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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Poincaré's definition of mathematics (?)
Poincaré is said to have given this definition of mathematics:
It is the art of giving the same name to different objects. I can not believe this quote is from Poincaré.
Did Poincaré really say this? ...
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The origin and use of the term "equianharmonic" (elliptic function)
In Weierstrass notation, the principal elliptic function $\wp$ is a solution of the differential equation
$$ (\wp')^2= 4\wp^3 -g_2\wp -g_3. $$
The case when $g_3=0$ is called lemniscatic (it ...
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Influence of Edmund Landau's list of four problems
At the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about prime numbers: Goldbach's conjecture, the twin prime conjecture, Legendre's conjecture (that there ...
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Original source of these 2 trigonometric identities
I am interested in knowing what is the original source/author of the following identities:
$\tan{\frac{\alpha}{2}}\tan{\frac{\beta}{2}}+\tan{\frac{\alpha}{2}}\tan{\frac{\gamma}{2}}+\tan{\frac{\beta}{2}...
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Were Priestly and Davey wrong about about "Order: A Theory with A View" being written by Ivan Rival?
The textbook Introduction to Lattices and Order by Priestly and Davey mentions in its first edition preface:
In a proselytizing article, Order: a. theory with a. view [in Kla.ssifikation und Ord:nung,...
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What was probability like before Kolmogorov?
How was probability studied or understood before Kolmogorov axiomatized it?
I mean Bernoulli and Gauss had already started inventing and using distributions way before Kolmogorov came into the scene. ...
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Zermelo's or Fraenkel's early consideration of something equivalent to countable Replacement
I have now claimed a few times on the internet, based on something (sensible!) I read, that at some point in the 1920s, that Zermelo at one point considered as a set theoretic axiom (schema) something ...
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Why did Clairaut's theorem take so long to prove?
I was reading the Wikipedia on Clairaut's Theorem (Symmetry of second derivatives) and the article accounts the significant amount of time and failed proofs occurred before the theorem was made fully ...
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What did George Boole contribute to order theory?
The Wikipedia page says for order theory says:
As explained before, orders are ubiquitous in mathematics. However, earliest explicit mentionings of partial orders are probably to be found not before ...
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What is Bertrand Russell citing Gilman for in "On the Notion of Order"?
In the first few pages of "On the Notion of Order", Bertrand Russell has the footnote:
The following account of the genesis of order is virtually identical with that of Mr. B. I. Gilman, ...
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When did Abel publish his test for the convergence of series?
Did Abel published of testing the convergence of series? If so, when did he published it. Also, did he offer a proof of the test? Or did he simply stated the test?
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Was religion not present at all in the Astronomy of the Ancient Greeks?
I attended a lecture on the history of Astronomy and Mathematics, and I was somewhat puzzled by how scientific the early Greeks were. Yes, I am aware that they have many of the greatest mathematicians ...
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The first commutative diagram
Cf. https://golem.ph.utexas.edu/category/2013/07/the_first_commutative_diagram.html
Is this the first ever commutative diagram? By commutative diagram I mean anything that shows an equality (or ...
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What are the second and third "Hebrew Algebras" Mary Everest Boole refer to?
In the book "Philosophy and Fun of Algebra", Mary Everest Boole has a chapter dedicated to what she calls "the first Hebrew algebra" (Chapter 6). She later refers to the "...
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What original mathematics arose from Jacquard loom and similar weaving devices?
Research mathematics is seldom directly applicable, but the questions we study are motivated by interplay with contemporary demands. As a combinatorialist, it's apparent that my field has benefited ...
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Engineering problems leading to mathematical research
I would like to know examples of mathematical research which had its origin in engineering problems (I am mainly interested in mechanical engineering and civil engineering) and which was actually ...
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Does "Metatron's cube" have a history and a serious name in geometry?
This is a figure that I saw while going down the rabbit hole of "Sacred Geometry" back when conspiracy theories and related nonsense were relatively harmless and fun to laugh at. A book ...
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Are there any well known mathematicians who were fascists?
I only recently learned that Pascual Jordan, a well known physicist, with significant contributions to the development of early quantum mechanics was a paid up member of the Nazi Party. He in fact ...
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Why was Cauchy studying Schur polynomials and related topics?
Let $\lambda_1 \geq \lambda_2 \geq \cdots \geq \lambda_n$ be nonnegative integers. The Schur polynomial $s_{\lambda}(x_1, \ldots, x_n)$ can be defined as the ratio
$$s_{\lambda}(x_1, x_2, \ldots, x_n) ...
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When did bounties and prize money for open mathematical problems start being a thing?
I'm a science/math journalist [ger] and currently I'm working on an article about the culture of prize money/bounties for solving open mathematical problems (Millennium Prize Problems and such). One ...
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Are there any arithmetic problems studied by Euler still open?
Fermat's last theorem, which Euler had studied in the case of certain exponents, was only solved in the 1990s. Also, a counterexample to Euler's sum of powers conjecture has been found quite recently (...
user17244
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Did Rayleigh or Ritz prove the Rayleigh–Ritz theorem?
The maximum eigenvalue of a real symmetric (or complex Hermitian) matrix is given as the maximum of the associated the quadratic form:
$$
\lambda_{\rm max}(A) = \max_{\|x\| = 1} x^*Ax. \tag{1}
$$
This ...
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How to build a protractor without a protractor?
We all know how to use a protractor, it is taught in elementary school. However, I was wondering what type of knowledge is required to build one from scratch.
For instance, was the understanding of $\...
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Who first proved necessity of Euclid's formula for pythagorean triples?
The following well-known formula for pythagorean triples is commonly called Euclid's formula:
If $a, b, c$ are three natural numbers with $a,c$ odd, $b$ even, $\gcd(a,b,c)=1$ and $a^2+b^2=c^2$, then ...
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Definition and Name Change of the Oscillation Function
I have two related questions:
Who first defined the oscillation function (perhaps under a different name)?
When did the switch from the phrase "saltus function"(*) to "oscillation ...
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How the asymptotic expansions of the Dawson integral and $\exp(x^2)\operatorname {erfc}(x)$ were originally obtained?
There are two well known asymptotic expansions of the Dawson integral $F(x)$ and the function $\exp(x^2)\operatorname {erfc}(x)$ as $x \rightarrow \infty$:
$$
F(x)\sim (1/2)(1/x+1/(2x^3)+ 3/(4x^5)+\...
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Why was it difficult to initially phrase compactness?
From beginnings of topology, it was clear that the closed interval $\left[a,b \right]$ of the real line had a certain property that was crucial for proving such theorems as the maximum value theorem ...
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Did John von Neumann solve any unsolved problem in mathematics?
I have searched and examined legendary stories of the problem-solving skills of von Neumann in mathematics.
With George Polya
With Dantzig
Maybe there are other stories showing that he is a great ...
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Old unsolved questions in mathematics
John Stillwell, in his textbook on arithmetic cites Erdos:
As the great
Hungarian problem-solver Paul Erdos liked to point out, if you can
think of an open problem that is more than 200 years old, ...
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When was Lipschitz equivalence first attributed to Lipschitz or did Lipschitz formulate it himself?
In his book Introduction to Metric and Topological Spaces, author Wilson A Sutherland in explaining the equivalence of metrics invoked the definition:
Two metrics $d_1, d_2$ on a set $X$ will be ...
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How were the works of axiomatization of probability progressed prior Kolmogorov?
In Probability Theory and Stochastic Processes with Applications, author Oliver Knill remarked:
The name "Kolmogorov axioms" honors a monograph of Kolmogorov from 1933 in which an ...
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When was the study of automorphic (and in particular modular) forms become "adelized"?
The theory of automorphic forms is stated in modern language as a function on the adelic points of some reductive group satisfying certain properties (see for instance, Chapter 7 of An Introduction to ...
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Examples of math problems which exhibited deceptive progress
I'm interested in gathering a list of problems in the history of maths where people were committed to a particular strategy for some time, only to find out that the approach was fundamentally flawed.
...
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What is the history of the Basel Problem before Euler and how did it inform him?
I am interested in the history of the Basel problem. More specifically, I'm interested in knowing the history of failed attempts before Euler's crack of it, so as to know what bits of evidence ...
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Exact source that Descartes had observed that $V-E+F=2$ for planar graphs
In recent literature, I have read that René Descartes had observed that $V-E+F=2$ for planar graphs. Is there any image of that page of book or article of Descartes?
Seeing real page that contains the ...
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Did Rene Descartes send or receive any letters (regarding mathematics) on 18.v.1638 (May 18, 1638)?
I dreamed about the date 18.v.1638 (May 18, 1638) last night.
As I currently do research on odd perfect numbers, and because Rene Descartes lived during the years 1596 to 1650, and as I am not a math ...
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Are there any famous female mathematicians who have written in Latin?
I am writing a book on modern mathematics and the Latin language. My main examples are Newton, Euler, Gauss, etc. and some others, but all men.
Is there a woman who has written important mathematics ...
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Origin of Problem 6 on the 1988 International Mathematical Olympiad
The recent Numberphile video on the famous Problem 6 of the 1988 IMO (mentioned in a recent answer on this site) got me wondering:
Who came up with this problem in the first place, and how did they ...
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What is the origin of the negation ( ¬ ) operator from logic?
I'm curious as to what the rationale was, and who the idea occurred to, for the ¬ symbol. I'll grant that more common mathematical symbols like +, −, × and ÷ are also likely unknown, but they seem to ...
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Why is $Ax^2+Bx+C=0$ called standard form of Quadratic Equation? And who declared it the standard form?
$Ax^2+Bx+C=0 $ is mentioned as standard form of quadratic equation in every textbook or encyclopaedia, but what's so special about it that its called standard form of quadratic equation.
Also, I am ...
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When did we first know the $11$ ways of opening up a cube?
Take a box in the shape of a cube and cut $7$ of its edges so that all the faces stay connected and flatten it out onto a table. It turns out, there are $11$ distinct meshes that emerge: https://math....
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Origin of the term "affixe"/"affix" in the geometric treatment of complex numbers
In current French mathematical tradition, when introducing complex numbers, it is common to hear about "complex plane of Argand-Cauchy".
What is particular in French treatment, it is the ...
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Secrecy in Mathematics
I've been told that Pythagoreans kept as a secret the incommensurability of certain quantities like the diagonal of the square. Are there other mathematical discoveries whose authors didn't want the ...
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Which are the most ancient theorems that negate the existence of some deeply valued entity?
Are there theorems earlier to the works of Abel and Galois showing that a problem that mathematicians had been trying to solve for a long time was actually unsolvable? Or are those works novel in the ...
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Why is the letter $b$ used to represent the y-intercept in the equation of straight line?
The slope-intercept form of a non-vertical line is $y=mx+b$. I have been told that the slope is called $m$ because it is the first letter of the French word for mountain. But why is there the letter $...
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Why are the symbols E, F, G, L, M, and N used for the coefficients of the fundamental forms?
In differential geometry, if $e_1$ and $e_2$ are bases for a tangent space $T_pM$, then the coefficients of the first fundamental form is:
$$\begin{align}E&:=\left<e_1,e_1\right>\\F&:=\...
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When did ordered pairs first appear?
I am interested in the history of the ordered pair.
When did ordered pairs as a concrete object, not necessarily defined in terms of sets, appear in a mathematical or logical setting?
The definition ...
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What mathematical expressions took a long time for a closed form to be found?
The Basel problem, $\sum_{n=1}^\infty{\frac{1}{n^2}}$, took 90 years for a closed form, $\frac{\pi^2}{6}$, to be found.
I'm curious to know what other mathematical expressions, especially those ...
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What were the main different homology theories in 1930 and how did they get united?
I am reading The Uses and Abuses of the History of Topos Theory by Colin McLarty. On page 353, the following is said:
An homology theory associates groups to topological spaces so that the group ...
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What does P. G. Tait mean by "double points"?
I am reading the following short paper:
P. G. Tait. Some elementary properties of closed plane curves. Messenger (2) 6 (1877), 132–133. JFM 09.0393.01
Here, Tait writes
The closed curves ...
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