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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27 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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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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156 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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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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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
92 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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361 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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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 (e.g., Galileo). ...
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129 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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365 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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271 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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261 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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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
78 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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1answer
109 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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105 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
98 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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121 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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147 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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159 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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251 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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123 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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517 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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63 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
239 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
434 views

What was the motivation for Cauchy's Integral Theorem?

How did Cauchy go about Cauchy's integral theorem? What was his motivation?
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59 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
97 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
135 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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220 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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137 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
233 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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57 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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181 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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219 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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52 views

The Hahn-Kolmogorov Extension Theorem

How did Hahn and Kolmogorov prove the Hahn-Kolmogorov Extension Theorem?
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185 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
67 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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119 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
488 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?
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1answer
68 views

Original paper of Gauss on his method of quadrature

I tried to find Gauss's original paper on his method of quadrature, but in vain. Is it translated into English? How about Legendre's paper?
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1answer
219 views

Origin of arcminutes, arcseconds, “arcthirds,” “arcfourths,” etc

This section of a Wikipedia article says [Modern time and angle notation] contrasts with the numbers used by Hellenistic and Renaissance astronomers, who used thirds, fourths, etc. for finer ...
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420 views

How did the modern understanding of Galois theory come about?

The "modern" understanding of the Galois group of a polynomial is as automorphisms of the splitting field of the polynomial which keep the base field fixed. These concepts were unknown to Galois, who ...
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221 views

Was “peasant multiplication” ever used as the predominant method of multiplication?

I've had a book for many years called Puzzles, Mazes, and Numbers which describes a method for performing multiplication as follows called "Russian peasant multiplication": There are two columns, on ...
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38 views

Rocket & drag equation?

i'm writing an assignment on firework rockets and their trajectory. Now of course im doing this with a lot of limitation as a realistic rocket calculation would be impossible to execute, at least for ...
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71 views

What is the relationship between the word “kernel” that means nullspace and the “kernel” of an integral transform?

One meaning of the word kernel is the set of $u$ so that $T(u)=0$. Another meaning of the word kernel is the "kernel" of an integral transform. Is there any relationship between these two? In ...
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109 views

What is the intuition behind Brahmagupta’s rule for multiplying negative numbers?

The rule says: The product (or quotient) of two debts is a fortune What I’m struggling with is what exactly is the product of two debts? What accounting need forces one to multiply debts? How do ...
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152 views

When were polynomial equations first factored?

The question pretty much says it all, though I have a specific example in mind. In the mid-1500s while working on his Ars Magna Cardano asked Tartaglia to solve the cubic $x^3=9x+10$. Using ...

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