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

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32
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5answers
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Examples of “Non-Logical Theorems” Proven by Logic

I am still an undergraduate student, and so perhaps I just haven't seen enough of the mathematical world. Question: What are some examples of mathematical logic solving open problem outside of ...
2
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1answer
87 views

Did the ancient Sumerians calculate the square root of two?

This post makes the claim: Not bad you might think, but compare it to the Summerian Kù of 51.85cm of the copper of Nippur and its derived unit SAR of 3600 Kù being 1866.6 meter being only 0.77% ...
4
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0answers
496 views

What is the origin of “how the Japanese multiply” / line multiplication?

A few months ago I made a video about a way to multiply numbers using lines (here) and it got really popular. I had heard about this trick before and I wanted to trace its origins. It seems to me to ...
6
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1answer
89 views

How did Le Verrier calculate Neptune's position?

In the Wikipdia article on Neptune the discovery is described as a mathematical achievement: Subsequent observations revealed substantial deviations from the tables, leading Bouvard to ...
4
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2answers
147 views

Who invented or used very first the double lined symbols $\mathbb{R},\mathbb{Q},\mathbb{N}$ etc

Who invented or used very first the double lined symbols $\mathbb{R},\mathbb{Q},\mathbb{N}$ etc. to represent the real number system, rational number system, natural number system respectively?
2
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1answer
43 views

Origin of Slater's condition

I've been looking all over the internet to answer this question: Slater's condition is a commonly used to certify that strong duality holds in a convex optimization problem. Although used in many ...
3
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1answer
186 views

What is this myth/legend and origin of related ideas?

There is a story I recently heard but the story teller (who read about it someone on the Internet) have forgotten the majority of the story, so there is little I can work on: my search attempts went ...
13
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7answers
541 views
0
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1answer
38 views

Sophie Germain primes

Why did Germain come up with her Germain primes? I am intrigued to know why Sophie came across these primes. Do they have any applications?
0
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1answer
64 views

Understanding the difference between relations and functions.

$R=\{(1,2),(1,3)\}$ is a relation but not function. The logic for this is that if the first element of every ordered pair must remain different, then it is said to be function. Otherwise, it's just ...
21
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3answers
698 views

Who named “Quotient groups”?

Who decided to call quotient groups quotient groups, and why did they choose that name? A lot of identities such as $$\frac{G/A}{B/A}\cong \frac{G}{B}$$ suggest that whoever invented the notation ...
3
votes
2answers
136 views

What is the intutive explanation of why the notation of matrices is as it is?

If I want to solve a system of linear equations, like 2x-y=1 x+2y=4 Then the matrix notation for the same would be: $$ \begin{bmatrix} 2 & -1 \\ 1 & 2 \\ \end{bmatrix} \begin{bmatrix} X\\ ...
2
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1answer
107 views

Why didn't Frege succeed in his attempts to reduce mathematics to logic?

My background: Sophomore-level understanding of mathematics and philosophical logic. All the explanations I have found online so far are either far too technical or too simplistic. Thanks in advance ...
1
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1answer
59 views

Why we can't define more mathematical constant?

I would like to know how many mathematical constant are there? I saw this link and I know the names. Who can define a mathematical constant? Someone can say that ...
0
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2answers
77 views

What is the meaning of calculating sine of a number?

When we calculate sine/cos/tan etc. of a number what exactly are we doing in terms of elementary mathematical concept, please try to explain in an intuitive and theoretical manner and as much as ...
7
votes
1answer
92 views

Who first proved the fundamental theorem of finitely generated (or finite) abelian groups?

The fundamental theorem of finitely generated abelian groups (or maybe just finite abelian groups) is well-known and can be found in just about any text on the theory of groups or abstract algebra. ...
7
votes
6answers
366 views

Interviews of famous modern mathematicians

I was wondering, are there any good collections of interviews of famous modern mathematicians? It can be text interviews, or audio or video recordings. I am not sure what exactly I mean by "modern". ...
2
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0answers
25 views

Cayley on “trivial transformations”

In his 1854 paper, "Deuxième mémoire sur les fonctions doublement périodiques" ("Second memoir on doubly periodic functions"), Cayley discusses (what we would today describe as) a certain class of ...
11
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2answers
487 views

History of Algebraic Geometry: Motivation behind definition of schemes

I am trying to read an article by Jean Dieudonne which talks about development of Algebraic Geometry. The article was being published in the journal "Advances in Mathematics" Volume 3, Issue 3, Pages ...
3
votes
1answer
98 views

Coincidence about nabla?

I was surprised to notice that gradient of function and Levi-Civita connection have the same notation, i.e. nabla sign $\nabla$. Moreover, extending any connection on tensors, one let it be ...
2
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1answer
74 views

Descartes on imaginary unit.

I heard once that Descartes defining the imaginary unit had to talk about the imagining of rise of the spirit over the real numbers because definition based on square root of a negative number could ...
12
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2answers
1k views

Has any error ever been found in Euclid's elements?

Has any error ever been found in Euclid's elements since its publication? Or it is still perfect from the view point of modern mathematics.
1
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1answer
99 views

is the decimal notation the “right” notation for arithmetic?

I am considering here the pre-decimal notations such as Roman numerals, Egyptian numerals etc. It seems reasonable that these must all be equivalent. And it seems that decimal notation (i.e. ...
3
votes
1answer
115 views

History of $p$-adic numbers

I'm interested in learning about the historical motivation and development of $p$-adic numbers. I haven't been able to find any books on the topic. I'd appreciate any references, including to more ...
0
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2answers
91 views

Why do some sources call calculus, “the calculus”?

No need to cite specific sources since I think it's a fairly common thing to see. What's up with that? Thank you Edit: I've seen it in several places. Here's where I'm currently looking at it at: ...
0
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1answer
55 views

About connection and topology

I'm looking for a good book (or article) about history of topology, and specially about the connection concept. I appreciate all your suggestions!!!
4
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0answers
126 views

History of a combinatoric problem: exchanging numbers by throwing stones

Another user recently asked a question on the Puzzling stack: Two spies throwing stones into a river. Suitably generalised, it becomes: Two spies (Alice and Bob) need to exchange a message. Each ...
0
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0answers
20 views

Homogeneous Spaces: The Erlangen Programme

This is a wholly a question of mathematics history. The Klein Erlangen programme is most pithily, if a little tersely, described in modern wording as a homogeneous space: a topological group acting ...
6
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1answer
64 views

Closed and Open Set - History of Terms

I know very little in the way of math history, but I question that was bothering me recently is where the terms open and closed came from in topology. I know that it's easy to ascribe a sense of ...
3
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0answers
93 views

In which field of science that we can prove $0! =1$ and what i can say to studentof high school if he asked about it's prove ?? [duplicate]

In mathematics there are some data , we have took them by convention and mathematics is not able to show us them proves , now want just to know if the "convention" term enough mathematics ...
9
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2answers
186 views

Newton's “Famous Blunder”?

On page $225$ of Isaac Newton on Mathematical Certainty and Method by Niccolo Guicciardini (see here for a link), I read In the following demonstration... Newton made a famous blunder... He wrote, ...
1
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0answers
57 views

Why are frames called “frames”?

Definition: A frame $F$ is a suplattice such that for any $x_{i}, y\in F$ (for $i\in I$, $I$ a set), we have $$y\wedge\left(\bigvee_{i\in I}x_i\right)=\bigvee_{i\in I}(y\wedge x_i).$$ Why are ...
15
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0answers
152 views

How and why did Weierstrass $\wp$ get its special symbol?

I kind of always hated drawing the Weierstrass $\wp$ symbol by hand, and it struck me as odd how and why it achieved its special status in the first place. After all, there are tons of other important ...
0
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0answers
51 views

Value of an elliptic integral of the first kind

The elliptic integral of the first kind $$ \int_0^{\pi/2}{\frac{du}{\sqrt{1-k^2\sin^2{u}}}} $$ cannot be expressed in terms of standard functions. But in the following context from The Pendulum by ...
0
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1answer
42 views

Reference Request: Nicole Oresme history

It says on Wikipedia that [Nicole Oresme] also worked on fractional powers, and the notion of probability over infinite sequences, ideas which would not be further developed for the next three and ...
2
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0answers
33 views

Corroboration of Weil anecdote

There is an anecdote at this comment: There is an urban legend on Weil that supposedly happened when Weil, Halmos and Mac Lane were all professors in Chicago during the notorious Stone age. Weil ...
2
votes
1answer
55 views

The term “Homotopy” was given by whom?

I want to know the names who define the term 'Homotopy' in algebraic topology in 1907. Are they Dehn and Paul Heegaard? What is the full name of Dehn? Thank you in advance.
2
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1answer
66 views

History of the Coefficients of Elliptic Curves — Why $a_6$? [duplicate]

I would like to know what is the motivation behind the naming convention of the Weierstrass form of elliptic curves given as $$E:y^2+a_1xy+a_3y=x^3+a_2x^2+a_4x+a_6.$$ I can see that $a_1,a_2,a_3,a_4$ ...
4
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5answers
432 views

How to defend Mathematics from “ignorant” people? [closed]

Some of my friends are blaming me to stop talking about and studying Math. But I love Math so much and I do Math almost everyday. The problem is that some of my friends told me "go and get a life". I ...
0
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0answers
208 views

What hints had John Nash to prove Riemann Hypothesis ?¿??

i have seen " A beatiful mind" and i have also read the book and sought in internet but i have not found how john nash wanted to prove Riemann Hypothesis by using Quantum mechanics or another method ...
6
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1answer
190 views

Chinese estimate for $\pi$. Were they lucky?

The famous chinese estimate $\pi\approx\frac{355}{113}$ is good. I think that is too good. As a continued fraction: $$\pi=[3:7,15,1,292,\ldots]$$ That $292$ is a bit too big. Is there a reason for a ...
8
votes
1answer
139 views

How did Kurt Gödel's Incompleteness Theorem affect the mathematical world?

Hi I am looking not to understand the Incompleteness Theorem, but to find out more about how and what this has effected the mathematics world. I am in high school, in Honors Algebra II, and I am ...
3
votes
2answers
62 views

How did Fourier arrive at the following regarding his series and coefficients?

I am reading Karen Saxe's "Beginning Functional Analysis." Perhaps it is poor exposition on her part, but she states: ...Fourier begins with an arbitrary function $f$ on the interval from $-\pi$ ...
3
votes
1answer
70 views

History of terminology: sheaves, presheaves, etc.

I've been looking at some old notes (1970s) on Riemann surfaces, trying to match up terminology with modern definitions (at least going by Wikipedia). The notes use the same terms as Gunning's ...
9
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0answers
198 views

How does a Lehmer Sieve work?

http://en.wikipedia.org/wiki/Lehmer_sieve Apparently a Lehmer Sieve was a mechanical device that used chains and pulleys to factor numbers and solve diophantine equations. It once was able to factor ...
4
votes
2answers
87 views

How did self-similarity come into mathematics?

As far as I understand the interest in self-similarity was born outside of mathematics. The textbooks I came across give a few objects as examples (tree, broccoli, river, etc) yet it's clear that the ...
2
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0answers
79 views

What did “logarithm” initially mean? [duplicate]

I just read that logarithms were not initially defined in terms of their inverse relationship to exponential functions (and that Euler was the first to develop them in this way). So how were they ...
5
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2answers
670 views

Why the name “square root”?

Why do we say that $\sqrt{a}$ is a square root of $a$? Is this because $\sqrt{a}$ is a root of the function $f(x)=x^2-a$? Cubic root similarly? Thanks in advance
30
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6answers
1k views

Why are integrals called integrals?

What is the historical background for this term? I cannot quite see what is integral about an integral, even if we go back to the viewing it as the area under a curve. It seems a strange choice of ...
1
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1answer
115 views

Why do different countries/regions have different methods of counting large numbers?

When we start counting large quantities of $10's$, the number system varies by country/region: Europe/US: $10^3$ (thousand, million, billion are all multiples of $10^3$) Japan/China/Korea: $10^4$ ...