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

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76 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
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1answer
84 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. ...
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6answers
265 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". ...
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0answers
22 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 ...
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2answers
435 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
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1answer
92 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
68 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 ...
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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.
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1answer
98 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
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1answer
101 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: ...
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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!!!
3
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0answers
108 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 ...
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0answers
19 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
55 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
91 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 ...
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2answers
181 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, ...
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0answers
48 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 ...
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0answers
116 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 ...
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0answers
43 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 ...
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1answer
41 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 ...
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0answers
32 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
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1answer
54 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
63 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 $a_1,a_2,a_3,a_4$ ...
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5answers
408 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 ...
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0answers
155 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
177 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
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1answer
136 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
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2answers
59 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
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1answer
60 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
163 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
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2answers
82 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
78 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 ...
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2answers
622 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
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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
93 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: $10^4$ ...
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1answer
125 views

History of the terms “prime” and “irreducible” in Ring Theory.

In ring theory, a nonzero, nonunit element $p$ of a integral domain is called irreducible if $p=ab$ implies that exactly one of $a$ and $b$ is a unit, and it's called prime if $p\mid ab$ implies that ...
4
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2answers
164 views

Why did the ancients hate the Parallel Postulate?

I am reading this book, Gödel's Proof, by James R. Newman, at location 117 (Kindle), it says, For various reasons, this axiom, (through a point outside a given line only one parallel to the line ...
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3answers
706 views

History of notation: “!”

Does anyone know where the factorial "!" symbol came from? I can't decide if it is my favorite or least favorite notation in mathematics...
3
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1answer
47 views

Translation of Paolo Ruffini's work on Galois theory

Paolo Ruffini famously wrote a work providing the first proof of the unsolvability of the quintic with the extraordinary title "Teoria Generale delle Equazioni, in cui si dimostra impossibile la ...
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0answers
33 views

Which came first, energy minimization or pde?

I'm interested in a historical perspective on pde. I would like to know more about the original derivation of pde. It seems like d'Alembert was working on the one dimensional wave equation $$ ...
2
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1answer
57 views

How did Napier rounded his logarithms?

How did Napier round his logarithms? Wikipedia says: By repeated subtractions Napier calculated $(1 − 10^{−7})^L$ for $L$ ranging from 1 to 100. The result for $L=100$ is approximately $0.99999 = ...
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3answers
99 views

Colloquialisms in Math Terminology

What are some of your favorite colloquial sounding names for mathematical objects, proofs, and so on? For example, manifolds are often described using an atlas and a neighborhood describes a small ...
3
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1answer
51 views

Why half coversed or coversed trigonometric functions are being deprecated?

As you can see here there are some names for some trigonometric functions that I can't find in any text or math related papers today. In my opinion this kind of approach will also make it easier to ...
2
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1answer
105 views

Reference Request - Early Calculus Papers

Question: I am looking for good references on the early calculus papers. Optimally, I want emphasis on the mathematics itself and I want that mathematics to be translated into modern terminology and ...
0
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0answers
19 views

How well-known are these contra-Bernoulli inequalities?

The standard and extremely useful Bernoulli inequality states that $(1+x)^n \ge 1+nx$ for positive integer $n$ and $x \ge 0$. I have needed an inequality of the form $(1+x)^n \le 1+c(n)x$ where $x$ ...
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2answers
77 views

What's the intuition behind definition of chaotic function?

I read books A First Course in Discrete Dynamical Systems by Richard A. Holmgren and An Introduction to Chaotic Dynamical Systems by Robert L. Devaney. I want to understand which concepts of "chaos" ...
3
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0answers
119 views

History of “Math is an Art” [closed]

For all its elegance I cannot bring myself to the conclusion that math is a form of art. As shown on the wikipedia page there is certainly math in art and art in math but what I wonder is how the ...
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3answers
99 views

Mathematical logic and foundations of mathematics in the 20th century

I would like some references regarding the foundations of mathematics in the 20th century, and mathematical logic, e.g. (1) I want to understand what happened to the foundation, what originated the ...
4
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1answer
171 views

What is “Bourbaki's style in mathematics”?

I know Nicolas Bourbaki "is the pseudonym of a group of (mainly) French mathematicians who publish an authoritative account of contemporary mathematics." But what characterizes "Bourbaki's style in ...