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

learn more… | top users | synonyms (1)

2
votes
1answer
43 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
152 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 ...
0
votes
0answers
29 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.
0
votes
0answers
21 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
145 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
votes
2answers
41 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. ...
2
votes
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 ...
4
votes
1answer
74 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 ...
7
votes
1answer
97 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 ...
3
votes
1answer
73 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
votes
0answers
52 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
62 views

Name of Wreath Product

Why is the wreath product so named? If possible, please provide a citation.
1
vote
0answers
46 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 ...
4
votes
0answers
42 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). ...
13
votes
0answers
103 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 ...
1
vote
0answers
23 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
67 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 ...
0
votes
1answer
51 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
votes
1answer
179 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 ...
10
votes
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 ...
0
votes
0answers
20 views

First instance of vertex cover problem

When was the vertex cover problem (or transversal set) first posed/considered?
0
votes
2answers
140 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 ...
1
vote
1answer
63 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
votes
1answer
122 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 ...
4
votes
6answers
135 views

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 ...
2
votes
0answers
94 views

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 ...
2
votes
1answer
72 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 ...
3
votes
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, ...
3
votes
2answers
58 views

Problem-Solving and other things in mathematics relations? [closed]

Problem-Solving and the standard curriculum in typical undergrad mathematics seems to be on different levels of difficulty. IN undergrad math, you learn new concepts and try some problems. However, ...
5
votes
1answer
149 views

Proof for de Moivre's Formula

I have a book that has a brief history of the complex numbers and it covers de Moivre's formula: $(\cos(x) + i\sin(x))^n = \cos(nx) + i\sin(nx)$. I am very curious as to how this result was ...
2
votes
0answers
33 views

Why have multiplicative operators precedence over additive operators?

Considering that addition is (in my understanding) a more basic operation than multiplication, would it not make sense to give it higher priority? That is to say, we would expect to encounter more ...
3
votes
0answers
63 views

When did the notion of the tangent space emerge?

When did the modern conception of/notation for the tangent space to a manifold come into use?
4
votes
2answers
52 views

Books / Articles on how mathematical education has changed over time

Can anyone recommend books/articles on approaches to teaching mathematics over centuries? How has it been changing since the beginning of mathematical education? Thank you
0
votes
1answer
85 views

In Whitehead & Russell's PM, what makes anything true or false?

It seems that truth and falsehood are fundamental to meanings and types. A proposition is defined as anything that is true or that is false. PM defines truth as "consisting in the fact that there is ...
1
vote
1answer
117 views

Why do some authors use terms “non-ascending” and “non-descending” instead of ascending and descending? [duplicate]

In my math book, everywhere the author has used "non-ascending" instead of descending and "non-descending" instead of ascending. I was wondering if there is some special meaning or use associated with ...
3
votes
1answer
39 views

Origin of period function model of primes

There is a web page attributed to Omar Pol, "Sobre el patrón de los números primos: Determinación geométrica de los números primos y perfectos." ("On the pattern of primes: Geometric Determination of ...
1
vote
0answers
29 views

Apolonius' definition of a parabola

I need help understanding what apollnius did when he defined a parabola and what he proved. "First let the diameter PM of the section be parallel to one of the sides of the axial triangle as AC, and ...
4
votes
2answers
120 views

Who first found the value of $\int_{-\infty}^{+\infty}e^{-x^2}dx$?

A fairly pretty technique of showing that $$\int_{-\infty}^{+\infty}e^{-x^2}dx = \sqrt{\pi}$$ is to square the integral, writing that square as the product of two integrals with integration variables ...
3
votes
1answer
35 views

Who first computed the Euler characteristic of a generalized flag manifold?

Let $G$ be a compact Lie group and $H$ a closed subgroup containing a maximal torus $T$ of $G$. Then the Euler characteristic of $G/H$ satisfies $$\chi(G/H) = \frac{|W_G|}{|W_H|},$$ where $W_G = ...
3
votes
0answers
90 views

No rigorous proofs from 200 B.C to 1870?

I'm reading: Mathematical thought from ancient to modern times by Kline. My question is about this pasasge: Beyond its achievements in subject matter, the nineteenth century reintroduced ...
7
votes
3answers
160 views

Moscow State Oral Exam

I have heard that during the 1960s, prospective students had to take an 'Oral Maths' exam (alongside written maths, physics and Russian literature). I having trouble imagining what type of exam this ...
1
vote
1answer
79 views

About terminology “Orthogonal” and “Orthonormal”

This question may not be of theoretical importance in Linear algebra, but I came to this question, while looking definition of orthogonal transformation in intuitive way. Let $V$ be an inner product ...
2
votes
0answers
125 views

Grothendieck's obituary. Anybody know the background behind this story?

"In a subsequent letter to Leila Schneps, Grothendieck said he would be prepared to share his research into physics with her if she could answer one question: “What is a metre?" " Source: ...
1
vote
1answer
93 views

How did Gauss discover the prime number theorem?

Carl Friedrich Gauss conjectured in his early youth that $$\lim_{x \rightarrow \infty} \frac{\pi(x)}{x/\log(x)} = 1.$$ Any idea how did he reach such result?
0
votes
1answer
57 views

Have Information Theoretic results been used in other branches of mathematics?

consider this a soft-question. Information Theory is fairly young branch of mathematics (60 years). I am interested in question, whether there have been any information theoretic results that had ...
3
votes
3answers
111 views

Examples of open problems solved through short proof

Are there good examples of reasonable open problems in mathematics that had an 'obvious' solution via application of a theorem already known/not yet found in mathematics but could have been found with ...
2
votes
1answer
110 views

An endless loop in a program that search for mathematical theorems and proofs − a milestone? [closed]

I don't know if there exist computer programs working on its own, trying to find and prove theorems, delivering proofs and go on searching for new theorems. But if (when) there are such programs, ...
2
votes
2answers
88 views

What is the most appropriate book for teaching, not the content but skills of mathematics

Hello Everyone I am a high school student currently doing Extension 1 Mathematics at my school. I am currently looking for a high quality mathematics book. Although I am not looking for a book, like ...
4
votes
2answers
115 views

Value of $\pi$ by Aryabhata

Aryabhata gave accurate approximate value of $\pi$. He wrote in Aryabhatiya following: add 4 to 100, multiply by 8 and then add 62,000. The result is approximately the circumference of circle of ...
0
votes
0answers
45 views

Lagrangian and Hamiltonian Mechanics

I am interested in how Lagrangian and Hamiltonian mechanics and then symplectic geometry was developed starting from Newtonian mechanics. We can start by assuming that Newtonian mechanics tells us ...