# 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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### 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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### 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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### 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  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'...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### The Hahn-Kolmogorov Extension Theorem

How did Hahn and Kolmogorov prove the Hahn-Kolmogorov Extension Theorem?
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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 ...