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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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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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86 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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77 views

Cauchy's Integral Theorem Motivation

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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86 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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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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109 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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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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142 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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165 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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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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140 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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53 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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99 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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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 ...
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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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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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130 views

Was further research done about the invention of Algebra?

In his book “A History of Mathematics”, Carl Boyer mentions that both AlKhwarizmi and Abd ElHamid Ibn Turk wrote their books on Algebra (“Aljabr w Almuqabla” and “Logical Necessities” respectively) at ...
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who proved discrete spectrum of Laplace-Beltrami on compact Riemannian manifolds?

The fact (!) that the Laplace-Beltrami operator on compact (connected) Riemannian manifolds has compact resolvent, and therefore has purely discrete spectrum, is well known. So far as I can tell, the ...
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66 views

What geometric results were first proven by assuming all real numbers are rational?

Pythagoras and his followers believed that all magnitudes are commensurable; that is, the ratio of two magnitudes of the same kind, like two lengths or two areas, is equal to the ratio of natural ...
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mathematical development

I have two questions regarding the development of mathematics: 1) Is there an example where in mathematics, a collaboration has led to the discovery of another result? I already know something like ...
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100 views

Level of maths of engineers in the Industrial Revolution

Did engineers like I.K. Brunel and his contemporaries employ calculus in their constructions? Or did they work just with 'rules of the thumb' and useful 'laws' like the square-cube...? What was the ...
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Why are permutations ($_nP_r$) called differently in non-English languages (“variations” in German)?

First of all, you should be at least a little familiar with combinatorics to understand that question. Some often used calculator keys in stochastic are the nCr and nPr ones. Edit: I've first asked ...
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If John Michell was more well known, would he rank above Isaac Newton in the history of science? [closed]

John Michell proposed black holes in the 18th century, hundreds of years before Schwarzschild and Einstein. His ideas were said to to be away head of his time, that he died in obscurity. I assume ...
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Who came up with a number of the theoretical plates equation?

In chromatography, the signal is shaped like a Gaussian peak, and it is plotted against time vs. instrument's signal. https://en.wikipedia.org/wiki/Chromatography#/media/File:Rt_5_12.png (a) One of ...
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86 views

Origin of Gauss-Newton method

The Gauss-Newton method can be derived from Newton's method, but I am unable to see how Gauss was linked with this method. It seems unlikely that he himself worked on the method, but I am at a loss.
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Who first proved Fubini's theorem for abstract measure spaces?

Fubini's theorem relates the double integral of a function $f(x,y)$ to an iterated integral with respect to $x$ and $y$. The basic idea of this theorem for Riemann integrals of continuous functions ...
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What are some good references elucidating the discovery/creation of Fourier Series?

I've always grappled with the topic of anything Fourier during my undergrad days. Until recently when revisiting why I learned what I did, I discovered how Fourier's desire to understand the flow of ...
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How widespread was the belief that the earth is round in Europe until the Renaissance?

Already Greek mathematicians in antiquity b.C. realized that the earth was round, and the idea was operative in Europe ever since. But how widespread was this belief in the centuries until the ...
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Irrational numbers math in old Roman age [duplicate]

I know that Hippasus proved that $√2$ is irrational number. My question is how were they doing the mathmatical operations like multiplication for rational numbers like 1.41421356237 I can do ...
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140 views

Why do we call Chinese monoid “Chinese”? Why not “American”?

Why do we call Chinese monoid "Chinese"? Why not "American"? You can find the definition of Chinese monoid from Wikipedia. https://en.wikipedia.org/wiki/Chinese_monoid
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What pythagorean table looked like?

Pythagoras introduced the multiplication table in Southern Italy about 500 BC, do we know how it looked like? Edit I do not mean the so called pytagorean/multiplication/times table but the actual ...
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139 views

How did Romans do multiplications?

The Romans hadn't indian numerals, but what 's worse hadn't the decimal system, yet produced amazing works of engineering and architecture. How was that possible? It's troublesome to make simple ...
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169 views

Does any extant Greek text prove that the area of an inscribed regular polygon increases with the number of sides?

Does any extant Greek text prove that the area of a regular polygon inscribed in a fixed circle increases with the number of sides in the polygon? I can't find such a proposition in Euclid, but the ...
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Earliest drawings of the plots of trigonometric functions

[Even though this question may seem as a duplicate of this question about the History of sine function, I'd like to ask it again - with a more specific title and a more specific focus (on specific ...
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Original document of the Gaussian integral

The Gaussian integral $$\intop_{-\infty}^{\infty} dx \exp(-x^2) = \sqrt{\pi} $$ is done in a very smart way. But where is the original document?
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Who used the symbol $S_n$ for “rotation reflection” as a symmetry operation?

I am looking for the origin of the symbol $S_n$ used by chemists to denote the symmetry operation consisting of a $\smash{\frac{2\pi}n}$ rotation ($C_n$) about an axis and a reflection in a plane ...