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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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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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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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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0answers
75 views
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:
...
5
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2answers
127 views
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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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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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 ...
5
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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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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 ...
5
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1answer
179 views
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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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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3answers
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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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138 views
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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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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77 views
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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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
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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1answer
541 views
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), ...
2
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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 ...
2
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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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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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3answers
5k views
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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75 views
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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2answers
246 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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2answers
3k views
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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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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0answers
74 views
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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0answers
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 ...
3
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1answer
92 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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41 views
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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1answer
116 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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1answer
89 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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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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3answers
200 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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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 ...
4
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0answers
124 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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101 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
99 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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3answers
338 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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1answer
59 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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2answers
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
52 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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1answer
367 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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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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1answer
98 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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2answers
120 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 ...
