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

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5
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1answer
157 views

How fast was the Turing's machine for breaking the enigma code?

We know that, recently, personal computers make around $10^9$ calculations per second, and I'm just curious about how many calculations was able to compute the machine invented by Turing for breaking ...
3
votes
2answers
77 views

Why do we think of group compositions as multiplication?

This has bothered me for some time: The composition in a group is usually denoted $xy$ or $x\cdot y$. Powers (note the word) are denoted by $x^n$, inverses by $x^{-1}$, and the neutral element by $1$. ...
0
votes
2answers
143 views

What comes after seconds?

Angles can be measured in different ways. For example, one can measure angles in degrees/minutes/seconds. So $1^\circ$ is divded into $60$ min. and $1$ min is divided into $60$ sec. That way a tenth ...
2
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0answers
68 views

How much math was “Broken” by Russell's Paradox?

As you know, the phrase "the set of all sets that don't contain themselves" caused a paradox that "broke" (made trivial) Naive set theory. How much mathematics had to be redone because of this? Most ...
5
votes
1answer
178 views

Why are logarithms of trigonometric functions useful?

I have noticed that in many trigonometric tables the logarithm of the trigonometric values are given. Why this is given and not the actual values of the trigonometric functions? For example, instead ...
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2answers
40 views

What are these numbers in a logarithmic table?

Below is an image from a table of logarithms. As an example, one sees that $\log(661.3) = 2.82\color{red}{040}$. In this logarithmic table there are some numbers to the right. My question is: What is ...
96
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15answers
9k views

Has lack of mathematical rigour killed anybody before? [closed]

One of my friends was asking me about tertiary level mathematics as opposed to high school mathematics, and naturally the topic of rigour came up. To provide him with a brief glimpse as to the ...
1
vote
1answer
32 views

Derivation of the discriminant of a cubic polynomial by algebraic manipulation.

The problem was asked before: Using Vieta's theorem for cubic equations to derive the cubic discriminant . I tried to solve it by purely algebraic manipulation but was faced with an explosion of ...
1
vote
5answers
93 views

What does the solution of a PDE represent?

So I took a course in PDE's this semester and now the semester is over and I'm still having issue with what exactly we solved for. I mean it in this sense, in your usual first or second calculus ...
1
vote
1answer
109 views

What is the difference (or relationship) between geometric length and arithmetic numbers?

In Abbott's Understanding Analysis there was a phrase like, "Ancient Greeks did not understand the difference (or relationship) between geometric length and arithmetic numbers." What is this ...
2
votes
1answer
26 views

Noether comment to Dedekind and Weber's work

I am trying to consult Emmy Noether's “Erläuterungen zur vorstehenden Abhandlung”, some sort of epilogue or comment to Richard Dedekind and Heinrich Weber's “Theorie der algebraischen Funktionen einer ...
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3answers
59 views

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 ...
0
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1answer
37 views

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 ...
5
votes
1answer
272 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 ...
3
votes
1answer
68 views

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 ...
3
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0answers
62 views

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 ...
2
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1answer
62 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 ...
0
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0answers
23 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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0answers
40 views

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: ⨽ ...
1
vote
2answers
75 views

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 ...
7
votes
1answer
98 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? ...
4
votes
0answers
77 views

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 ...
0
votes
1answer
50 views

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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0answers
65 views

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 ...
3
votes
1answer
53 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 ...
2
votes
2answers
91 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 ...
0
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0answers
40 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 ...
10
votes
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 ...
2
votes
4answers
76 views

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!
0
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0answers
54 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 ...
0
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0answers
172 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?
0
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1answer
18 views

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 ...
0
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3answers
43 views

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 ...
2
votes
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} \! ...
3
votes
3answers
168 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
49 views

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.
1
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1answer
38 views

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 ?
10
votes
2answers
147 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. ...
0
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2answers
43 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. ...
4
votes
1answer
71 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 ...
4
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1answer
85 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 ...
8
votes
1answer
109 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 ...
2
votes
1answer
87 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 ...
2
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0answers
68 views

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 ...
3
votes
0answers
78 views

Name of Wreath Product

Why is the wreath product so named? If possible, please provide a citation.
1
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0answers
64 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
49 views

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). ...
15
votes
1answer
215 views

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
29 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 ...
2
votes
1answer
73 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 ...