Questions tagged [math-history]
Use this tag for questions concerning history of mathematics, historical primacies of results, and evolution of terminology, symbols, and notations. Consider if History of Science and Mathematics Stack Exchange is a better place to ask your question.
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Motivating Gauss's suggestions of prize problems for the Goettingen university.
(This question was posted before in History of Science and Mathematics stackexchange, but since I recieved no comments after 6 days, I decided to reask it here.)
P. 220-221 of volume 12 of Gauss's ...
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How did Issac Newton write integral symbol? [migrated]
Issac Newton is known as the discoverer of the FTC(Fundamental Theorem of Calculus), so maybe he wrote the integral symbol and derivative symbol. I know he wrote the derivative symbol as $\dot y$ but ...
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Descartes’ Translation Problem
One of the issues Descartes came across in his work on the translation between algebra and geometry was representing a set of equations of multiple unknowns ( a system of $n$ equations and n unknowns ...
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How did Newton compute derivatives by first computing power series?
I've read that the way we compute power series these days is not how it was originally done. These days, we compute the derivatives of the function we wish to expand in order to compute the power ...
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I am asking about the first to prove this Theorem. [closed]
It's a well know fact that if a matrix $A_{n \times n}$ satisfies $|A|<1$ in the operator norm, than it's Neumann series converges and is equal to $A^{-1}$.
The question is: Can we trace back to ...
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Mystery integral in the first issue of Annals of Mathematics
Vol 1. No. 1 of Annals of Mathematics has an "Exercises" section with this unusual integral sent in by a Professor Lewis Green Barbour:
$$\int_{\frac \pi 2}^\pi \sqrt{1-\frac 1 2 \cos^2\...
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Does math use diacritics?
Most languages using Latin script use diacritics to modify letters. In mathematics, it often seems necessary to introduce many symbols and modifiers, such as $f'$ for derivatives or $M^\text{T}$ for ...
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Famous False Theorems in Analysis
Until about the 1870s, an example of a well-known false theorem in real analysis was Ampere's theorem, which has the following false statement.
Propotision.(Ampere's Theorem)
Any continuous function ...
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First usage of "intersection graph" in a publication?
I am wondering about the first published use of the concept of an intersection graph.
At first I thought this 1966 paper by Erdos is the first publication defining and using intersection graphs ...
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Gödel on the “True Reason” for Incompleteness
In footnote 48a of his famous paper on incompleteness, Gödel writes:
[T]he true reason for the incompleteness inherent in all formal systems of mathematics is that the formation of ever higher types ...
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What happened to wavelet.org? [closed]
I am currently working with wavelets. From my online research, it seems to have peaked in popularity at the end of the 90s, even though few hidden gems that summarize the wavelet theory pretty well ...
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Curious about the meaning of the term '&c' in Legendre's paper [closed]
In Legendre's paper "De Nouvelles Méthodes pour la Détermination des Orbites des Comètes", the term $\&c$ is used. I'm not familiar with that terminology, but it seems to me that it ...
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Hudde's cubic proof
I've been following the proof of Hudde's description of Cardano's method of cubic roots shown here https://proofwiki.org/wiki/Cardano's_Formula. Does anyone know where this proof comes from? I can't ...
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Something like first Betti number that is $-1$ for a $2$-sphere
I told some advanced high-school students informally about homology (i.e. the "number of holes" in a space, by which I really mean the first Betti number), and one of them seemed to think ...
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Why does Euclid need the Parallel Postulate to prove equal chords are equidistant from the center?
Euclid's Proposition III.14 proves that chords are of equal length iff they are equidistant from the center. Euclid's proof is long and complicated, repeatedly invoking the Pythagorean Theorem, which ...
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Are there $N_n$ lattices generalizing the $N_5$ lattice?
$M_3$ and $N_5$ lattice, respectively, is a widely used notation for these two lattices.
I'm wondering what the indices mean.
For the M case, I found in the book of B. A. Davey, H. A. Priestley, ...
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primes and binomial coefficients
Lets us denote by $\mathbb{P}$ the set of prime numbers.
It is well known that, given an integer $p>1$ :
$$\boxed{p\in\mathbb{P}\Leftrightarrow\forall k\in\{1,\cdots,p-1\},\,p\mid\binom pk}$$
I ...
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Historical proof of Bézout's theorem
Bézout's theorem says that given $f, g$ homogeneous polynomials over $\mathbb{CP}^2$ with degrees $n, m$ respectively, the number of intersections of their zero sets is exactly $nm$, counted with ...
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What does Euler mean when he says "Let the arc z be infinitely small ; there will be sin.z=z and cos.z=1..."?
I am referring to, specifically the sin.z=z and cos.z=1. I am reading Euler's Introductio In Analysin Infinitorium, Vol. I, Ch. VIII and he jumps from binomials to ...
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History of Group Actions as their own Structures [closed]
I'm interested in when (and how) the modern idea of a group action developed and how group actions became their own algebraic structures.
As far as i can tell in the 19th century group actions were ...
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The lattices $M_3$ and $N_5$
Why are $M_3$ and $N_5$ lattices in the theory of lattices called so?
They are well known for that their existence as a sublattice signifies lack of modularity/distributivity, yet their names are a ...
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Book containing the following line
I came across the image below on social network and I feel quite excited about the line. I wonder if anyone knows what is the book (maybe a paper or an introductory note)? To the best of my knowledge, ...
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Historical order of introduction of numerical methods for PDE: finite difference, element, volume, and spectral methods.
I wanted to ask the community if what I believe is the order of the introduction of these methods are ballpark correct, and the order they were introduced. It would be appreciated if folks could tell ...
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On the concept of "similarity"
According to "The Words of Mathematics" by Steven Schwartzman, similarity in mathematics means "two similar things [that] look as if they're "one and the same" in respect to a ...
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A quotation of George Dantzig [closed]
In a Chinese book, it is alleged that George Bernard Dantzig said something along the following lines.
It was almost impossible for someone who had never been exposed to applied problems and had only ...
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What is the takeaway from this reference to repeated inversions of circles in circles (Felix Klein, 1893)?
(This is kind of an explain-like-I'm-five question. "This looks interesting, but I don't get it at all. Explain it to me.")
In 1893 Felix Klein wrote (1, 2) — or maybe "said," ...
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What are some important results of type theory?
It would be great to have an overview of some of the most important results in type theory.
What are in your opinion some of the most important results/widely applicable results in type theory ...
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Which came first: Integration of vector field over the surface S or integration of forms over manifold?
In integral calculus it is studied the integral of vector field over the surface S and in smooth manifold is studied the integration of forms.
Let $\varphi: U\longrightarrow S$ be a parametrization of ...
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Why is, for example, the theory of ordinary differential equations considered less pure than number theory?
This is a bit of a soft question, but why is it that number theory is considered the most "pure" branch of mathematics, and something like, say, the theory of differential equations, ...
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How to separate cubic equations into two conic sections: Deep dive into Omar Khayyam
Lots of people have asked how to use Khayyam's method but I am studying for my dissertation so really need to understand the why. What I really don't understand/ can't find useful proofs for is how he ...
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Origin of Definition of Handedness in Knot Theory
I read that to determine the handedness of a crossing, you look at a small, almost-straight segment of rope that has the overcrossing. You then check to see if that segment has an overall slope that ...
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Why mathematical reasoning is built on two-valued logic?
I have a very basic question.
How would you answer to somebody that is asking you why in mathematics we use two-valued logic as the very ground of math reasoning instead of some multi-valued logic?
Is ...
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Can we say that the rational numbers are a "larger set" than the natural numbers?
When mathematicians discovered the cardinality of sets, we learned that $$\operatorname {Card} \left(\Bbb N\right)=\aleph_0$$ and
$$\operatorname {Card} \left(\Bbb Q\right)= \aleph_0$$
So, is it okay ...
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Math History Reference Request: Open-Access Introduction Textbooks, Recently Published from $2015-2022$
As of recent, I have deeply read through Stephen Hawking’s “A Brief History of Time”, Thomas Levenson’s “The Hunt for Vulcan”, and Howard Eve’s “Foundations and Fundamental Concepts of Mathematics”. ...
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Where does the term non-singular (in non-singular matrices) come from?
Non-singular matrices are invertible and has determinant $\neq 0$. Does the term non-singular come from the determinant being able to take more than one value (which is any non-zero real value)?
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What is the history of the wave and heat equation?
I have a project in which we need talk to about the history of the wave and heat equation. I can’t seem to find much information about it( ie when it was discovered/derived, who discovered it, and any ...
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when was the terminology of "general" vs "special" linear group first used?
This is a reference request. I would like to understand the first use of the phrase "special linear group" to denote $SL_n$. In particular, I would like to understand whether it predates the ...
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Why don't we use "integral ring" instead of "integral domain"? [duplicate]
The word "integral domain" sounds like something about a "field", "region" or "area", but it is actually stands for a "special kind" of ring. Are ...
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Historical names used for variables, e.g. y=f(x). Why not z=f(y)?
The traditional rule for quantity symbols in math is to use first letters of Latin alphabet for constants, and last letters for variables.
I just wonder why the two most used variable symbols, $x$ and ...
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Where did the Idea to solve a weak form of a PDE solves the strong form approximately come from?
I am a student of civil engineering, focussing on the finite element method for solving partial differential equations approximately.
During my lectures, as well as in books targeted at engineers, the ...
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Will mathematicians ever define zero as denominator?
As you all know, Zero as a denominator is a no-go in maths. I always wonder if this could ever change.
For example you can’t use negative integers in the root but mathematicians defined complex ...
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Can you recommend me a book about the history of complex analysis?
I am writing an article about the beauty of complex analysis and need some chronological details. Is there any particular book where I can read and learn about the topic?
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Who first noted that entries in the powers of an adjacency matrix of a graph count the number of walks on the graph?
The Wikipedia article on powers of an adjacency matrix presently (as of 2022) notes the neat combinatorial fact that, given an adjacency matrix $A$ of some graph, entries of the $n$th power of the ...
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Who derived the Riemann-von Mangoldt formula for Dirichlet $L$-functions?
I was trying to find a reference for who derived the Riemann-von Mangoldt formula for Dirichlet $L$-functions, written in Davenport's Multiplicative Number Theory as
$$N(T,\chi)=\frac{T}{\pi}\log\frac{...
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Euclid's definition of a prime
In Euclid's Elements, Book VII, Definition 11, Euclid states that
A prime number is that which is measured by a unit alone.
As I understand it, this means that a prime number's only divisor is 1. ...
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How to show the similarity notation?
I have defined a similarity measure $U_{sim}(T_t,T_{t-1})$ which is the similarity metric between two items. Now I wanna show the the similarity between $T_t$ and all previous $T_i$s. I represented ...
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Really: why is the Kelvin transform harmonic?
So, it is a famous fact that if $u:\mathbb{R}^n \to \mathbb{R}$ is an harmonic function, then its Kelvin transform
$$
(Ku)(x) := \frac{1}{|x|^{n-2}} u\left(\frac{x}{|x|^2} \right)
$$
is harmonic too. ...
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In its earliest usage, did the notation "5 x 3" mean "five groups of three" or "five, placed into each of three groups"?
In today's time, if I take a look at what language we use to read out "5 x 3", it could be read out as "five-times three" (that is: three, five-times, as in five groups of three), ...
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Examples of inappropriate credit in mathematics [duplicate]
What are some known cases of inappropriate credit in mathematics?
Here, "inappropriate credit" means a common attribution that is not totally fair because someone who also discovered the ...
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Identifying the original Godel sentence in his 1931 paper
I've been exploring Godel's original 1931 paper On Formally Undecidable Propositions of Principia Mathematica and Related Systems (I'm using an English-translated version found here). And to pre-empt ...
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