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3
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76 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
99 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 $e$,...
9
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2answers
128 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 ...
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 (...
7
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2answers
141 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
66 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
71 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
59 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 ...
5
votes
1answer
374 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
28 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
114 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
votes
2answers
510 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: $$\overline{\text{M}}\,\overline{\text{L}}\,\overline{\text{V}}\...
1
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3answers
157 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
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2answers
147 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
votes
0answers
68 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 ...
2
votes
2answers
115 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 ...
0
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0answers
21 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
66 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
votes
1answer
50 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
votes
1answer
63 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?
2
votes
1answer
68 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
votes
1answer
253 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 ...
1
vote
1answer
114 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
votes
1answer
112 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: https://books.google.com/books?id=s4pw4GyHTRcC&pg=PA222#v=onepage&q&f=...
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0answers
27 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 ...
0
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0answers
31 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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votes
3answers
218 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?
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1answer
82 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
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1answer
41 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
votes
1answer
49 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
votes
1answer
81 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 ...
3
votes
1answer
74 views

Who found the method for matrix inversion and how was the method(s) derived?

I understand how to go about the process for finding an inverse of a square matrix but how did the algorithm come about?
7
votes
1answer
150 views

Sources of morality in mathematics

Long ago, I have heard one of my mathematic teachers claim several times that a result, a conjecture should hold "moralement" in French ("morally" in English). Since then, I have heard the same ...
24
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11answers
4k views

Why is Lebesgue so often spelled “Lebesque”?

Henri Lebesgue (1875-1941) was a French mathematician, best known for inventing the theory of measure and integration that bears his name. As far as I know, "Lebesgue" is the correct spelling of his ...
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2answers
943 views

Who decides after whom a theorem or conjecture is named?

Who decides after whom a theorem is named? When someone discovers and proves a theorem, it is almost always named after that person. But how about when person A conjectures a theorem, and B proves it?...
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0answers
41 views

Clarification of a quote on Riemann-Roch Theorem

I find this quote in Martin Krieger, Doing Mathematics: Convention, Subject, Calculation, Analogy, New Jersey, World Scientific Publishing, 2003, p. 223. "Hilbert then shows how one of Dedekind's ...
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votes
1answer
74 views

Is there any realtion exists between Fermat's Last theroem & Hypatia [closed]

Is there any realtion exists between Fermat's Last theroem & Hypatia. I recently watched documentary regarding Fermat's Last theroem. I just want to know is this theroem somehow related to Hypatia ...
0
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0answers
50 views

Who thought applying real value definite integral to contour integral firstly?

Who thought applying real value definite integral to contour integral firstly? Example $$ \int_{0}^{\infty} \frac{\sin{(x)}}{x} dx $$ $$ \int_{0}^{2\pi} \log{(\sin{(x)})} dx $$
3
votes
1answer
167 views

How did Bernoulli approximate $e$?

Researching on the internet, it is easy to find that Bernoulli was the first to give a one-digit approximation for $e$ (specifically, $2.5<e<3$). But, I cannot find any source describing ...
3
votes
1answer
78 views

What field of mathematics does one first get introduced to non-elementary functions?

Knowing not much else other than basic linear algebra, single-variable and multivariable calculus, I would like to expand my mathematical knowledge . I've always found non-elementary functions, such ...
2
votes
1answer
75 views

Why is it called a 'cofactor', and is there some intuition or geometric interpretation?

My hope is that understanding the reason why things are named the way they are in mathematics will help aid in developing mathematical maturity and intuition. Often things are named, and then explain ...
1
vote
1answer
172 views

How did Guillaume de l'Hôpital “devise” his rule?

I saw on Wikipedia, the proof of general case of L'Hopital's rule was given by "Taylor, 1952". But L'Hopital was born in 1661, then how he came to know about this "rule", and if he just conjectured ...
0
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0answers
54 views

Grothendiek and singular points

My question relates to the following thread I opened some weeks ago: A question regarding Grothendieck , topos and (adelic??) points Specifically, consider this paragraph: At 1:14:30 and after, ...
15
votes
2answers
2k views

Who is the “father of number theory”?

I noticed that some sources state Fermat as the father of modern number theory while others say Gauss. I am trying to start a paper on the history of number theory for a presentation, but I cannot ...
7
votes
1answer
246 views

What did Lagrange, Euler, Gauss etc. learn in order to know what they knew?

What did the great mathematician, like Cauchy, Lagrange, Euler and Gauss, learn in order to know what they knew? It seems that they were extremely good in the most basic rules/structures/issues of ...
101
votes
15answers
14k views

Why do both sine and cosine exist?

Cosine is just a change in the argument of sine, and vice versa. $$\sin(x+\pi/2)=\cos(x)$$ $$\cos(x-\pi/2)=\sin(x)$$ So why do we have both of them? Do they both exist simply for convenience in ...
4
votes
2answers
254 views

How do we call a pair of sets between which there is a bijection that need not have additional property?

Let $A,B$ be sets and let $f: A \to B$. Then we say that $A,B$ are isomorphic under $f$ if $f$ is a linear function that maps $A$ onto $B$ in a one-to-one manner; that $A,B$ are homeomorphic under $f$ ...
5
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0answers
117 views

Original proof of Taylor's theorem

There are numerous proofs for Taylor's theorem, but What's the original proof for Taylor's theorem (by Taylor?)? In Wikipedia it says: Taylor's theorem is named after the mathematician Brook ...
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1answer
399 views

Origin of the word Mathematics and in which condition it did come of?

From which word, Mathematics has come from? Just tried to know. Help me out to know that. Also let me know the literature-change of this term.
4
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1answer
116 views

Is there an English version of Johann Bernoulli's integral calculus lectures?

The name of lectures of integral calculus written by Johann or Jeans Bernoulli (he is called by both names as far as I know) might be " lecciones mathematicæ de calculo integral"; I must mention that, ...