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

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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
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 ...
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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 ...
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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 ...
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1answer
69 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?
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1answer
110 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 ...
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2answers
906 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 ...
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0answers
40 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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1answer
70 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 ...
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0answers
40 views

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

Who thought applying real value definite integral to contour integral firstly? Example $$ \int_{0}^{\infty} \frac{\sin{(x)}}{x} dx $$ $$ \int_{0}^{2\pi} \log{(\sin{(x)})} dx $$
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1answer
146 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 ...
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1answer
73 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 ...
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1answer
56 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 ...
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1answer
157 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
53 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, ...
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2answers
1k 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 ...
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1answer
209 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 ...
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15answers
13k 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 ...
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2answers
243 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
89 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
268 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
81 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
80 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
49 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 ...
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2answers
110 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. ...
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2answers
224 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 ...
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3answers
130 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.
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0answers
26 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
163 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
38 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 ...
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4answers
137 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
109 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
58 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
87 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
137 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
61 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? ...
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2answers
43 views

Logarithms and Taylor Series

Before Log Tables, how were they able to compute expressions such as $2^{2.221}$? I understand they could take a Taylor expansion of $\frac{1}{x}$, but how were they able to condense the expansion ...
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0answers
84 views

Demonstrative geometry around the world and its significance.

This is not exactly a mathematical question. I am from Pakistan; and over here students are taught a subject 'demonstrative geometry' (as a part of mathematics) from secondary level education. ...
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3answers
108 views

What is a space? Where does the word come from?

I was asked the question: "What is a space?". Wikipedia says it is a set with added structure, but then why don't we call a group a space, or a ring? The Princeton companion doesn't even have an entry ...
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1answer
607 views

The word “integral” in calculus unrelated to “integral” / “integer” in algebra?

I think that the word integral in calculus is nothing to do with integer or integer numbers. But why is integral is chosen for integration? In algebra, integral means related to integers, and this is ...
0
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3answers
207 views

Why do mathematicians use $\oplus$ instead of $+$?

What is the historical reason for using $\oplus$ instead of $+$ to denote operations that are generally thought of as addition? Similarly, why is $\otimes$ used instead of $\times$ (or just $\cdot$) ...
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2answers
87 views

A post for the rejected — influential papers that had trouble getting published [closed]

Having your paper rejected feels a lot like getting dumped. But while there are plenty of good ways to alleviate the pain of romantic rejection, there seem to be few outlets to alleviate intellectual ...
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0answers
115 views

What was the original motivation for matrix multiplication? [duplicate]

When I took linear algebra class in my freshman year, the multiplication operation for matrices was defined without any apparent motivation. Given an $m$-times-$n$ matrix $A$ and an $n$-times-$p$ ...
5
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1answer
109 views

Could Euclid have proven that multiplication of real numbers distributes over addition?

In Euclid's day, the modern notion of real number did not exist; Euclid did not believe that the length of a line segment was a quantity measurable by number. But he did think it made sense to talk ...
7
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1answer
149 views

Could Euclid have proven that real number multiplication is commutative?

In Euclid's day, the modern notion of real number did not exist; Euclid did not believe that the length of a line segment was a quantity measurable by number. But he did think it made sense to talk ...
2
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1answer
72 views

Books and sources concerning the mathematics of Leibniz and the feud with Newton

I am trying to find books and other sources concerning the mathematical history of Leibniz, including the controversy due to the independent discoveries of calculus by both Newton and Leibniz. I can't ...
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2answers
63 views

a maximum of 128 independent rules

Can anyone tell me what these 128 rules are in the following paragraph? Are they the rules dominating Conway's automaton or other kind of rules like the whole universe rules that could be summarized ...
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0answers
62 views

Where does the term “Ring” come from in Algebra? [duplicate]

Group and Field make some sense to me, but I can't see why the structures that are closed under two binary operations would indicate "ring".
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2answers
77 views

Impact factor Vs Rating of Maths journals

I have heard of a Maths journal having $A^*$, $A$, $B$ and $C$ rating, and have also heard of impact factor of $1.3$, $0.6, 0.33$, et-cetera. Can someone please clarify me on what these two actually ...