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

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Is $k=\int_1^\pi t^{-1}dt$ such that $e^k=\pi$ an important number in math literature?

Wolfram gives an answer $k \approx 1.1447$ but I don't know if it is also irrational or just a truncated number. Does this number have any significance? Could it be related with the Euler's formula?
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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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20 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
50 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
45 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 ...
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1answer
172 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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19 views

First instance of vertex cover problem

When was the vertex cover problem (or transversal set) first posed/considered?
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2answers
137 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
51 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 ...
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1answer
111 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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6answers
128 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 ...
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754 views

Did ancient Greek mathematicians use AC somewhere in their geometric theorems implicitly?

Maybe no, because only in the case of dealing with something infinite AC becomes important and Greeks weren't infinity-friendly people. Maybe yes, because "choosing a point from a line" plays a key ...
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0answers
75 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 ...
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1answer
65 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
44 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, ...
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2answers
50 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, ...
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1answer
111 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 ...
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38 views

Use of $h$ in the Newton Quotient [migrated]

Why do we typically use $h$ for $$\frac{\mathrm{d}f}{\mathrm{d}x}=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$$ A student asked me this the other day. My guess was that it was originally height, because ...
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0answers
29 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 ...
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0answers
59 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?
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27 views

Citation: earliest incidence of the Borel localization theorem [migrated]

The Borel localization theorem in (Borel) equivariant cohomology states that if $T$ is a torus and $M$ a smooth $T$-manifold, with fixed point set $M^T$, then upon localizing the coefficient ring ...
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2answers
49 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
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1answer
78 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 ...
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1answer
100 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 ...
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1answer
33 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 ...
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24 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 ...
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2answers
113 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 ...
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1answer
28 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 = ...
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0answers
85 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 ...
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3answers
129 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 ...
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1answer
76 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 ...
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79 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: ...
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1answer
84 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?
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1answer
53 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 ...
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3answers
84 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
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1answer
109 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
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2answers
62 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 ...
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2answers
107 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 ...
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38 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 ...
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1answer
30 views

Necessary and sufficient condition for a number to be regular

Background: A number is said to be (sexagesimally) regular if its reciprocal has a finite sexagesimal expansion (that is, a finite expansion when expressed as a radix fraction for base 60). With the ...
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27 views

Looking for an English translation of Descartes's mathematical works

Good day to everyone! I am looking for an English translation of Descartes' mathematical works (particularly in elementary number theory). Would someone be kind enough as to point me to an ...
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3answers
87 views

geometry developments during the Islamic Golden Age (7-13 century)

Can anybody refer me to publications on geometry during the Islamic Golden Age? My interest is especially on Arab geometry an non-Euclidean geometry. But searching for sources was a saddening ...
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47 views

Chi-square or chi-squared?

The $\chi^2$ test/distribution is referred to as either "chi-square" (more frequently) or else "chi-squared" (less frequently). What is the history behind the name? Footnote 2 in this paper by Peter ...
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3answers
399 views

What is the oldest math source that we know of?

What is the oldest math source that we know of? Or to put it differently, what is the first math that was ever done?
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87 views

Did Landau prove that there is a prime on $(x,(1+1/5)x)?$

Was Landau the first to prove that there is a prime on $(x,\frac{6}{5}x )?$ In his Handbuch $^1$ discussing the limit $$\lim_{n\to\infty} (\pi((1+\epsilon)x)-\pi(x))=\infty $$ he seems to say that ...
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133 views

What is the most cited mathematical paper?

Just out of curiosity: What is the paper with the largest number of citations in all of mathematics? I think it is Shannon's A Mathematical Theory of ...
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1answer
83 views

Euler Vs. Diderot

I'm reading The Music of the Primes by Marcus Du Sautoy and I came across a page with the following excerpt about Leonhard Euler: "The role of the court mathematician is perfectly illustrated by a ...
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85 views

Who First Considered This Generalization of the Fibonacci Numbers?

I am looking for the author who originally researched a generalization of the Fibonacci numbers, which Koshy, in Chapter 7 his book Fibonacci and Lucas Numbers with Application refers to as the ...