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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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2answers
63 views

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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0answers
55 views

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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2answers
3k views

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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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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0answers
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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4k views

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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2answers
65 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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80 views

What is the most difficult question in math? [closed]

I found in internet this, $\dfrac{\dfrac{5}{\displaystyle\oint 4\; 56iint\prod \;3setR3^{^{\underline{\circ}}}\widehat 5*675*65/3/7}2.9,78}{2}.45.1,3\dfrac{457}{1,5}$ But I think, this is trolling ...
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127 views
+50

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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30 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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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
60 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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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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0answers
20 views

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
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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1answer
90 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 ...
4
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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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0answers
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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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
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
59 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
66 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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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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20answers
21k views

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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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_{\...
12
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5answers
287 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{\...
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4answers
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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mathematics was recreated on a foundation of number concepts rather than geometrical ones

In Richard Courant and Fritz John's book Introduction to Calculus and Analysis Volume I, says In modern times mathematics was recreated and vastly expanded on a foundation of number ...
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3answers
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Why was Sheaf cohomology invented?

Sheaf cohomology was first introduced into algebraic geometry by Serre. He used Čech cohomology to define sheaf cohomology. Grothendieck then later gave a more abstract definition of the right derived ...
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36 views

Why did the number of types of integrals got lower from the beginning of the $20^{th}$ to this day?

There is an old $(\text{circa } 1930)$ and interesting book in calculus: Edwards' Treatise on Integral Calculus. This book has a very complete list of cases of integrals, for example, these ...
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1answer
60 views

Cauchy's real line and math philosophy till XIX

I have to write an essay concerning philosophy of mathematics until the end of $XIX$ century. I've heard that the reason why the Cauchy's theorem (if continuous functions $f_n \rightarrow f$ then $f$ ...
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53 views

Left and right inverse

Does anybody knows who is the first person to coin the term "left inverse" and "right Inverse" ? And why is it named that way?
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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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1answer
36 views

Eulers identity history

When Euler discovered/invented $e^{ix} = \cos(x)+i\sin(x)$. Did he doubt his calculations for a length of time? Was it Readily accepted by the mathematical community quickly or did they object at ...
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1answer
73 views

History and future of algebraic curves and the like?

Now that Fermat's last theorem has been proven, and also elliptic curves see widespread use in simple everyday applications, I would love to learn how the related theories came into beeing, how they ...
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0answers
69 views

Is Leibnizian calculus embeddable in first order logic?

We just published an article making what we feel is a plausible case in favor of an affirmative answer in Foundations of Science, see preprint here. The basic argument is that while such a requirement ...
2
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1answer
48 views

Have humans ever used the Log Scale convention in the past rather than the Linear one?

There are many examples where our senses are based off of log scales such as volume of a noise, ability to guess (i.e.) plus or minus a power of 10 with Fermi, and even when we measure pain on 1 to 10 ...
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3answers
214 views

Product of permutation cycles, transpositions. Are there different conventions in the order?

From this answer I get that within each cycle you map each element to the one on the right, when taking the product of cycles the one on the right should be performed first, as a typical operator. ...
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1answer
39 views

Ratio vs division

I remember reading somewhere that in ancient times they were not treating a ratio like a division as we do. I was wondering is there a subtle distinction between the concept of the ratio and the idea ...
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1answer
59 views

Why wasn't Mahāvīra's definition of division by zero accepted?

He wrote a book (Ganita Sara Samgraha) where he defined the result of operation of division by zero A number remains unchanged when divided by zero. I think this kind of makes sense. I know ...
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0answers
59 views

What is “Squaring the Circle”

I am unclear about what "Squaring the Circle" is, let alone how people tried to solve it. Please tell me if "Squaring the Circle" means finding square and circle with same area OR finding square and ...
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5answers
91 views

Can we prove that plumb line is vertical to ground?

Using a plumb line to make sure a wall is vertical for instance, is as far as I know one of the most primary tools in the sense that the very-very ancient builders used it as an instrument. I was ...
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1answer
90 views

Was there a golden age of industrial mathematics that is now over?

I read "The Man Who Loved Only Numbers," a great book about Paul Erdős, last summer. The book describes Ronald Graham, a super interesting character who worked on discrete math and graph theory at AT&...
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1answer
38 views

What does the word “Comprehension” mean in the Axiom of Comprehension?

I understand roughly what the Axiom of Comprehension means, that any predicate can be used to construct a set of the elements that satisfy the predicate. But in English terms, where does the word "...