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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222 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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1answer
42 views

History of the Darboux-Froda theorem

I am curious about the history of the so-called Darboux-Froda theorem, which is the following theorem: a monotone function $f:[0,1]\rightarrow \mathbb{R}$ has at most countably many points of ...
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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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1answer
66 views

Why 360° is assigned to circle full turn ? Not any other number? [duplicate]

Please look at this question https://math.stackexchange.com/posts/comments/9011243?noredirect=1 A user comment this so I thought of asking here You mean why did we decide on using 360 degrees? I don'...
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What is the etymology behind sine, cosine, tangent, etc.?

I heard somewhere that it was actually a mistake in translation. What's the correct story?
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1answer
235 views

Were there proofs of the Lebesgue Differentiation Theorem without using maximal functions?

Is there a proof of the Lebesgue Differentiation Theorem that does not involve the Hardy-Littlewood Maximal Function? For example, did Lebesgue prove it? If there is such a proof, where can I find it?...
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1answer
954 views

Who is John B. Walsh?

Stochastic Partial Differential Equations (SPDEs) have received much attention in recent years, culminating in the fields medal of Martin Hairer. A rigorous mathematical starting point for the studies ...
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History of supremum with parameters

I had the following 'history of mathematics' question: Who first used the notion of supremum explicitly involving parameters? Let me provide a positive example of the latter notion: Baire defines 𝑀(𝑓...
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1answer
100 views

Armstrong numbers - who is or was Armstrong?

According to Wolfram's MathWorld article "Narcissistic Number", such numbers are also called "Armstrong numbers". Such a number is an $n$-digit number $N$ such that: $$N = {d_1}^n +...
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1answer
103 views

A Survey of Modern Algebra, 1st Edition (Birkhoff and Mac Lane): The Direct Product

Good people, so this is a very specific request I have from you relating to my almost manic obsession with tracking down the first use of particular terminology in mathematics. Background information: ...
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1answer
164 views

History of Direct Sums and Direct Products

So I like to get down into the details of how certain mathematical concepts came to be, and purely as a matter of curiosity, I was wondering if anyone know which mathematician first gave the ...
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Why do we call a linear mapping "linear mapping"?

According to P. M. Cohn's Classic Algebra, for historical reasons we call a linear mapping "linear mapping". What are the historical reasons that led to the adoption of the term "linear ...
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First Use of the Short Exact Sequence

A question I've been curious about for a long period of time and tried to find the answer to myself a number of times (but apparently never been able to figure out just the right thing to type into ...
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2answers
369 views

I am searching for a book of this form and content, is there any?

I would like to know is there a book that is both a history of mathematics and a collection of open problems? I know that there exist many books that cover either larger or smaller periods of the ...
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1answer
117 views

Is multiplication postulated axiomatically in Peano arithmetic?

I figured this question is better suited to this stackexchange. I give some mathematical details, but this is primarily an HSM question. According to this post, the existence of multiplication in ...
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1answer
184 views

How did Gaussian and Eisenstein integers get their names?

I can separate this into two questions at some point if necessary, but it's possible that sources for the answer to one will provide the answer to the other at the same time. I learned about ...
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1answer
139 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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Were all the branches of Mathematics always considered part of a single discipline "Mathematics"?

I've read arguments and statements in internet arguing about Mathematics being a science or a language. To me, certain branches of Mathematics fit more with the definition of language and others with ...
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1answer
128 views

How long have all the mathematicians working in the respective fields known the theory of categories

Vague the question: how long have all the mathematicians working in the respective fields known the theory of categories? More specific questions: Is it true that all modern working algebraic ...
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1answer
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History of the inverse matrix

I know the definition and the procedure to calculate the inverse of a matrix, but I want to know the history of starting the idea of an inverse matrix. mathematicians must have faced a real life ...
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1answer
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Who said that math or statistics is not free from class interest?

I'm not 100% sure this is the right site for this question, but here it goes. An already dead professor said in a lecture that Stalin (or perhaps another communist leader) wrote once something along ...
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1answer
122 views

What is the origin of the "problem of Brahmagupta" of constructing inscribed quadrangle with given sides?

I am looking for a source of the following construction problem: Construct an inscribed quadrangle with given sides. I know it under the name problem of Brahmagupta, but I do not know any evidence ...
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139 views

History of points with coordinates notation

In this MathEducator StackExchange article, "Notation of points with coordinates", it's posed the question about what is the best notation for geometrical points and their coordinates: $P(3, ...
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1answer
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Who first defined the "equal-delta" or "delta over equal" ($\triangleq$) symbol?

The symbol $\triangleq$ is sometimes used in mathematics (and physics) for a definition. It is instantiated for instance in the Unicode Character 'DELTA EQUAL TO' (U+225C). The notation $t \triangleq ...
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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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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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1answer
150 views

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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Madhava and $\pi$

I recently learned that Madhava of Kerala (c.1340–c.1425) was the first to discover the following formula for $\pi$: $$\frac{\pi}4\ =\ 1 - \frac13+\frac15 - \frac17 + \frac19 - \frac1{11} + \cdots$$ ...
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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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1answer
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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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1answer
87 views

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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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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1answer
141 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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22answers
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Literary works authored by mathematicians

At a first glance, Mathematics and Literature look like two completely unrelated subjects. I wonder whether there are examples of acclaimed mathematicians which wrote novels, poems, or other ...
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2answers
587 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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1answer
141 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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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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478 views

Who was L. Aubry?

In his magnificent book Number Theory: An approach through history, from Hammurapi to Legendre, André Weil quotes the article Solution de quelques questions d'analyse indéterminée, by L. Aubry (Sphinx-...
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Historical example of research papers being misinterpreted due to poor wording and creating controversy? [duplicate]

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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0answers
72 views

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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586 views

Did Euler ever write $f(x)$, with parentheses?

Euler is often credited with introducing the notation $f(x)$, and people cite the example $f(\frac{x}{a}+c)$, where he had to use parentheses around the function argument. On the other hand, when the ...
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1answer
230 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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130 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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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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2k views

How did mathematicians notate the empty set before $\varnothing$?

Recently, I learned that $\emptyset$ or $\varnothing$ is a relatively new notation for the empty set and was created in 1939. I know $\{\}$ is also used along with $\{\cdot\}$ to denote empty sets. ...
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1answer
145 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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What role has Whitehead's Conjecture played in the thinking on the plurality of set theories?

I am curious about the history of the Whitehead's Conjecture, as this was the first natural mathematical statement, in the sense that mathematicians were actually interested in the answer, that was ...
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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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371 views

Did Archimedes view fractions as "numbers"?

For quite some time I had the wrong impression that classical Greek mathematicians didn't use fractions. (I don't remember where I had this from.) But I recently looked into Heath's book about ...

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