” come into use as the highest exponent in an expansion?

Answer(s) to the question What is a 3rd-order Fresnel lens? are disappointing to me, in that the term 3rd order does not refer to anything like a third-order series expansion. But this leads me to a ...
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Introduction of shape parameters in the formulation of probability distribution

I'm familiar with the definition of location, scale, and shape parameters, and the type of distributions they parametrized. I'm interested in understanding how shape parameters became part of the ...
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History of a contour integral method for summing series

A folklore result I have seen used in evaluations of infinite sums is the following clever use of the residue theorem: $$\begin{align*}\sum_{1}^\infty f(k)&=\frac1{2\pi i}\oint f(z)\pi\cot\pi z\,\...
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1answer
134 views

How did philosophers and scientists in the 18th century view mathematical explanation?

The 18th century saw a rise in the use of mathematical formalisms to account for natural phenomena. Works of Lagrange, Euler, d'Alembert, etc., were groundbreaking in the history of mechanics and ...
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1answer
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Using paper of known density to calculate area under a curve [duplicate]

Ive never seen a source for this, but I had a professor a few years back that a low tech way of calculating the area under a curve (definite integral) was to use a piece of paper with known thickness/...
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2answers
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Origin and use of the adjective “improper” in mathematics

Anybody with elementary mathematical education will have seen improper fractions to refer to fractions where the numerator is greater than or equal to the denominator. At a certain point in calculus ...
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1answer
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Who is credited for formalising the theory of isomorphisms?

The concept of an isomorphism is very interesting: a rigorous, formal way of expressing similarity between two objects. When and how did this idea of similarity become formalised as a bijective ...
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Who are credited for angle transformation formulae and law of sines in trignometry

I'd like to who are credited for discovering angle transformation formulae $$ \sin(A\pm B)=\sin(A)\cos( B)\pm\cos(A)\sin(B) $$ $$ \cos(A\pm B)=\cos(A)\cos( B)\mp\sin(A)\sin(B) $$ $$ \tan(A\pm B)=\...
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What is the origin of Arabic numerals

I was taught that the numerals {0,1,2,...,9} are from the Arab alphabet. But they look completely different from today's Arab letters. I wonder what is the origin of Arabic numerals? Edit: The web ...
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Who are the top mathematicians who were ignored due to their unconventional approach?

A perfect example would be Srinivasa Ramanujan It is known that the conventional community throughout history have been close-minded towards great men of science and mathematics.(eg. Galileo) ...
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Why was the 'differential entropy' from information theory so named?

The entropy of a distribution $p$ on a discrete set $\mathcal{X}$ is defined as $$H(p) = -\sum_{x \in \mathcal{X}} p_x \log p_x.$$ Shannon in his classic paper [1] defines the analogue for continuous ...
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How long has the order of priority of arithmetical operations been widely taught in high schools?

Browsing Facebook, I often come across posts like this, to test peoples' understanding of order of operations. This inevitably prompts a deluge of answers that either misunderstand the concept or ...
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History of various definitions of topology

I have been reading Point Set Topology for a while, and turns out that there are various possible ways to define a topology. Most popular one is using open set axioms. Another one is using closure ...
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Remarkable numerical calculations before electronic computers

I know the story that Cole found the factoring of the big number $2^{67}-1$. Is there any other remarkable achievement of hand calculation?
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Why does Michael Stifel's version of Pascal's Triangle look the way it does?

Today I've come across Michael Stifel's version of Pascal's Triangle, which I've seen referred to as the Figurate Triangle or the Triangle of Figurate Numbers as seen in Combinatorics: Ancient and ...
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Was multivariable calculus particularly prominent in Italy?

From my classes I don't hear about a lot of italian mathematicians, but two of them, Fubini and Tonelli, are both related to multivariable calculus. Is there a reason for this? Just a coincidence? Or ...
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Who achieved the analytic continuation of the Gamma function?

Originally, the gamma function $\Gamma(x)$ is defined as $$ \Gamma(x )=\int_0^\infty e^{-t} t^{x-1} dt .$$ This definition works for $Re(x)> 0 $ only. So, who extended into the whole complex ...
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What calculation did Halley or anyone else do to estimate the effects of Jupiter and Saturn on Halley's comet's return in 1758/9?

This answer to the question First observation that the movement of a planet or asteroid in its orbit was affected by another planet says: In 1705, with the mathematical assistance of Issac Newton, ...
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How was the notion of the metacenter of a floating body discovered?

Does anybody knows how this important notion of hydrostatics was discovered? I have read that it is about someone walking up and down the mountains of Latin America trying to disprove Cartesian ...
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Who did the drawings in Hilbert's and Cohn-Vossen's “Anschauliche Geometrie”?

Hilbert's and Cohn-Vossen's wonderful book "Anschauliche Geometrie" ("Geometry and the Imagination") from 1932 contains a lot of great illustrations which, given the time of publication, must have ...
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What is the earliest instance of the use of an algorithm to solve problems?

In reading a description on Usenet of a NIST competition for selecting a standard cipher, I read: Consider that the best currently known methods for factoring use randomization: Construct enough ...
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Why are there 24 hours in a day?

The question could be answered in a number of ways: Historically (e.g. Egyptians did for <...> reasons) Mathematically (It is a highly composite number) I'm looking for a mathematical answer. I'...