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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What was Richard Courant's saying about mathematical research apart from applications?

I remember reading somewhere (perhaps in The Mathematical Experience) that Richard Courant wrote something to the effect that, without applications to guide the river of mathematical discovery, ...
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Why is “h” used for height? [closed]

In Mathematics, it is common to use $h$ for height in various languages, including those whose word for height does not start with h. Why is that?
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1 vote
1 answer
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Why was the cubic specifically so hard to solve?

I'm a huge fan of the history of Algebra and, recently, I've noticed a bit of an oddity. Degree one equations have been known (and solved) for as long as human history. For degree two equations, we ...
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0 votes
4 answers
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What set of criteria led Hamilton to discover the quaternions?

Frobenius's theorem states that the only finite-dimensional, associative division algebras over $\mathbb R$ are: $\mathbb R, \mathbb C, \mathbb H$ (where the last of these are the quaternions). So one ...
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Where can I find a copy of Dieudonné's 'Infinitesimal Calculus'?

I found a copy of the French version 'Calcul infinitésimal' online but the English edition seems to only be available on Amazon for a very hefty price, or in American libraries which I do not have ...
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10 votes
5 answers
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What makes the right angle special enough to be distinguished in the French metric system?

When introducting the metric system, the French tried to decimalise the degrees used for angles. They defined the right angle to contain 100 gradians. Why was the right angle chosen? A somewhat ...
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1 vote
1 answer
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Why two words "summation" and "addition" do exist in literature?

We all come across these two words in literature: summation, addition. I personally do not know any difference between them and I view both of them the same in all mathematical aspects. Is there any ...
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7 votes
1 answer
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Was a mathematical connection involved when introducing "graph" of a function and "graph" in graph theory?

A colleague and I were having a discussion about mathematical similarities between graphs of functions and graphs as used in graph theory: Simple graphs can be defined in terms of pair (of vertices), ...
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2 votes
1 answer
207 views

History of the definition of complex derivative

Almost all of modern complex analysis (Cauchy residue theorem, analytic continuation, etc) depend on the definition of a complex derivative. That definition requires the derivative at a point $z_0$ is ...
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2 votes
2 answers
647 views

Where can I find Grothendieck's letter of resignation from Bourbaki?

I encountered Grothendieck's resignation letter from Bourbaki along with its English translation not too long ago on the web, but for now it seems it's nowhere to be found. I've scoured through the ...
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3 votes
1 answer
164 views

Who is Donald Fisk?

In stochastic calculus, the name Stratonovich appears all over the place. However, even though Donald Fisk supposedly obtained similar results, his name appears nowhere. Who was Donald Fisk? I cannot ...
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0 answers
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When and how did signal processing reach the core of functional analysis?

Functional analysis and signal processing have a strong bond and I am trying to understand how and when it all started. Technically, signal processing is heavily based on Fourier analysis, which helps ...
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14 votes
3 answers
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Historical example of research papers being misinterpreted due to poor wording and creating controversy?

Is there any example of major controversy in the scientific community caused due to poor wording and/or misinterpretation of words?
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8 votes
2 answers
285 views

Why was solving polynomial equations historically considered so interesting?

From reading a few accounts of the unsolvability of the quintic, I am told that, e.g., there were public contests in which people competed to solve polynomial equations, and that over the course of ...
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5 votes
2 answers
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When did they begin to make left and right shoes?

In the memoirs of the Polish mathematician Hugo Steinhaus ("Mathematician for all seasons", vol. I, English translation, Springer, 2015) he recollects a conversation with Henri Lebesgue in ...
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1 vote
1 answer
148 views

Abel-Runge lemma [closed]

I read recently that there exists an Abel-Runge lemma. What is it? Google does not give an answer. I know about Abel's lemma (the summation by parts) and the Runge-Kutta method but I have never heard ...
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2 votes
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Who established the current standard demonstration of Euler-Lagrange equation in calculus of variations?

Who established the current standard(*) demonstration of Euler-Lagrange equations in calculus of variations, that is, $\displaystyle\frac{\partial f}{\partial y}-\frac{d}{dx}\frac{\partial f}{\partial ...
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1 vote
0 answers
140 views

The exclamation mark over a relation symbol

My old linear-algebra teacher, whom I can no longer ask, wrote on a black board an exclamation mark over the binary symbol of a logical formula, the main symbol of which is that binary symbol, to say ...
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3 votes
1 answer
106 views

Reference request for Gauss's original discovery of the special property of the $j$ function

In Interchapter VII of his biography of Gauss, W.K. Buhler describes Gauss's discovery of one of the important properties that characterize the $j$ invariant (Klein's absolute invariant; Gauss called ...
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Historicity of Euclid. Looking for the references of Euclid in ancient texts that has survived [duplicate]

The general consensus is that Euclid was a real historical figure. Wikipedia https://en.wikipedia.org/wiki/Euclid concludes on the hypothesis that Euclid was not a real person, "This hypothesis ...
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2 votes
1 answer
193 views

How did Kepler's teacher Mästlin calculate the Golden section?

In a letter to Kepler, his former professor Michael Mästlin mentioned that he had calculated the golden section to the 9th decimal place. Why was it considered notable? What method$^\dagger$ did ...
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-1 votes
1 answer
176 views

Did Egon Pearson have a PhD?

Did the statistician Egon Pearson have a PhD? If not, to what extent did he write a dissertation?
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1 vote
1 answer
104 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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1 vote
1 answer
205 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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3 votes
3 answers
301 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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0 votes
1 answer
106 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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4 votes
0 answers
135 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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1 vote
0 answers
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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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1 vote
1 answer
103 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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8 votes
3 answers
364 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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0 votes
1 answer
66 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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0 votes
2 answers
283 views

What happened to the original sources of Euclid's Elements?

I am aware of the fact that Euclid's Elements is a compilation of the works of previous Greek mathematicians like Thales, Pythagoras (his school), Eudoxus, Theaetetus, etc. However, I want to know the ...
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0 votes
1 answer
57 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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2 votes
1 answer
456 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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1 vote
0 answers
139 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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4 votes
1 answer
147 views

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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-1 votes
2 answers
205 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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1 vote
0 answers
105 views

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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1 vote
0 answers
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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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3 votes
4 answers
467 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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2 votes
0 answers
113 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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3 votes
1 answer
120 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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1 vote
0 answers
56 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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0 votes
2 answers
213 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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2 votes
1 answer
206 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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3 votes
1 answer
162 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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3 votes
2 answers
309 views

Does the practice of viewing modern mathematics as the necessary direction in which ancient mathematics must have evolved have a name?

I have noticed a tendency among some historians and scholars of mathematics to regard the mathematics of antiquity as a less developed version of modern mathematics. This view reminds me of the belief ...
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3 votes
0 answers
106 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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0 votes
0 answers
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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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2 votes
0 answers
81 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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