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

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17 views

Did the symbol for expectation value originate in bra-ket notation?

I was just wondering, whether the common $\langle x \rangle$ symbol for the expectation value of a variable originates in the bra-ket notation of quantum physics? I would think that a fundamental ...
1
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1answer
19 views

On non-modular lattices and orto-modularity

I would like to have a definition for non-modular lattices which clearly sets them appart from their modular counterparts, thereby focusing on their main distinctive feature. Besides, I would be very ...
1
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1answer
144 views

Why did Euclid call 6 a perfect number?

The old Greek did not consider $1$ a number. Nevertheless Euclid called $6 = 1+2+3$ a perfect number. How could he use $1$ which was not a number?
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0answers
53 views

Connection of Fourier's work with Fredholm's

Im trying to formulate for myself in what sense Fredholms work on the Dirichlet problem is connected to Fouriers work on the heat equation. Fourier idea seems to have fundamental problems with ...
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1answer
46 views

Why do we use a single 'dash' for difference : $-$ and a double 'dash' for sum: $+$? [closed]

Why do we use a single 'dash' for difference : $-$ and a double 'dash' for sum: $+$? Just a shower thought: Who came up with this notation? It kind of makes it look like the difference is simpler ...
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0answers
12 views

On Symmetric Bilinear Forms by Milnor and Husemoller

Note: I am not sure the question is worth to be asked. But I have always been curious about this... The usual practice in mathematics is to put the names of authors in alphabetic order. However, ...
2
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1answer
75 views

History of Riesz spectral theory on compact maps and the Fredholm alternative's place in it.

Im reading Lax book in functional analysis. He proves the Fredholm alternative for compact operators. I.e For compact maps $C$ and for $T=I-C$ we have ; i)$u \in R_{T}$ iff $(u,\ell)=0$ for all ...
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5answers
1k views

Mathematicians who overcame academic failure to achieve success [closed]

Does anyone have any story of mathematicians who overcame "academic failure" or setbacks to achieve success later as a result of their perseverance? This is a soft question, that hopefully can inspire ...
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0answers
22 views

Power Set, Theory of Linear Algebra, and Axiomatic Systems

So for homework, my History of Math professor gave us these three questions: Explain why the power set of a set S (collection of all subsets) has the same cardinality as the set [all functions from ...
3
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2answers
232 views

Why we still diagonalize compact operators even tho we lack invertibility.

We know that any compact symmetric operator on a Hilbert space, has a orthogonal base of eigenvectors. But we also know that $0$ is in the spectrum if $X$ is infinite dimensional, which makes the ...
3
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0answers
37 views

The motivation for quivers?

I would like to know about the reasons (I mean, methodological reasons, not just a penchant for innovation in terminology) for Pierre Gabriel to make use of quivers. Is it fair to say he wanted to ...
2
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2answers
88 views

Proving $n\sin(\frac{\pi}{n})<\pi<n\tan(\frac{\pi}{n})$ ; obtaining results from it.

I was reading The Simpsons and the Mathematical Secrets when I encountered the story of $\pi$. It mentions how Archimedes devised a method to place a lower and upper bound on $\pi$ by bounding a ...
2
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1answer
34 views

Solving cubics with complex numbers, before complex numbers.

An aside in another website reads: Complex numbers were used to solve cubic polynomials, before complex numbers were invented. I tried Googling this technique but didn't get anywhere. What is ...
2
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0answers
23 views

What is a point to give the Abel's Test for product series convergence a place in introductory textbooks?

One of the hypotheses of the Abel's test for product series convergence is stronger than the corresponding Dirichlet's test; that is, the former imposes the convergence of one of the series and the ...
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2answers
47 views

Value of a number

How does one define a value of a number? What is the value of the number 4? Asked differently, how does one show that a certain number is greater than another number? After this, one might ask how do ...
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0answers
47 views

Was Ramsey mistaken in thinking that the same proposition can be both elementary and non-elementary in form?

According to Ramsey's Foundations of Mathematics, chapter III, suppose $'a', 'b', ..., 'z'$ were all the individuals, then $\phi{a}.\phi(b)...\phi(z)$ expresses the same proposition as $(x)\phi(x)$ ...
3
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1answer
58 views

Why is the notation $\frac{\partial f}{\partial x}$ used? [duplicate]

I am wondering why the notation $\frac{df}{dx}$ isn't used for partial derivatives, because it seems to me like someone could tell that it was a partial derivative if they knew that $f$ was a function ...
3
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0answers
67 views

Motivation of Vieta's transformation

The depressed cubic equation $y^3 +py + q = 0$ can be solved with Vieta's transformation (or Vieta's substitution) $y = z - \frac{p}{3 \cdot z}.$ This reduces the cubic equation to a quadratic ...
5
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1answer
66 views

Is the natural exponential function defined as being its own derivative?

Is $e^x$ actually defined as being the function $f$ for which $\dfrac{d}{dx}f=f$? By which I mean not "does the identity hold", of course I know it does and that this definition is sufficient for ...
5
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1answer
56 views

History: Probability Theory

Of course they're both major oversimplifications, but which of (1) and (2) is closer to the truth? Lebesgue invents measure theory and then Kolmogorov notices that measure theory can be used to ...
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0answers
39 views

The genesis of vectors

In a recent post that I've visited, the user is asking about what is the between a vector field and a scalar field. There are good answers, and I could answer using the example that $\mathbb{R}$ (as ...
21
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1answer
1k views

What did Hilbert actually want for his second problem?

When I read about the historical background of Gödel's incompleteness theorems, it is often mentioned that he was essentially responding to Hilbert, who was trying to prove the consistency of ...
6
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2answers
112 views

Where did the angle convention originate?

Where did the angle convention (in mathematics) come from? One would imagine that a clockwise direction would be more 'natural' (given sundials & the like, also a magnetic compass dial). Also, ...
2
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2answers
62 views

Who invented the notation $Df$ for the derivative?

We are often taught that $f'$ came from Newton and $\frac{df}{dx}$ came from Leibniz, but who introduced $Df$? Are there other notations for this simple idea by famous mathematicians?
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3answers
55 views

The meaning of notation with two letters inside of parentheses

What does the notation in the red box mean?
3
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0answers
57 views

Mathematical texts: white background or tan [closed]

Why is it that while the vast majority of mathematical textbooks are printed on white paper, a select few are printed on that tan, sand-colored paper that sometimes shows up? I find the latter very ...
2
votes
1answer
89 views

What exactly did Hermann Weyl mean?

"The introduction of numbers as coordinates is an act of violence." - Hermann Weyl. A lot of people like this quote, apparently. They also seem to associate it to the manifold context in the obvious ...
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0answers
23 views

On a curve every point of which is a point of ramification

The title of my post is the same as the title of a known article written by Sierpinski where he introduced its famous triangle. In the book Handbook of the history of general topology by Lowen said ...
2
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1answer
102 views

Euler's derivation of e?

Does anyone know where I can read Euler's original derivation of the infinite series used to define $e$? I mean the series as defined in the wikipedia page about $e$.
6
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2answers
448 views

How to convert Roman numerals with dashes?

What does the dash mean over the symbols here? How to convert these Roman numerals to numbers? Textual equivalent of the image: ...
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3answers
109 views

Why is variable called “variable” in mathematics if in fact it's immutable?

I've never thought of this issue until recently when I've been using Haskell to build a substantial project. In Haskell (and functional programming languages in general), most so-called "variables" ...
3
votes
2answers
115 views

Who's the “Author” of the integrating factor method?

I've always been interested in how someone discovered this method, it felt pretty magical when I first learnt it, and I've been wondering who discovered/how was it derived for the first time. Does ...
3
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0answers
59 views

On the (Pre-)History of Sheaf Theory

In the wikipedia page on sheaf theory I found the following statement which somehow puzzled me: some of the facets of sheaf theory can also be traced back as far as Leibniz. Could anyone explain ...
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0answers
22 views

In the problem of dividing a line in extreme and mean ratios, how do I show that 1 and x are incommensurable?

In other words, the line is divided at x such that 1/x = x/(1 - x). The problem hints at using the Euclidean algorithm to prove that 1 and x are incommensurable. Also need to show that the proportion ...
2
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2answers
105 views

What (previously and currently unsolved) problems motivate the study/development of analysis?

As I had ever know there are at least two (previously unsolved) problems motivate the study/development of abstract algebra: (1) the ancient Greeks' three problems in compass-and-straightedge ...
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0answers
20 views

Did Euler talk about Eulerian circuits?

The Wikipedia article on Eulerian paths states: Euler proved that a necessary condition for the existence of Eulerian circuits is that all vertices in the graph have an even degree, and stated ...
0
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0answers
48 views

Weak Law of Large Numbers - Bernoulli's proof

Question concerning Bernoulli's demonstration of Bernoulli's Weak Law of Large Numbers. Although, I get the general sense of the third lemma, I don't really get the formulation of it, more ...
0
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1answer
46 views

Spanish translation for the term operad?

I would like to know which is the correct term in Spanish for operad(s)? https://en.wikipedia.org/wiki/Operad_theory I cannot be operador, since that is reserved for operators. I do not see anything ...
2
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1answer
59 views

What was the original purpose for the binary system?

Obviously computers weren't around when binary was first created... was there a particular use for binary back then or was it just developed as another number system?
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1answer
60 views

Where did the notation $\Bbb Z/n\Bbb Z$ came from?

Where did the notation $\Bbb Z/n\Bbb Z$ came from? By this I mean the ring $(\Bbb Z, +_{\bmod n},\cdot _{\bmod n})$. Shouldn't the "$n\Bbb Z$" part be an equivalence relation(to quotient the set?)?
3
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1answer
243 views

A question about Homotopy (Michael Harris's recent book)

In the recent book "Mathematics without Apologies: Portrait of a Problematic Vocation" by Michael Harris there is some passage I want to call your attention on. Specifically, pages 211-212. Could ...
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0answers
56 views

"Problems worthy of attack prove their worth by fighting back.”

That is quote has been attributed to Piet Hein, inventor of the Soma cube, which is how I know of him. Q. Is the attribution correct? I wonder because the quote has a nice ring in English that ...
7
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1answer
95 views

History of the power series for $e^x$ and compound interest

As discussed in How did Bernoulli approximate $e$?, Bernoulli showed that $2\frac{1}{2} < e < 3$ in this paper: ...
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0answers
23 views

Different ideal vs. dual lattice

I found this statement in a text trying to explain what the different ideal by Dedekind is: "The main idea needed to construct the different ideal is to do something in number fields that is ...
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0answers
29 views

Developable surfaces in $\mathbb{R}^4$

It is known that there are developable surfaces in $\mathbb{R}^4$ which are not ruled: the famous example is of Hilbert and Cohn-Vossen in their book "Geometry and the Imagination" (p. 342). The ...
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3answers
146 views

Cool math theorem names/terms? [closed]

Does anyone know any other cool math theorem names/math terms besides the no-ghost theorem and the monstrous moonshine?
0
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1answer
70 views

Who (which) was the mathematician “Abel” who countered Cauchy's “proof?” [closed]

...as in this quotation: "Cauchy's approach to rigour didn't save him from errors, however. He 'proved' incorrectly that the limit of a convergent series of continuous functions is continuous. Abel ...
1
vote
1answer
40 views

On the Hasse diagram for ideals

When consulting the wikipedia regarding prime ideals, the following Hasse diagram (is it also a lattice?) is provided as representation: https://en.wikipedia.org/wiki/Prime_ideal Any idea of who ...
0
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1answer
45 views

Dedekind's “different”: sources, definition, original name

I am interested in getting the original information regarding Dedekind's idea of the "different" (regarding ideals). Particularly, I am interested in: 1- Knowing the original German name he used for ...
0
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1answer
72 views

Technical meaning of “profinite circle”

In a private exchange with a professional mathematician, I found the following statement: the "small etale topos" of a finite field is a "profinite circle", and thus looks like circle. Could anyone ...