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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42 views

Did the formation of Differential Geometry come before Differential Topology/ Topology in general?

I’m pretty interested in the history of mathematics, and it has always been my belief that the great pioneers of Differential Geometry were Gauss and Riemann, and the father of topology was mostly ...
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48 views

Source of L’Hôpital’s 1696 Calculus textbook

A calculus textbook I’m using references a calculus book of L’Hôpital in which he illustrates his rule, which is taught in many calculus classes. Does anyone have a source as a scanned PDF? I’d love ...
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155 views

Notations for Laplacian: $\nabla^2$ vs. $\Delta$

For a (sufficiently smooth) function $f\colon \Bbb R^n\to\Bbb R$, the Laplacian of $f$ is defined to be $\sum_{j=1}^n \frac{\partial^2 f}{\partial x_j^2}$. There are two notations for the Laplacian ...
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32 views

Pefsu problem explanation

Problem no. 12 from Moscow Mathematical Papyrus: Example of calculation of $13$ heqats of grain If someone says to you: Take $13$ heqats of grain to make them into $18$ jugs of beer Note that the ...
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107 views

Who bet against the usefulness of matrix inversion – or is it a myth?

In my linear-algebra and numerics courses, I frequently heard an anecdote about some professor betting – literally, with money – that there would never be any application where computing the actual ...
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87 views

How did Fermat come up with his Last Theorem?

It's usually believed that Fermat's claim that he had a proof for the Last Theorem is false, and that it might have been more of a conjecture. Or considering it took many centuries and advanced ...
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1answer
97 views

When did contemporary practices for indicating ecliptic longitude supplant those containing zodiacal signs?

Ecliptic longitude may be expressed in degrees; my understanding is that prior to the 19th century, expressions of ecliptic longitude contained zodiacal signs. What contemporaneous accounts describe ...
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313 views

Proof by "accident"

Are there any examples in the history of mathematics of a mathematical proof that was found by accident, in the sence that in the effort of proving it, ending up proving something intuitively ...
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53 views

In which units did Sir Isaac Newton define force at that time as SI system didn't existed then? [duplicate]

Sir Isaac Newton led the foundation of his famous laws of motion during the 17th Century but at that time SI system hadn't existed. So in which units did he define force? Did he define it in some ...
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49 views

What monograph on celestial mechanics did Jürgen Moser coauthor the 2nd and considerably expanded English language edition of with Carl Ludwig Siegel?

Comments under the Space SE question How do orbits around Jacobi ellipsoids behave? include: Periodic orbits around a rotating ellipsoid "This paper extends results obtained during the ...
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349 views

Who introduced recurrence relations and sequences?

I want to know who was the first scholar or mathematician to have introduced and formulate the concept of recurrence relations, that is finding a function given the how one value of a sequence is ...
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62 views

Is there a translation to Lagrange's Réflexions sur la résolution algébrique des équations?

I was interested in reading his work, but I couldn't find a translation in google, is there any? I can understand Spanish and English
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Original Proof of the Schwarz lemma

The classical Schwarz lemma from one-variable complex analysis states that a holomorphic map $f : \Delta(r) \to \Delta(R)$ between two disks in the complex plane such that $f(0)=0$ satisfies $$|f(z)| \...
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114 views

Did fractals already exist in the 17th century?

We can read Wikipedia: The essential idea of fractional or fractal dimensions has a long history in mathematics that can be traced back to the 1600s, but the terms fractal and fractal dimension were ...
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XIX century Russian math prodigies who published in Crelle

I recall there being two Russian math prodigies who published a joint paper in the Crelle's journal at the age of 18 or so. I think they lived in the XIX century. What were their names? I can't ...
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How did Fermat find tangent lines of Folium of Descartes?

The wikipedia article about Folium of Descartes says: Descartes challenged Pierre de Fermat to find the tangent line to the curve at an arbitrary point since Fermat had recently discovered a method ...
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4answers
351 views

Whatever happened to quaternions?

Quaternions were made up by Hamilton. They are an extension of complex numbers. It is said that he first introduced "3d tertions". He was thinking what the relation between i and j had to be ...
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102 views

What kind of mathematics had Max Ernst in mind?

Max Ernst was a painter belonging to the Dadaistic movement. One of his paintings shows Euclid in a somewhat, well, let's say Dadaistic fashion (although fashion and Dadaism don't go along well). We ...
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1answer
97 views

When were equivalence classes formalized?

Neither wikipedia or the first few pages of Google are showing me much about the history of the development of equivalence classes. When was this notion first formalized? Footnote: I originally asked ...
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49 views

Help understanding Egyptian circle

I was reading this Wikipedia page searching for the Egyptian area of circle and there is a following picture there: Trying to understand what is meant by this since it is under the "Area" ...
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1answer
108 views

Aziz of Complex Analysis

Does anyone know about Prof. Abdul Aziz on whose name Aziz's theorem is named? Aziz's theorem is a theorem about the location of zeros of polynomials.
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1answer
144 views

What did Fourier mean by stating that every function can be decomposed into sine and cosine functions?

Fourier stated that every function can be decomposed into sine and cosine functions. Was he referring to periodic functions only? To a certain class only? I ask, because it seems clear (at least to me)...
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1answer
109 views

What does the Fourier transform have to do with heat?

For example the current version of the Fourier analysis article on Wikipedia says the study is: […] named after Joseph Fourier, who showed that representing a function as a sum of trigonometric ...
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96 views

Collatz letter to Professor Mays

According to a translation of the letter of Collatz to Professor Mays in 1980, Collatz mentions that he hasn't figured out whether the number n = 80 resulted in a cycle or not, concerning the collatz ...
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34 views

First appearance of relations commutator,anticommutator with quaternion product

My query is the following, what is the first textual reference of the usage of commutator and anticommutator regarding quaternions in a similar way relative how it is done in the wikipedia article of ...
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61 views

Continuation on Galois’ lost memoir(s): was Poisson right in his review of Galois’ memoir?

A recent question asked whether Galois’ “lost” memoir has been since recovered (similar to Abel’s lost memoir). The memoir referenced in the question is the one Galois submitted to the French “...
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58 views

What is the origin of the "imaginary" in imaginary numbers? [duplicate]

When was the imaginary number, i, introduced? Why was it called imaginary? Isn't it just as imaginary as a negative number? Aren't all numbers imaginary, for that matter? I am not interested in the ...
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Is there any example of a long-standing mathematical conjecture whose resolution did not require advanced knowledge?

Famous conjectures whose solutions took decades or centuries were usually resolved with the help of sophisticated theories and techniques unknown at the time the conjecture was first claimed. Is there ...
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2answers
263 views

Who discovered this closed form formula for the n-th prime number?

The following is a formula for the $n$-th prime number ($[\,]$ represents the floor function). Who was the first person to discover it? The value of this formula: people have been exploring the ...
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96 views

What is the origin of the term “Telescoping Series”?

I looked into Carl. B. Boyer and Morris Kline books of math history, some calculus books like Apostol and Swokowski, many pages on the internet and even the Tractatus de Seriebus Infinitis of Jacobi ...
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66 views

Counterweights in the overhang problem

In their amazing paper Overhang (Amer. Math. Monthly 116 (2009), 19–44), Mike Paterson and Uri Zwick revisited the old chestnut of how much of an overhang one can achieve by stacking bricks at the ...
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1answer
151 views

Confusion on the original article by Lucas

I am currently researching on all primality tests deriving from Lucas' original paper Théorie des Fonctions Numériques Simplement Périodiques, which is of course known for its great deal of confusion. ...
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1answer
154 views

Why is the number of elements in a group called "order"?

This is a question that I have for a long time, Maybe it is something silly, but I really want to know. Why is the number of elements in a group called "order"? I mean, the word "order&...
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1answer
143 views

Recording current development of research mathematics

Are there historians of science that are systematically recording current activity in research mathematics ? For example, a decade ago there was a lot of stuff through blogs and Mathoverflow, nowadays ...
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194 views

What are some notable contributions of mathematical logic to mathematics (outside of mathematical logic)?

I have been reading an introductory text in mathematical logic (Holden, 1995). The final chapter presents the resolution of Hilberts's tenth problem concerning the integer roots of an arbitrary ...
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1answer
112 views

Why did Øystein Ore's lattice-based approach disappear?

I was watching this series of lectures on universal algebra on YouTube and the instructor, Charlotte Aten, mentioned that Øystein Ore studied lattices with the goal of using lattices as a unifying ...
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1answer
187 views

Lost memoir of Évariste Galois

According to the Wikipedia article on Évariste Galois He submitted his memoir on equation theory several times, but it was never published in his lifetime due to various events. Though his first ...
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2answers
173 views

When did the notion of space, geometric space appear?

When in history did the notion of space, geometric space appear? I. e. when in history geometric space was treated or thought of as a whole, as the site in which all geometric objects exist? When I ...
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0answers
115 views

How did Hamilton conclude the quaternions had to be four dimensional?

I have seen many times before that Hamilton started off believing he would need a three-dimensional system over the reals in order to describe 3D rotations. He considered numbers of the form $a + bi + ...
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2answers
142 views

Origin of the term "field" (in "vector field")

I am reposting a thread from "physics stack exchange" : I was wondering - Why do we use the word "field" to describe a vector field? i.e., a field is "an expanse of open or ...
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0answers
271 views

Is it true that Empress Elisabeth of Austria did math?

I have encountered a user on Math Stack Exchange with writing in his bio that Empress Elisabeth of Austria ("Sisi") did some math and she was famous for an unsolvable integral: $$\int_{0}^{1}...
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10answers
8k views

Has physics ever given a physical significance to a mathematically abstract idea?

Consider a fundamental concept in maths that was created to 'solve' a problem that simply couldn't be solved by any other approach (or maybe for some other reason). Now let's assume that this concept ...
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4answers
335 views

Why are the standards of mathematical proof still unsettled?

Please see the embold phrases below. I'm just a laywoman, and I'm just seeking simple answers. I last took math when I was 17. I read Has the standard of mathematical proofs changed over time?, but ...
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2answers
85 views

Do we know of any ancient 'Introduction to Mathematics' in Ancient Greece, besides "The Elements"? [duplicate]

Given that Euclid's work is titled "The Elements", it is safe to imply that it is a compendium of elementary results of Ancient Greek Geometry. Other works, such as those of Apollonius, ...
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62 views

Who first proved that the existence of a Euclidean algorithm implies unique factorization?

In Simachew's "A Survey on Euclidean Number Fields", he said that Gauss used the existence of a Euclidean algorithm in Gaussian integers to prove that it has unique factorization. Also, he ...
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2answers
95 views

Different conventions between Fourier Transform and Characteristic Function

While it is clear that there are several conventions for Fourier transforms of intragrable functions on $\mathbb{R}$, I don't think I have ever seen anything different from the three following ...
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2answers
200 views

Reverse subtraction: has any culture had a symbol (call it $\oplus$) where $A \oplus B$ (read in the same direction as in the language) $:= B - A$?

The standard use of the minus sign is such that $A-B$ means you subtract B from A. Thus $$5-2 = 3.$$ Has any culture used a symbol (let's call it $\oplus$) where $A \oplus B$ means you subtract A from ...
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3answers
172 views

Best history of Maxwell and his equations

I've done my B.S. in Electrical Engineering as well as mathematics but I'd like to get a proper, or complete history of Maxwell and the history of his derivation of the equations and the newness of ...
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1answer
157 views

Origins of Zariski topology

Why did Zariski feel the need to define his famous topology? Was this notion used in one form or another prior to him in algebraic geometry?
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61 views

Origin of Lang's proof of the Cayley-Hamilton theorem

Is the proof of the Cayley-Hamilton theorem given by Serge Lang in Algebra (page 561) an original one, or has it been borrowed from some earlier sources? Who came up with it first? (Lang's proof is ...

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