Use this tag for questions concerning history of mathematics, historical primacies of results, and evolution of terminology, symbols, and notations.

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History and early development of Mathematics

Please provide references (books, articles, websites) that describe the conceptual development of calculus, complex numbers, group theory and matrix. I am curious about how the Mathematicians ...
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On Dedekind's prime ideals

Prime ideals were an essential tool for Dedekind to save or restore unique factorization. Is it fair to say that the shift from Kummer's ideal numbers to Dedekind's ideals (with prime ideals, and so ...
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1answer
238 views

What does “hom” stand for in hom-sets and hom-functors?

With given category $\mathcal{C}$ and its objects $A$ and $B$, a hom-set $\hom_\mathcal{C}(A, B)$ is the collection of all morphisms from $A$ to $B$. There is also a related notion of hom-functor ...
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A question regarding Kummer [closed]

As you know, Ernst Kummer noticed that examples such as $$6 = 2\cdot 3 \text{ or } 6 = 3 \cdot 2 \text{ and, crucially } 6 = (1 + \sqrt{-5}) (1 -\sqrt{-5}) $$ proved the failure of unique ...
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Why didn't Bernoulli and Euler use an integral comparison to estimate the solution to the Basel problem?

I was reading the history of the Basel problem in William Duhnam's book, Euler - The Master of Us All. The book tells how Jakob Bernouili did some clever manipulation to show that the sum of $1/n^2 ...
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1answer
50 views

Original paper by Gauss on gaussian integers

Could anyone provide me with the title and date of Gauss's paper where he first introduces gaussian integers and proves their unique factorization? If you could also provide me with his exact proof ...
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22 views

Maltsev on Algebraic Systems

As far as I know, it was A.I Maltsev who fist coined the term "Algebraic systems" in a paper from 1953. Then Birkoff, MacLane and others extended its usage and appplications. My question is a simple ...
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Notations for interior product

There are two symbols in the Unicode "Supplementary Mathematical Operators" range whose names intrigue me 2A3C: INTERIOR PRODUCT: ⨼ (like $\lnot$ upside down) 2A3D: RIGHTHAND INTERIOR PRODUCT: ⨽ ...
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2answers
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Why is the letter “F” used for the curvature 2-form?

Given a differentiable manifold $X$, a vector bundle $E\to X$ and a connection $A$ on $E$. The curvature $2$-form of the connection is a $2$-form with values on the endomorphisms of $E$ defined as ...
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1answer
85 views

(Co)homology theory and electrical circuit

I have read that one of the origins of the theory of (co)homology is the study of electrical circuits by Poincare. I'd like to know more about that. Could someone sugest any reference on this subject? ...
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0answers
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In the mean value theorem, we are guaranteed $c$ such that $f'(c) = (f(b)-f(a))/(b-a)$. Does $c$ have a name?

The Mean Value Theorem says approximately that for differentiable $f$, there is a $c \in (a,b)$ such that $$ f'(c) = \frac{f(b)-f(a)}{b - a}. $$ I presume that the number $f'(c)$ is the mean value. My ...
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1answer
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On Gaussian Primes

Some primes in the ring of integers (17, for example) cease to behave as such in the ring of gaussian integers, while others (7, for instance) keep being prime there as well. The former are of the ...
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When did Liouville come up with the first transcendental numbers?

There are some conflicting sources regarding this. It is a matter of fact that Liouville defined what it was for a number to be approximated to degree $n$ by rational numbers. He then effectively ...
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1answer
51 views

who coined the prime ideals?

I know that Ernst Kummer first made used of "ideal complex numbers", and, hinging on that, Dedekind later introduced his "ideals" in Vorlesungen über Zahlentheorie. But, who coined the term "prime ...
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2answers
73 views

Calculus without functions (or, how did Newton differentiate?)

I was recently reading about how functions did not really exist at the time of Newton and Leibniz; They thought in terms of geometry. That makes me curious. I can understand that derivation would be ...
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0answers
39 views

DeMoivre's approximation to the ratio of $\binom{n}{n/2}$ to $2^n$

I'm reading Stigler's History of Statistics and am trying to understand as many of the derivations as I can. Stigler begins his discussion of DeMoivre's contributions by stating the result that the ...
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2answers
1k views

Who discovered the first explicit formula for the n-th prime?

I just found out on Wolfram that there is a formula for the n-th prime in terms of elementary functions. I wonder who found it and if he was rewarded for this. The formula (here) is: Also shown at ...
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4answers
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motivating diagonalization of a matrix [duplicate]

I have to teach about diagonalization of a matrix to a first year undergrad student and I was wondering what would be a good way to motivate this concept. I would appreciate any suggestions. Thanks!
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0answers
53 views

Historical calculations of $tan^{-1}x $ and $e^x$

SineBhaskara_I One reads that $tan^{-1}(x) $ series expansion existed in early (Indian) history. But like the Sine trigonometric function, did any similar approximation exist as well? The query ...
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0answers
38 views

Who is the inventor of slovin's formula?

And how can I use it in the population contain 10000 people with confidence interval 95%? Also, why there is only a few information about the inventor in the web?
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1answer
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Table of Contents from André Weil's Edition of Kummer's papers

I would be very grateful if someone could provide me with the table of contents of Volume 1 (pertaining Number Theory) of Andre Weil's edition of Ernst Kummer's papers, published by Springer Verlag in ...
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Cross products and determinants in $\mathbb{R}^3$

I know that the absolute value of determinant of three vectors in $\mathbb{R}^3$ is the volume of the parallelepiped determined by the three vectors. The volume can be computed by basic calculation ...
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1answer
44 views

estimation of a unit circle - how to show a relationship

It has been eons since I've done any trigonometry, but I just can't prove how this following relationship holds for $n = 4, 8, 16, 32, \dots$ The relation is: $$ 2 \biggl( \! \frac{A_{2n}}{n} \! ...
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3answers
160 views

Why did it take mathematicians so long to discover non-Euclidean geometry?

Why did it take mathematicians so long to realise that Euclid's fifth postulate is independent of the other 4? Why didn't people like Lagrange notice that a sphere is a model for a non-Euclidean ...
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0answers
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Who discovered the Inverse Function Theorem?

I was wondering who discovered this theorem, I can't find this information in Wiki or with a simple google research and all my books do not report the author.
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How Leibniz invented the Binary System?

Do you know which reasoning and observations made Leibniz invent the Binary system ? Some say that he was inspired by Chinese mathematicians do we have any record of how he came with this idea ?
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2answers
146 views

When, how & who first gave this calculation of $\pi$

I came across this interesting method to calculate $\pi$. Why is it true and who first presented it? To calculate $\pi$, multiply by $4$, the product of fractions formed by using, as the numerators. ...
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2answers
42 views

Functions applied from the right

In some of the older books by Nathan Jacobson (like Lie Algebras and Lectures in Abstract Algebra), a convention is used that is quite uncommon at least today: Functions are applied from the right. ...
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1answer
44 views

History Behind Integral Error Between $\pi$ and $22/7$

Looking at an expression for $\pi$ $$\pi = \frac{22}7-\int_0^1 \frac{x^4(1-x)^4}{1+x^2} \ dx$$ it seems to me that the integral expression is the error between the approximation $\frac{22}7$ and ...
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1answer
76 views

Maths Discoveries thanks to Computer Science

Which discoveries have been made in mathematics thanks to computer science ? For example fractals have been discovered thanks to computers (correct me if im wrong) do you know any similar discoveries ...
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1answer
101 views

What came first, the $\forall$ or the $\exists$? [closed]

I imagine that these symbols originated in one of the following ways: "I will declare a symbol for "for all." I will just use the letter "A" flipped upside-down. Yes, let $\forall$ represent "for ...
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1answer
81 views

How was the functorial factorization axiom “frequently misstated”?

In modern times, a model category is frequently required to have functorial factorizations of morphisms into (fibration/acyclic cofibration) and (acyclic fibration/cofibration). But the precise ...
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Inverse Function Theorem. On the classical method of proof.

The proof most commonly of the Inverse Function Theorem seen in textbooks of relies on the Banach fixed-point theorem. QUESTION. It is possible to say, using historical references, which ...
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0answers
68 views

Name of Wreath Product

Why is the wreath product so named? If possible, please provide a citation.
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0answers
51 views

What really is inductive reasoning?

I am looking for concrete information on "induction" in the old sense of the word. Now it is used to refer to proof by "mathematical induction"; however, I am aware that it also means inductive ...
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0answers
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Why row vectors in stochastic processes?

It seems reasonable to state that column vectors $\mathbf{x}$ are the most frequently seen standard notation, often using $\mathbf{x}^\intercal$ to denote a row vector (transposed column vector). ...
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Why would I define Alexander–Spanier cohomology?

I think I can motivate the definitions of simplicial, singular, de Rham, Čech, and sheaf (co)homology, more or less. I might want to understand bordism, and start by trying to understand ...
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0answers
27 views

History of Dihedral Groups?

I'm trying to write a brief historical outline for a project concerning Dihedral Groups, but It has been to hard for me to find information about the first time these groups appeared on literature. If ...
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1answer
68 views

Problem solved by a complete layman

Unfortunately, (for the complete layman) since the last century, not only the answers but also the problems themselves have most often been impossible to understand. I found the question interesting ...
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1answer
53 views

Matrix equation: solving $AB(A^{-1})(D^T)(C-1 )= E$ for $D$

The question is: Assuming that all the following matrices are of the same size and nonsingular, solve $AB(A^{-1})(D^T)(C-1 )= E$ for matrix $D$. So far I got to $D^T = EC(B^{-1})$, but I do not know ...
2
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1answer
180 views

What is an ordinary differential equation equation that is yet to be solved?

In another word, the ODE i am talking about is very special that an special method must be developed in order to solve solely that ODE approximately in infinite series. An standard method mean it ...
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3answers
3k views

What is the meaning of the expression Q.E.D.? Is it similar to ■ appearing at the end of a theorem?

I am curious about the meaning of the word Q.E.D. that is often written after a proof of a theorem (some math books use this convention). Edit: Is it similar to the box being placed after a proof of ...
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0answers
21 views

First instance of vertex cover problem

When was the vertex cover problem (or transversal set) first posed/considered?
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142 views

The word “times” for multiplication…? [closed]

The word "times" for multiplication operation which is quite touching to the concept of time (feeling time this way 0*1=0). When was introduced that term? Did any other language have the kind of term ...
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1answer
64 views

Why must there be an infinite number of lines in an absolute geometry?

Why must there be an infinite number of lines in an absolute geometry? I see that there must be an infinite number of points pretty trivially due to the protractor postulate, and there are an infinite ...
8
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1answer
128 views

Is there any connection between the symbol $\supset$ when it means implication and its meaning as superset? [duplicate]

A rather old-fashioned symbol for logical implication is $\supset$ (see list of logic symbols). For example $p \supset q$ means $p \implies q$ or $p \rightarrow q$ in more recent notations. Is there ...
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Notable examples of “impossible” results ruled out by earlier barrier or no-go theorems or widespread beliefs

there is a certain style of type of proof in mathematics something like a "barrier theorem" but which also relates to widespread mathematical beliefs/ "conventional wisdom". an example would be the ...
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What is the legacy of Bourbaki?

As I was preparing a short lecture (for amateurs) on the mathematics of the '900, I realized that this year marks the 70-th anniversary of the founding of the Bourbaki group. I remember that Bourbaki ...
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1answer
73 views

Intuitively speaking, why was there a need to “eliminate” quantified variables in mathematical logic?

I'm trying to wrap my head around the understanding of lambda-calculus, from a math/computing/logic standpoint and am reading more about its very genesis. This has taken me to 1924 - Schonfinkel's ...
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1answer
45 views

How to find out who firstly introduced a mathematical concept?

I am wondering if there is any way that one can find out the introducer of a given mathematical concept. For example, if I want to write that "Reduced free groups were firstly introduced in Habegger, ...