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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Why is gamma function defined such that $\Gamma (n)=(n-1)!$ rather then $\Gamma(n)=n!$ [duplicate]

Why is gamma function defined such that $\Gamma (n)=(n-1)!$ rather then $\Gamma(n)=n!$, The latter ssems far more logical.
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Unable to find certain paper

Can anyone help me by providing the following paper L. Gegenbauer, Note ¨uber die Anzahl der Primzahlen, Sitzungsber, SBer. Kais . Akad. Wissensch. Wien (Math.)$95$, II ($1887$) ? Any help would be ...
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Infinite primes history

I am little confused with who was the first to modify Euclid's argument of infinitude of primes from $p_{1}p_{2}...p_{r}+1$ to $p_{1}p_{2}...p_{r}-1$? Some writers say it was E.E. Kummer ,($1878$) (...
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Which Smirnov is behind the Smirnov topology?

Good old Steen and Seebach discuss the Smirnov deleted sequence topology in their Counterexamples in Topology (2nd ed. 1978). This is also reported as the $K$-topology, in e.g. Wikipedia etc. ...
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Emile Borel and Henri Lebesgue and the history of measure theory

I know that both of these guys are from France and lived around the same time period so they must have had some sort of collaboration of understanding of each others works. What I am curious about is, ...
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Examples of combinatorial optimization problems that after some theoretical result was solved analytically

I am looking for examples of combinatorial optimization problems, if any, which after some theoretical result allowed other representations, thus supporting other formulations (for instance, from ...
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History of $\sin(nx) = 2^{n-1} \prod_{0}^{n-1} \sin\left(x + \frac{\pi k}{n}\right)$

What is the name of this identity? Who discovered this identity? What is the history behind this? I have looked up on Wikipedia with little documentation of the identity see finite product of ...
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How were complex geometric shapes drawn without computers?

How did mathematicians create drawings of complex geometric shapes in the past, without 3d graphics in computers? Here is one example of what I’m talking about, drawn in the 16th century:
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Who first invented/introduced the concept of the trace of a Matrix and Why?

Could anyone give any information about the invention of the concept of the trace of a Matrix, as this concept is so important and useful in linear algebra. I searched on the internet, but found ...
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Why did we invent number system (notations), if we were doing well without that? [closed]

I think we could be comparing the quantities without numbers: Ex: If we have to compare John's sticks with James', then we could keep eliminating one on one from both of them, and the one who ends up ...
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Who first discovered the matrix and the quotient field of polynomials representations for complex numbers?

Who first realized that the field of complex numbers is isomorphic to the set of real matrices following the form $\left(\begin{array}{cc} a & -b \\ b & a\end{array}\right)$? Hamilton? What is ...
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Why are “Wiener chaos” called like that?

This is a very soft question, but I was wondering from where does the term "Chaos" come, in the Wiener chaos theory?
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$\lim_\limits{x \to \infty} \frac1x \sum_\limits{n\leq x}\mu(n)=0 \iff$ Prime Number Theorem

I'm reading Analytic Number theory from Tom. M. Apostol's Introduction to Analytic Number Theory. In the fourth Chapter of the book he proves the equivalence of Prime number theorem with the ...
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Could the multiplication be a not well defined operation?

I was thinking about the fundamentals of arithmetic, and in particular about the concept of number. I'm not an expert of the history of math, but I suppose that all started when one realized that ...
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Sum of $n^{-s}$ over squarefree numbers

I read about $$ \sum_{n\in\mathcal{Q}}n^{-s} = \prod_{p}(1+p^{-s}) $$ in a book. Who first discovered this equation? Did it first appear in a paper? Here $\mathcal{Q}$ is the set of squarefree ...
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Moscow papyrus deriving approximation of $\pi$

I have posted a similar question here. What I am interested now is how to derive the approximation of $\pi$ from the following text: Example of calculating a basket. You are given a basket with a ...
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What was the very first use of calculus derivatives?

I am making this research about derivatives and their history. I'd like to know why were derivatives invented in the first place, to find minima and maxima for functions by calculating tangents of the ...
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synthetic division, use for long division of integers?

I've been reading an older math book (Theory of Equation, Thomas, 1938) that describes the technique of Synthetic Division for polynomials. I must admit I had assumed it would have been forgotten ...
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First uses of the Ping-Pong Lemma

I am interested in knowing the origins of this useful result, but I haven't been able to precisely pinpoint the context of its first use. Most texts seem to indicate the result originally comes from ...
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John Conway and 15·92

The Economist featured an obituary of John Conway (https://www.economist.com/obituary/2020/04/23/john-conway-died-on-april-11th, may be paywalled) which includes a photograph of him in what I guess is ...
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History of normal operator (matrix)

I need help please, i'm looking for a little history of the normality of the linear operators (like matrices), the creator.....ect and why we need linear operator to be normal (example of real life). ...
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How did math borrow 'factor' as in commercial agent? [closed]

I was researching factors as factor intermediaries, and its etymology on Etymonline. factor (n.) early 15c., "commercial agent, deputy, one who buys or sells for another," from Middle French ...
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Origin and source of this quote pertaining to the Monster group

I asked an almost exact question on History of Science and Mathematics SE. I vaguely remember reading a quote/listening to a statement by (I think) John Conway which I can paraphrase as follows: "I ...
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1answer
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Quadratic equations in Ancient Egypt.

From my reading, I understand that the Ancient Egyptians had some knowledge of solving quadratic equations. Is it known what applications they used this knowledge for, or whether they were studying ...
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Diophantine method

I am having a problem in understanding the following problem: Find $\sqrt{15}$ using Diophantine method. I am aware of what Diophantine equations are, but totally stuck when asked to find $\sqrt{15}$...
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Why is faithful actions called faithful and who first called it faithful?

I want to know why is faithful actions called faithful and who first called it faithful? Definition: An action $G$ on $X$ is faithful when ${g_1 \neq g_2 \Rightarrow g_1 x \neq g_2 x}$ for some ${x ...
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Who first proved that a fraction writable with coprime denominators is an integer?

Let $a$ and $b$ be two coprime integers and $q \in \mathbb{Q}^*$. If $qa,\ qb \in \mathbb{Z}$ then $q \in \mathbb{Z}.$ From which historical mathematician does this lemma come? Any references?
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History of quaternions representing rotations.

I looked all over, but I cannot find anything about the history of representing rotations by quaternions. Who first came up with this extremely clever idea?
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What does RESSOL stand for?

Does anybody know what the acronym RESSOL, which is another name for the Tonelli-Shanks Algorithm), stand for? I would say that it might mean something like "Residue Solver", but I can not find any ...
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A question about Hamilton in his search for a field-structure on $\mathbb{R}^n$

If I'm not mistaken, the following is true: Let $n$ be a positive integer and $+,\times:\mathbb{R}^n\times \mathbb{R}^n \to \mathbb{R}^n$ be an addition and multiplication map which turn $(\mathbb{R}^...
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What motivated people like Euclid to create such a general axiomatic systems like the one in the book Elements so early in history?

I think I understand why people wanted (and still wants of course) to prove some mathematical statements. Example of that would be proof of Pythagorean theorem. People noticed earlier than Pythagoras ...
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A “new” general formula for the quadratic equation?

Maybe the question is very trivial in a sense. So, it doesn't work for anyone. A few years ago, when I was a seventh-grade student, I had found a quadratic formula for myself. Unfortunately, I didn't ...
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Partial ordering and equivalence relation

How did our earlier scientists come to know that a relation is a partial order iff it reflexive, antisymmetric, and transitive (RAT), and that a relation is an equivalence relation iff it is reflexive,...
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1answer
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Can you convert a categorical proposition into a zeroth order proposition?

I am a student learning mathematical logic as a hobby. When I say "zeroth order" I mean "not predicate logic". Question: Is it possible to convert a categorical proposition into a zeroth-order ...
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ancient use of stereographic projection

I just started reviewing Differential Geometry extrinsically. I came across the following information: “... .Now suppose our user is content to have a $map^1$ which makes it easy to navigate along ...
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1answer
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Why we say Riemann zeta function and not Euler zeta function?

I'm confused zeta function was introduced in the first by the Swiss mathematician Leonhard Euler in 1737 and it were extend by Riemann to the complex plane , But Why the name " zeta function " refer ...
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Mathematical discoveries that have occurred by cleverly linking two initially unrelated topics?

I have heard mathematical proofs often require cleverly linking two areas of maths which initially seem disconnected. Could anyone provide an example of this, as I feel at my level of study, many ...
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2answers
158 views

Why did the Egyptians not represent $2/3$ as a sum of unit fractions in the Rhind papyrus?

The following is taken verbatim from the MathWorld Wolfram page on Egyptian fractions: An Egyptian fraction is a sum of positive (usually) distinct unit fractions. The famous Rhind papyrus, dated ...
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Prime-only tables of logarithms

Two of the essential properties of logarithms are that $$\log_a xy = \log_a x + \log_a y$$ and the property which follows from it $$\log_a x^y = y \log_a x$$ Therefore, as long as you are willing to ...
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1answer
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Apollonius fundamental properties of conic sections

I am reading an old book which mentions the fundamental properties of conic sections in this way: It was pointed out that the application of areas, as set forth in the second Book of Euclid and ...
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1answer
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Questions about the Conjecture $ X Y Z $ [closed]

I really have a hard time asking this question. Because my mathematical background is almost at school level. I do not know in which theories of mathematics these questions are addressed. ...
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1answer
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Theon method of extracting square roots

I am confused about a certain sentence in the book The works of Archimedes where a method of extracting a square root by Ptolemy is explained. I will write here only the last step because the sentence ...
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Riemann's explicit formula – proof & convergence

From the Wikipedia article on the prime counting function: Of profound importance, Bernhard Riemann proved that the prime-counting function is exactly $$\pi (x)=\operatorname{R}(x)-\sum_{\rho}\...
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1answer
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Where did the bracket notation for vectors come from and is using parentheses to represent vectors valid?

In class I learned that a vector can be represented using <>, a column vector, and unit vector notation. However, one of the old math books that I study from notes that a vector in unit vector form ...
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Related to doing a bibliography analysis

When doing a Literature review on a mathematics topic (same for other subjects too), I found that the articles can be searched through "document search" option in scopus or web of science, and the ...
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1answer
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How to calculate logarithms by using a necklace? [closed]

I have read that before the french revolution on various salons it was a popular trick to calculate logarithms just by using a necklace. Could someone from your community explain this trick?
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Kolmogorov Probability Theory Question

I'm reading link: Foundations of theory of probability - Kolmogorov and have some questions regarding this historical text. I'm a bit stuck, so any guidance is appreciated. Thanks! In the axioms ...
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Gram-Schimidt process(trying to understand the projection operator)

For Gram-Schmidt process, the projection operator is defined by $proj_u(v)=\frac{<v,u>}{<u,u>}u$. Can someone give me an reference for interpreting this projection operator? What do $<v,...
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1answer
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About how people come up with Gamma distribution

The gamma distribution is given by $f(x)= \frac{1}{\Gamma(\alpha) \theta^{\alpha}} x^{\alpha-1} e^{\frac{-x}{\theta}}$. I know this is a special type of Poisson distribution where it is counting the n ...
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What would you recommend for the math thinking course?

We're going to make a new math course for kids as intermediary between middle and high school with math profile (for preparation to entrance exams to high school), and before the main part (arithmetic,...

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