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)

0
votes
0answers
21 views

First instance of vertex cover problem

When was the vertex cover problem (or transversal set) first posed/considered?
0
votes
2answers
159 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
73 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
137 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 ...
5
votes
6answers
147 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
108 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
74 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
49 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
66 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
187 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
37 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
64 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
92 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
167 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
49 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
31 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
123 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
41 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 = ...
2
votes
0answers
98 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
189 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
81 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
138 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
113 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
64 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
144 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
122 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
112 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
138 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
53 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 ...
1
vote
1answer
56 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 ...
0
votes
0answers
31 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 ...
2
votes
3answers
114 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 ...
1
vote
0answers
65 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 ...
1
vote
3answers
416 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?
9
votes
0answers
98 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 ...
10
votes
0answers
253 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 ...
3
votes
1answer
124 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 ...
2
votes
0answers
90 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 ...
1
vote
2answers
163 views

Understanding the concepts of division and fractions

$\require{cancel}$ I'm having some issues regarding division so I will start by asking how this concept was developed throughout the ages: What was the first civilization to introduce the idea of ...
22
votes
0answers
337 views

To what extent were mathematicians in previous centuries aware of the lack of rigour in their methods?

By modern standards, much of pre-modern mathematics isn't rigorous. Famous examples include Euler's solution to the Basel problem or literally anything involving sets before Cantor and Russel came ...
6
votes
1answer
105 views

Algebra on a Louvre tablet

Problem: On a Louvre tablet of about 300 B.C. are four problems concerning rectangles of unit area and given semiperimeter. Let the sides and semiperimeter be $x,y$ and $a$. Then we have ...
6
votes
0answers
491 views

2015-related question: why are Lucas-Carmichael numbers named after Lucas?

Summary 2015 is a so called Lucas-Carmichael number. I believe (for reasons that I will explain below) that the 'Carmichael' in the name is a reference to ordinary Carmichael numbers and not to the ...
7
votes
1answer
95 views

How was 78557 originally suspected to be a Sierpinski number?

A Sierpinski number is an odd number $k$ such that $k2^n+1$ takes only composite values. In 1962, Selfridge proved that $78557$ is a Sierpinski number. It remains the smallest known such number. How ...
36
votes
12answers
3k views

What are some theorems that currently only have computer-assisted proofs?

What are some theorems that currently only have computer-assisted proofs? For example, there's the four colour theorem. I am very curious about this and would like to generate a list.
10
votes
2answers
159 views

Infinite series for the arctangent from the tangent of half-angle formula

From Hodge's biography of Turing: He had found the infinite series for the "inverse tangent function", starting from the trigonometrical formula for $\tan\left(\frac{1}{2}x\right)$.* The ...
24
votes
4answers
1k views

Why is “mathematical induction” called “mathematical”?

One of my whims is that I never write "mathematical induction" but just "induction". We are doing maths, so what is the point about precising? We don't say "Let $f$ be a mathematical function from the ...
6
votes
2answers
205 views

What are some mathematical problems which have been forgotten?

As mathematicians continue to study mathematics, often times they run into a problem which takes a considerable amount of effort to solve. For instance, trying to factor polynomials has lead to a ...
3
votes
2answers
58 views

Why does the radius come before the angle?

Based on my understanding, when delineating two variables (for a coordinate system or otherwise) convention is to label the 'independent variable' first, then the 'dependent variable'. So for a ...
5
votes
1answer
270 views

Why did Fermat care about characterizing primes on the form $p=x^{2}+ny^{2}$?

Im currently trying to figure out the genesis of quadratic reprocity by using Cox and Lemmermeyers books. I also got a copy of some works of Fermat but it is in German. It seems like there is some ...