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

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Historical use of k in proof by induction

Does anybody know the history of why the symbol k is used in proof by induction? As an example, in physics the symbol p is used for momentum because Newton called it impetus, and the letters i and m ...
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2answers
189 views

Andrew Wiles' Abel Prize for FLT - delayed or not? [closed]

Andrew Wiles was recently awarded the Abel Prize for his work proving Fermat's Last Theorem (FLT). The Abel Prize has existed for 14 years. From my layperson's perspective, it would seem that he ...
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1answer
58 views

Mersenne numbers fail primality test at 2047 itself. How could we believe Mersennes are primes?

M$_{11}=2047$ is a composite number. How could one, not check the primaility of such a small number and believe that all Mersenne numbers are primes?
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1answer
45 views

Why is it called the *Inverse* Galois Problem?

This is just a very quick question and hopefully not poorly received. Question: Why is it called the inverse galois problem? The very brief statement given on wikipedia says Is every finite ...
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0answers
58 views

Largest prime known to ancients

As is well known, Fermat couldn't check the primality of $F_{5} = 2^{2^{5}} + 1$. This raises an interesting question : what was the largest prime number that was known to ancients (particularly ...
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0answers
26 views

Why is the Weierstrass test called the M-Test [duplicate]

Is there any reason why we call this test an $M$-test? The presence of $M_n$'s in the standard formulation?
3
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4answers
125 views

Who found the expression $n^2 - n + 41 $ for generating prime numbers?

I am doing some research and I cannot seem to find the answer anywhere so does anyone know who found the expression $n^2 - n + 41 $ for generating prime numbers?
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0answers
141 views

Who is the mathematician “Jacques” in this anecdote?

Who is the mathematician "Jacques" in this anecdote, which I read on p. 260 of The Mathematical Magpie by Clifton Fadiman, who quotes it from the 1942 memoir The Last Time I Saw Paris by Elliot Paul? ...
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1answer
30 views

On applications of Alexander's Theorem

I would like to know a bit about applications of the Alexander Theorem from Knot and Braid Theory. I would be very interested in learning about possible applications for the description of everyday ...
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1answer
73 views

Developments from Charles Peirce's logic diagrams?

These last weeks I have been revisiting Charles Sanders Peirce's logical or thought diagrams (what he called, alpha, beta and gamma diagramms) and I found many of them highly interesting. Some ...
26
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5answers
2k views

Why are turns not used as the default angle measure?

Why is $2\pi$ radians not replaced by $1$ turn in formulas? The majority of them would be simpler. If such a replacement was proposed earlier, why was it declined?
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1answer
49 views

Order of operation in math

Who decides order of operation in any math calculation. Is it scientific or arbitrary? e.g. 1+4-6x7+7
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0answers
19 views

About Special and Extra-special $p$-groups

A $p$-group $G$ is said to be special $p$-group if $Z(G)=[G,G]=$ elementary abelian. A $p$-group $G$ is said to be extra-special if $Z(G)=[G,G]=$ elementary abelian of order $p$. The ...
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2answers
95 views

Differentiation and integration

Which came first : Differentiation or Integration? If one of them was developed to solve certain types of problems, was the other developed for backward compatibility, or was it an independent ...
6
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2answers
97 views

How do people calculate values for trig functions?

This may sound like a stupid question, but I'm wondering how people originally calculated specific values for trig functions before calculators existed. Did they just draw circles and manually measure ...
7
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3answers
67 views

Fermat's Challenge of composition of numbers

In his letter to Carcavi (August 1659), Fermat mentions the following challenge There is no number, one less than a multiple of $3$, composed of a square and the triple of another square. ...
3
votes
1answer
64 views

Are there any instances of significant progress deriving from mathematical 'silliness'? [closed]

Last night I thought I'd be silly finding the eigenvalues of a $2\times2$ matrix $A$ with real components. Instead of calculating $\det(A-\lambda I)=0$ I tried to compute the determinant by ...
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0answers
39 views

About the domain of the Gamma function

I started to read about the history of the Gamma Function. There are three places I liked most, The early history of the factorial function (p. 239 - 243) Leonhard Euler's Integral: An Historical ...
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5answers
232 views

Is $22/7$ an often used approximation for $\pi$?

It is $\pi$-day and the internet is full of stories about $\pi$. One story mentions that "an approximation -- $22/7$ -- is used in many calculations." I have never actually used $22/7$ as an ...
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votes
2answers
128 views

What will mathematicians do when they run out of letters in the Greek and English alphabets? [closed]

Like x,y,z are commonly understood to be dimensions and theta is an angle and Pi is a specific irrational constant, and Tau is half of Pi, etc. etc. etc. They must be running out of letters by now. ...
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0answers
45 views

Define the word 'smooth' in explict mathematical language?

Note in the comments of this question: Create a formula that creates a curve between two points ... that someone was asking me to define what is meant by the word "smooth". Given that one of the ...
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0answers
55 views

Ignoring the lack of rigor, is this a fair argument to make when considering if 0^0 should be equivalent to 1? [closed]

The Professor of Mathematics argued that 0^0 is undefined because the limits $0^x$ and $x^0$ as x approaches 0 don't agree. That seemed logical to me, but then Scott pointed out in the comments that ...
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1answer
37 views

Looking for in depth material on a formal propositional calculus using only the NAND connective

I am looking for secondary literature on a formal propositional calculus which has the NAND connective as its sole connective. I am coming upon many pages which briefly state that Nicod had shown ...
3
votes
1answer
78 views

Why is a $\sigma$-algebra defined as such?

We know that a $\sigma$-algebra is a collection of sets closed under countable set operations. My question is: how was it determined that this is the right collection? i.e., how was it determined ...
2
votes
1answer
42 views

Kempe's proof of the four colour theorem

What exactly was Kempe's error in his proof of the four colour theorem? What I understand of his general idea is by the following case: Suppose an uncoloured "country" is surrounded by countries of ...
2
votes
2answers
75 views

Ideas for a history of math paper (with an emphasis on the mathematics), having to do with 19/20th century logic?

So I'm currently taking a history of math course and I need to write a 15 page paper in place of my final. It's a 400 level course (high undergrad) so the paper needs to have emphasis on the ...
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1answer
75 views

Seemingly contradictory results [duplicate]

The following infinite sums produce remarkable results. $1+2+3+4+...=-\frac{1}{12}$ $1-2+3-4 +...=\frac{1}{4}$ So how are these results compatible with the statement; that integers are closed ...
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17answers
3k views

Good “history of mathematical ideas” book?

All too often, mathematical history books include far too much material on the private lives of the personalities involved and not enough information on the actual ideas. Mathematics is a living ...
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0answers
18 views

Cartesian coordinates conventions

Is there any historical account of how did the Cartesian coordinate system get its current conventions of orientation and representation? Are there any mathematical reasons for these conventions?
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0answers
18 views

Weiertrass equation of an elliptic curve.

We know that every elliptic curve is a non-singular $\textbf{cubic}$ projective curve (curve of genus 1), but we can transform this in the Weiertrass form $$y^2 + a_1xy + a_3y = x^3 + a_2x^2 +a_4x ...
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0answers
44 views

Hermite's identity for sum of floor function

In Hermite's 1884 paper "Sur quelques conséquences arithmétiques des formules de la théorie des fonctions elliptiques", volume 5 of Acta Mathematica, pages 310-315, he proves what is often called ...
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0answers
24 views

On the origin of the notion of polynomial between Banach spaces

I have already asked here a few questions about polynomials in Banach spaces (Counterexample of polynomials in infinite dimensional Banach spaces, Mujica's "Complex analysis in Banach ...
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2answers
168 views

How did Leibniz prove that $\sin (x)$ is not an algebraic function of $x$?

In the Wikipedia article about transcendental numbers we can read the following: The name "transcendental" comes from Leibniz in his 1682 paper where he proved that sin(x) is not an algebraic ...
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2answers
75 views

Any surviving contemporary manuscripts by ancient mathematicians?

As I understand it, most of what we know about ancient mathematics comes from copies, quotations, and summaries by later scribes and scholars. Medieval Arab mathematicians in particular are given ...
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1answer
62 views

Why are there two different notations for negation in boolean logic?

For the boolean variable $x$, there are two notations for its negation: $\neg x$ and $\bar x$. So why are there two different notations?
5
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2answers
64 views

Original usage of 'Bénabou cosmos'

A (Bénabou) cosmos is a bicomplete closed symmetric monoidal category (see, for example, the $n$Lab). However, I can't find the paper where Bénabou first uses this term - googling turns up nothing. ...
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0answers
36 views

Who extended the Euler Product Formula to all real $s>1$?

I believe Euler discovered this identity but only wrote them for particular values of $s$, then Chebychev extended to real $s>1$. However, I read in the book Riemann's Zeta Function, H.M. Edwards ...
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2answers
562 views

What does “Mathematics of Computation” mean?

I visited this link: http://www.ams.org/journals/mcom/1950-04-030/S0025-5718-50-99474-9/ And I a bit confused by its title "Mathematics of Computation". I am not a native English speaker. Could ...
2
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1answer
100 views

Origin of delta

Why does delta mean change? What is the origin of delta? I understand that upper-cased delta is used in this way and that delta is the fourth letter of the Greek alphabet. I also read that delta is ...
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0answers
166 views

Fréchet L-Spaces

According to the paper The emergence of open sets, closed sets, and limit points in analysis and topology famous mathematician Maurice Fréchet who introduced the concept of metric spaces has also ...
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2answers
64 views

Looking for details on historical math anecdote

My memory is very sketchy here so bear with me. A fairly prominent 19th or 20th century mathematician was captured by a military force, probably invaders. He claimed that he was just a civilian, a ...
6
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1answer
44 views

Epicycles as precursors of Fourier series

How convincing an argument can be formulated to claim that the Ptolemaic epicycles were actually an early precursor of Fourier series? Ptolemy lived ~200AD, and so well pre-dates Fourier ~1800.
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1answer
41 views

Which are the most used and correct nomenclature for gradient, divergence, curl and Laplace operator in differents contexts?

I used to write these operator in this way: $\vec{\nabla}$ for divergence and gradient and for Laplace operator $\vec{\nabla}^2$. But I have noticed that in some books and website divergence is ...
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2answers
645 views

Is it to the students' advantage to learn the language of infinitesimals? [closed]

A colleague of mine asked an interesting question reproduced below with his permission. It is reasonable to ask whether it is to the students' advantage to learn the language of infinitesimals - ...
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0answers
118 views

Why is the symbol for the exterior product a meet rather than a join?

I've moved this over to HSM. It seems odd that something that looks so much like a join [see below] would get given "the wrong symbol". It's even worse when you dualise it and get something called ...
4
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1answer
164 views

Why is $s$ used for arc length?

Why is $s$ used for arc length? I looked around online, but I can't find a definite answer. Thank you!
3
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1answer
80 views

Circle is similar to a polygon with infinite number of sides

It is know from the time of Euclid, that a circle is similar to a polygon with infinite number of sides. But this ^^ is informal. Do you know any formalization where it appears that a circle is a ...
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2answers
102 views

Why was $\aleph$ (aleph) chosen for infinities?

Why did Cantor choose a letter from the Hebrew alphabet to represent infinities, rather than using some Greek letter?
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1answer
82 views

Can we build mathematics without studying it?

This is one question that I can never get the answer of, because I am too young at this moment. My question is that can a common person like me, not a genius, just a normal person, build mathematics ...
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0answers
53 views

A Taylor Expansion before Taylor

Taylor expansion was introduced in its currently well known form by Brook Taylor. Though the concept as this page says, has been formulated by James Gregory. Among his other works, Gregory established ...