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64 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
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2answers
111 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
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 ...
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0answers
63 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
49 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
61 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
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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
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1answer
252 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
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1answer
102 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
111 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
25 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
30 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
198 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
78 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 ...
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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 ...
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1answer
48 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
76 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
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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
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1answer
143 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 ...
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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 ...
12
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2answers
941 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
49 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
164 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
73 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
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1answer
171 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 ...
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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
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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
242 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 ...
100
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
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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 $f$ ...
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0answers
114 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
384 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
112 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, ...
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0answers
98 views

A Mathematical Tour of Budapest?

(This might be a better fit at the Travel site. If so, let me know and I'll flag it to have it migrated.) I'm planning on taking a brief trip to Budapest soon. Many hugely influential mathematicians ...
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2answers
61 views

Orthogonality properties in Newton's calculus.

In a lecture notes, there is written: Isaac Newton uses orthogonality properties to establish the principles of calculus. The definitions of derivative and integral for this author is based on ...
2
votes
2answers
138 views

L'Hôpital or L'Hospital? [duplicate]

This may be a stupid question but I just want clarification about the use of the name of this rule. Well, most of the time what I see is L'Hospital's Rule, like in Baby Rudin and many other places. ...
2
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2answers
262 views

Why there is no “Nobel Prize” in mathematics however it is one of the most important fields in sciences in the side of research?

Mathematics is really a field of inventions and research where we find interesting problems some of which we can solve and others which remain open. I'm sorry to ask this question because I see it ...
3
votes
3answers
132 views

Is there a name for set of numbers $\mathbb{Q} + i\mathbb{Q}$

Just out of curiosity is there a standard name for a set of numbers $\mathbb{Q} + i\mathbb{Q}$ where $\mathbb{Q}$ stands for set of rational numbers, $i$ your complex number.
3
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0answers
33 views

What was Gauss' 2nd Factorization Method?

Reading Jean-Luc Chabert's A History of Algorithms, I learned that Gauss, prompted by the poor state-of-the-art, designed two distinct methods for fast integer factorization. Chabert's book discusses ...
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3answers
221 views

how did Cardano obtain three solutions for cubic?

So, if I am not mistaken Complex numbers were discovered after Cardano's method. But from Cardano's Method on Wikipedia, it says to get the three solutions, we should use the root of unity. In that ...
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0answers
41 views

Gauss and $\int \frac{dn}{\log n}$

In [1], page 2, Edwards shows a tabuled table by Gauss, for $x$ (distinct and uniformly distributed values from $5\cdot 10^5$ to $3\cdot 10^6$), the count of primes$<x$, the symbol $\int \frac{dn}{\...
3
votes
4answers
142 views

Is there a purpose behind a function?

As I understand it, a function is a relation between two sets of numbers where as for every input value there is only assigned one output. Or for every $x$ there is only one $y$. What I don't ...
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0answers
119 views

A question regarding Grothendieck , topos and (adelic??) points

I am having a look at this conference by Bertrand Toen about Grothendieck's work. At 1:14:30 and after, Toen presents the new objects emerging from topos theory in algebraic geometry. He takes the ...
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0answers
63 views

Hieroglyphic from Herschel to Babbage?

John Herschel sent a letter to Charles Babbage in which he included this hieroglyphic with the message "Interpret it, it contains a great discovery". Personally I have no clue what it could mean. ...
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2answers
95 views

Historical Approach to $\lim_{x \to 0} \frac{e^{\alpha x} - e^{\beta x}}{x}$, without L'Hospital's Rule

I encountered this problem, amongst others, in the slightly older Calculus textbook Piskunov's Differential and Integral Calculus when I was working with a student: Calculate the limit $$ \lim_{x \to ...
5
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1answer
146 views

Are there papers or books that explain why Bernhard Riemann believed that his hypothesis is true?

I would like to know what are the mathematical reasons for which Bernhard Riemann believed that his hypothesis is true, and I would like to know if those mathematical reasons were cited in his ...
3
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1answer
64 views

Emil Artin on visualization of matrices

Someone called my attention to the fact that Emil Artin made very important remarks on the visual representation of matrices in some of his books. Could anyone tell me which precise book that is? ...