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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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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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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 ...
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56 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.
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43 views

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
73 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 ...
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2answers
1k 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 ...
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73 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 ...
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50 views

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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22 views

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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67 views

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
111 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
75 views

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
87 views

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
78 views

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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92 views

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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155 views

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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308 views

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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1answer
82 views

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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2answers
158 views

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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172 views

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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5answers
185 views

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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75 views

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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1answer
58 views

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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95 views

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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79 views

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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1answer
57 views

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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2answers
110 views

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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135 views

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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0answers
144 views

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'...
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2answers
209 views

Did the Idea of Universal Gravitation predate Newton?

"Baba wrote over 60 books, almost everyone on a different topic, writing on issues from astronomy, identified stars that European scientists technology could not discover until the late 1800s, ...
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1answer
104 views

Who first proved that only primes of the form $4k+1$ divide odd integers of the form $n^2+1$?

I am writing a paper and I would like to cite the person(s) who proved that only primes of the form $4k+1$ can evenly divide odd integers of the form $n^2+1$? For example, if $n=8$, $n^2 + 1 = 65$ ...
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1answer
196 views

Why didn't John von Neumann win the Turing Award, Fields Medal or Nobel Prize?

From what I've read in Wikipedia, John von Neumann made a stupendous number of contributions to economics, computer science and mathematics. Why, then, didn't he receive a top award in any of these ...
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Courant (1943) and History of Finite Element Method

I am interested in the history of Finite Element Methods and Methods of Weighted Residuals (MWR), especially reduced quadrature and collocation methods. I have a paper coming out called “Orthogonal ...
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59 views

Mathematical analysis vs. Practical genius

Concerning the role of mathematics in technological inventions: which books would you suggest that examine the historical relation between mathematical analysis & practical wisdom? For example, ...
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1answer
95 views

Earliest Instances of a Slope/Direction Field for a First-Order ODE

Background When first encountering slope fields in calculus or elementary differential equations, students often ask "What is the purpose?" A concise answer is that slope fields provide a way to ...
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1answer
90 views

Cauchy's Integral Theorem Motivation

How did Cauchy go about Cauchy's integral theorem? What was his motivation?
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46 views

Where is the first reference to the “Z combinator”, a call-by-value fix-point combinator?

I'd like to know the earliest reference to the Z-combinator. This could be either where the name was first coined, or even the first discussion of a need for an applicative-order Y combinator. I didn'...
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1answer
87 views

Is there any relation of the word “normal” with a subgroup being normal?

From Gallian, Contemporary Abstract Algebra: ...if G is a group and H is a subgroup of G, it is not always true that aH = Ha for all a in G. There are certain situations where this does hold, ...
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1answer
99 views

How did Peano prove his existence theorem without Ascoli's theorem?

In modern proofs of the Peano Existence Theorem for ordinary differential equations, Ascoli's theorem is used. Ascoli's theorem came after Peano's proof. Did Peano prove a form of Ascoli's theorem in ...
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201 views

Did the author of Alice in Wonderland make any substantial original discoveries in mathematics?

Charles Lutwidge Dodgson, better known by his pen name of Lewis Carroll, was a mathematics lecturer at Oxford University and today is primarily famous for his fanciful stories laced with mathematical ...
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73 views

The Integral as a Uniform Limit of Step Functions

Who first realized that it is possible to define the integral of a function as the limit of the integrals of a sequence of step functions that converge uniformly to the given function? This is ...
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2answers
126 views

Riemann's Contribution to Integration

What did Riemann do for the theory of integration? I am asking because I hear his name a lot in relation to integration and it is often implied that he made large contributions, but I do not know ...
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0answers
47 views

Where the term elasticity (of a function) come from?

Elasticity of a function is a mathematical concept that is widely used in economics. In particular, price elasticity of demand or supply. But generally elasticity in economic is the measurement of how ...
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2answers
150 views

How did Newton and Leibniz interpret the integral?

How did Newton and Leibniz think about the integral? Did they only see it as an anti-derivative or did they also think of it as the area under a curve?
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2answers
173 views

When was the term “corollary” first used in proofs?

A dictionary search of the word "corollary" immediately yields the usual definition that all people involved with mathematics are used to dealing with. However, this surely comes from the Latin "...
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45 views

The Hahn-Kolmogorov Extension Theorem

How did Hahn and Kolmogorov prove the Hahn-Kolmogorov Extension Theorem?
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90 views

Discovery of the Power Series Form of the Exponential Function

How was the power series form of the exponential function disovered? Was it just observed? By the exponential function, I mean the solution to the differential equation $\frac{df}{dx} = f$ with the ...
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1answer
57 views

Where did the story about Newcomb observing Benford’s Law come from?

The story goes that in the 1880s Newcomb noticed that logarithm tables were more worn down towards the beginning of the book (where the leading digit of the logs were 1). This led him to formulate an ...
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89 views

Egyptian number system?

How did ancient Egyptians know that they have to choose the symbols for multiple of 10 in their Egyptian number system, since at that time hindu-arabic system was not there and no one knows what is 1,...
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1answer
186 views

How did Ruffini discover his method of polynomial division?

How did Ruffini discover his method of polynomial division? At that time was it known that polynomial division works similar to integer division?