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Have historians of the classical period responded to C. K. Raju's critique?

C. K. Raju has some criticisms of the traditional take on Euclid in particular and Western history in general. Have modern historians of the classical period responded to his critique?
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Did Joseph Fourier ever make a pure mathematical mistake?

Cited by "Imre Lakatos and the Guises of Reason" John David Kadvany, 2001: It is remarkable that the nineteenth century was a time of error for mathematics: not trivial oversights or amateur ...
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When did Euler find his formula for $\zeta(2n)$

Does anybody know when Euler found his famous formula $$\zeta(2n)=\frac{(-1)^{n-1}(2\pi)^{2n}B_{2n}}{2(2n)!}?$$
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Simple Proof of the Euler Identity $\exp{i\theta}=\cos{\theta}+i\sin{\theta}$

my question is too simple. We know all that if we define the exponential function on $\mathbb{C}$ then we define the real part and imaginary part of $\exp{it}$ as $\cos{t}$ and $\sin{t}$. So if we ...
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How mathematics would be different if the first derivations, conjectures and theorems would be others? [on hold]

I've realised that mathematics is nothing else that an implication of some assumptions (plus the assumptions themselves, of course). We have axioms and we derive new "things", new rules, ideas, ...
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606 views

Is the Galois group associated to a random polynomial solvable with probability 0?

Choose a random polynomial $P\in\mathbb{Z}[x]$ of degree $n$ and coefficients $\leq n$ and $\geq-n$. Let $r_1,\ldots,r_n$ be the roots of $P$ and consider $$G=\operatorname{Gal}(\mathbb{Q}(r_1,\...
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2answers
39 views

What is the mathematical term describing a pipe or a tube?

I am interested in this unanswered question Pipe-fitting conditions in 3D and so I was trying to find information about it. If the 3D curve $f(x(t), y(t), z(t)) = 0$ is a line I think that the pipe ...
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4answers
8k views

Are We Teaching Pre-Calc Wrong?

It took some 1,250 years to move from the integral of a quadratic to that of a fourth degree polynomial. When we jump too fast to the magical algorithm, when we fail to acknowledge the effort that ...
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1answer
83 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 ...
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What is Ptolemy holding in his picture on Wikipedia? [migrated]

I would like to know the name of the device Ptolemy is holding in his picture
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27 views

Inclusion-exclusion formula and its alias names

I am reading Probability by A. N. Shiryaev. One of the problems refers to "inclusion-exclusion formulas", also known as Poincaré’s formulas, Poincaré’s theorems, Poincaré’s identities. One of my ...
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2answers
404 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 ...
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151 views

How did Hecke come up with Hecke-operators?

I'm currently studying Hecke-operators and I'm curious how Hecke came up with them. The original definition he gave in his paper is $$\left( f \mid T_n\right) (z) = n^{k - 1} \sum_{ad = n, \, b \mod d,...
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2answers
66 views

Why is matrix multiplication called 'multiplication' if it is non-commutative?

This question begins with the assumption that matrix multiplication was termed 'multiplication' as a form of comparison/parallel to multiplication of integers and real numbers. Why was matrix ...
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2answers
87 views

Why weren't “degrees” replaced with a more intuitive angle measure?

$\bf History$ It is speculated that the seemingly arbitrary number $360$ used to indicate a full revolution in degrees was chosen because the Babylonians counted in base $60$ and $60 \times 6 = 360$. ...
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2answers
61 views

Origin of Almost Perfect Numbers

Let $N$ be a positive integer. $N$ is called a perfect number if the sum of its positive divisors denoted by $\sigma(N)=2N$. For example $6$ is a perfect number since: $\sigma(N)=1+2+3+6=12=2(6)$. ...
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6answers
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What did Newton and Leibniz actually discover?

Most popular sources credit Newton and Leibniz with the creation and the discovery of calculus. However there are many things that are normally regarded as a part of calculus (such as the notion of a ...
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3answers
2k views

Why has the Perfect cuboid problem not been solved yet?

Why hasn't Perfect Cuboid Problem been solved yet, whereas (possibly) more nontrivial ones such as FLT and Sphere packing have been solved? I understand that calling some problems more nontrivial ...
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9answers
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Why do people use “it is easy to prove”?

Math is not generally what I am doing, but I have to read some literature and articles in dynamic systems and complexity theory. What I noticed is that authors tend to use (quite frequently) the ...
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3answers
325 views

Historic proof of the area of a circle

The area of a circle radius $R$ is $\pi R^2$ which is quite easy to prove with integral calculus. Consider a ring of radius $\mathrm{d}r$ at a distance $r$ from the centre. This ring has area $2\pi r ...
3
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1answer
276 views

What is Euler's proof of his formula ${e^{ix}=\cos(x)+i\sin(x)}$

I've read several proofs of the Euler's formula $$e^{ix}=\cos(x)+i\sin(x)$$ but I want to know how Euler's himself prove it at the first time, how did he think about it?
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20answers
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What are some examples of when Mathematics 'accidentally' discovered something about the world?

I do not remember precisely what the equations or who the relevant mathematicians and physicists were, but I recall being told the following story. I apologise in advance if I have misunderstood ...
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0answers
31 views

Historically accurate alternatives to men of mathematics? [migrated]

I have heard that the book "Men of Mathematics" by E. Bell is a very entertaining book composed of biographies of several influential mathematicians, and is in fact one of the most popular popular ...
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1answer
131 views

What is the motivation behind the arbitrary union topological axiom?

1. Why is the arbitrary union axiom in the definition of topology necessary? 2. Why is it useful? Why might we expect ("intuitively") that it should be useful? 3. What is the (historical) ...
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5answers
595 views

How to Axiomize the Notion of “Continuous Space”?

EDIT (to clear up controversy and misunderstandings caused by my poor wording): Historically, Riesz's efforts to try and make rigorous a notion of a "continuous space" (as opposed to "discrete ones") ...
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2answers
184 views

Why $a^2+b^2=c^2$ is named after Pythagoras? It is known by earlier generations before him such as the Chinese. [closed]

Why $a^2+b^2=c^2$ is named after Pythagoras? It is known by earlier generations before him such as the Chinese. It is because he proved it and not other generations? Or Pythagoras put it into ...
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2answers
79 views

Who is M. Montel?

From V.I. Arnold's Experimental Mathematics: Not having achieved what they desired, they pretended to desire what they had achieved. –M. Montel Who is M. Montel? Is he related to the ...
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0answers
71 views

Why did Fermat publish so little? [closed]

Fermat published very little during his lifetime. Why is this the case?
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7answers
7k views

Why don't we use base 6 or 11?

Another question on this site asks why we have chosen our number system to be decimal base 10. There are others asking basically the same thing as well. I'm not really satisfied with any of the ...
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0answers
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Does the collection of algebraic/number-theoretic methods applied to Euclidean Geometry have a name?

I am currently writing an essay on the history of geometry. To educate myself on the subject, I sometimes read the following Wikipedia article on the history of Euclidean Geometry. It seems to me that,...
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3answers
95 views

How (or why) did Topology become so central to modern mathematics?

It is frequently said that topology is nowadays one of the central pillars of modern mathematics (ex. "Because of its central place in a broad spectrum of mathematics") The field has managed to ...
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1answer
91 views

Was Riemann really the first person to define definite integrals?

So I am doing a study on Riemann, and one of his big things is apparently the "Riemann integral". My understanding is that this concept was meerly the first definition of a definite integral, and ...
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2answers
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Are infinitesimals dangerous?

Amir Alexander is a historian of mathematics. His new book is entitled "Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World". See here. Two questions: (1) In what sense are ...
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677 views

What is… A Parsimonious History?

Interpreting historical mathematicians involves a recognition of the fact that most of them viewed the continuum as not being made out of points. Rather they viewed points as marking locations on a ...
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3answers
101 views

There are many numeral systems. Why do we only use the $0-9$ Hindu-Arabic numeral system?

Here is a list of other systems: Babylonian numerals Egyptian numerals Aegean numerals May numerals Chinese numerals These system are far older than the current system. How did it get to be known ...
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4answers
2k views

Is mathematical history written by the victors?

The question is the title of a recent piece in the Notices of the American Mathematical Society, by twelve authors (of which I am one). The contention is that traditional history of mathematics is ...
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33 views

Serendipitous discoveries in mathematics [duplicate]

I have recently been reading about serendipitous discoveries in science and I found them quite inspiring. Most of those discoveries are in Chemistry. I'm looking for examples of these kinds of ...
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3answers
2k views

Unexpected approximations which have led to important mathematical discoveries

On a regular basis, one sees at MSE approximate numerology questions like Prove $\log_{{1}/{4}} \frac{8}{7}> \log_{{1}/{5}} \frac{5}{4}$, Prove $\left(\dfrac{2}{5}\right)^{{2}/{5}}<\ln{2}$, ...
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1answer
41 views

What is the name for the set of all integers greater than 1?

Ancient Greek Mathematicians such as Euclid defined a number as "a multitude of units." For them, a number was a member of the set of all integers greater than one. Does this set have a name in ...
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17 views

Origins of Operations Research and original meanings to different terms? [closed]

I am confused by Reliability Engineering to the extent that sometimes the terms used are graph-theoretical: this aspired to be researched here and here. In comparison, terms are sometimes more slack, ...
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0answers
60 views

Origin of the Riemann-Lebesgue lemma

When and where did Riemann and Lebesgue give the well known Riemann-Lebesgue lemma? A "lemma" is usually used as a stepping stone to a larger result rather than as a statement of interest by itself. ...
2
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1answer
67 views

What was the “real” first equation? [closed]

The first equation ever written, using a modern equals sign, has TWO versions: Version 1: Wiki link and Another link gives $$ 14x+15=71 $$ But from a UK maths textbook, it gives $$ 14\sqrt{x}+15=...
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3answers
1k views

Motivation for/history of Jacobi's triple product identity

I'm taking a short number theory course this summer. The first topic we covered was Jacobi's triple product identity. I still have no sense of why this is important, how it arises, how it might have ...
2
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1answer
53 views

What is the motivation behind the Bessel function of second kind

I am studying Bessel function and found the good reference by G.N. Watson At some point in page 58 he introduces the following expression due to Hankel: \begin{eqnarray} \lim_{\nu \to n} \frac{J_{\...
38
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3answers
5k views

Why, historically, do we multiply matrices as we do?

Multiplication of matrices — taking the dot product of the $i$th row of the first matrix and the $j$th column of the second to yield the $ij$th entry of the product — is not a very ...
12
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5answers
288 views

What is the difference between $\frac{\mathrm{d}}{\mathrm{d}x}$ and $\frac{\partial}{\partial x}$?

Is there not any difference between $\frac{\mathrm{d}}{\mathrm{d}x}$ and $\frac{\partial}{\partial x}$ as long as your function has one variable? $f(x) = x^3\implies \left\{\begin{align}&\dfrac{\...
5
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1answer
103 views

Who introduced the notation $\lesssim$?

Who in history introduced the notation $X\lesssim Y$ for meaning $X\leq CY$ for some constant $C$? I've seen this notation in modern literature in PDE a lot. (See for instance the notation section of ...
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4answers
254 views

What are the disadvantages of non-standard analysis?

Most students are first taught standard analysis, and the might learn about NSA later on. However, what has kept NSA from becoming the standard? At least from what I've been told, it is much more ...