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

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1answer
66 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.
0
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1answer
214 views

Who is the inventor of slovin's formula?

And how can I use it in the population contain 10000 people with confidence interval 95%? Also, why there is only a few information about the inventor in the web?
5
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1answer
992 views

Is there any English version of Récoltes et Semailles?

I felt like my question isn't appropriate for MO, so I though maybe I should post it here. I want to read Alexander Grothendieck's "Récoltes et Semailles", but I don't know any French. I can easily ...
38
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14answers
4k views

Examples of famous problems resolved easily

Have there been examples of seemingly long standing hard problems, answered quite easily possibly with tools existing at the time the problems were made? More modern examples would be nice. An example ...
0
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2answers
39 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 ...
-5
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1answer
96 views

Fields medalists who didn't study mathematics in college or university [closed]

I would like to know Fields medalists who didn't study mathematics in college or university if any. EDIT The question was put on hold as primarily opinion based. I guess they think "first rate ...
4
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1answer
51 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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6answers
3k views

Why don't we use base 6 or 11?

Another question on this site asks why we have chosen our number system to be decimal base 10. There are others asking basically the same thing as well. I'm not really satisfied with any of the ...
11
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3answers
2k views

Why has the Perfect cuboid problem not been solved yet?

Why hasn't Perfect Cuboid Problem been solved yet, whereas (possibly) more nontrivial ones such as FLT and Sphere packing have been solved? I understand that calling some problems more nontrivial ...
1
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0answers
45 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 ...
4
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1answer
79 views

Origin of the Integral (Theory Behind It - How it came about)?

How exactly was the integral derived? Like similarly to how the difference quotient explains where the derivative came from, what can we use to explain the origins of the integral? Like how does ...
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3answers
89 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 ...
2
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2answers
65 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. ...
162
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16answers
11k views

In the history of mathematics, has there ever been a mistake?

I was just wondering whether or not there have been mistakes in mathematics. Not a conjecture that ended up being false, but a theorem which had a proof that was accepted for a nontrivial amount of ...
1
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1answer
136 views

What is the name of this proof of, “$\sqrt{2}$ is irrational”?

Usually the proof of $\sqrt2$ is irrational is done by contradiction(e.g. here), but I found another similar but short proof in the book "Beginning Algebra for College Students" by Lloyd Lincoln ...
6
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2answers
771 views

How exactly do you measure circumference or diameter?

I am absolutely confused about trying to calculate circumference. And I do not mean using the math formula, I mean back in old days when people had very primitive tools, and had to make the ...
0
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2answers
204 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
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3answers
68 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
21 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 ...
16
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1answer
262 views

Why would I define Alexander–Spanier cohomology?

I think I can motivate the definitions of simplicial, singular, de Rham, Čech, and sheaf (co)homology, more or less. I might want to understand bordism, and start by trying to understand ...
3
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4answers
119 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 ...
1
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0answers
33 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 ...
12
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2answers
354 views

Hao Wang's $\mathfrak S$ system/$\Sigma$ system: a “transfinite type” theory that avoids the Goedel's theorems.

Long ago, while I was reading a book ($*$) about the various way to build set theories (Zermelo-Freankel, Von Neumann–Bernays–Gödel, and type theories), I read about a variant of type theory with ...
14
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1answer
547 views

successful absurd formalities

Has anyone published in print or on a web site or elsewhere a compilation of successful illogical formal arguments? By those I mean arguments that follow a form in disregard of the legality of its ...
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0answers
77 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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1answer
42 views

How Leibniz invented the Binary System?

Do you know which reasoning and observations made Leibniz invent the Binary system ? Some say that he was inspired by Chinese mathematicians do we have any record of how he came with this idea ?
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2answers
68 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 ...
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0answers
29 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. ...
9
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1answer
144 views

Is there any connection between the symbol $\supset$ when it means implication and its meaning as superset? [duplicate]

A rather old-fashioned symbol for logical implication is $\supset$ (see list of logic symbols). For example $p \supset q$ means $p \implies q$ or $p \rightarrow q$ in more recent notations. Is there ...
26
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1answer
396 views

To what extent were mathematicians in previous centuries aware of the lack of rigour in their methods?

By modern standards, much of pre-modern mathematics isn't rigorous. Famous examples include Euler's solution to the Basel problem or literally anything involving sets before Cantor and Russel came ...
9
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1answer
333 views

Exactly who popularized the modern definition of domain and codomain of functions?

In Whitehead and Russell's Principia, domain is the referents of relation; converse domain is the relata. Modern function in mathematics is just one special case of relation whose referent is unique ...
3
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1answer
52 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
262 views

Why the SVD is named so…

The SVD stands for Singular Value Decomposition. After decomposing a data matrix $\mathbf X$ using SVD, it results in three matrices, two matrices with the singular vectors $\mathbf U$ and $\mathbf ...
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2answers
38 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 ...
68
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11answers
13k views

Is zero odd or even?

Some books say even numbers start from two but if you consider the number line concept, I think zero should be even because it is in between -1 and +1 (i.e in between 2 odd numbers). What is the real ...
3
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2answers
68 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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0answers
37 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. ...
10
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1answer
531 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 ...
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1answer
54 views

Inverse functions multivalued or not?

The square root of $y$ is usually defined as the positive solution $x$ to $y=x^2$, so the negative variant is not considered. In the same way, the inverse cosinus and sinus give the solution on ...
0
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3answers
173 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 $\cdot$) ...
4
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0answers
69 views

First appearance of modern definition of a group [migrated]

What is the first appearance in print of the modern definition of an abstract group? To qualify, it should be a formal definition, contain the word "elements" (so Burnside's 1897 restriction to ...
18
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1answer
5k views

Strange old multiplication table

Today I read an article about chalk boards from 1917 discovered in an Oklahoma school. One of the chalkboards included the following curious image: (Oklahoma City Public Schools) The article ...
2
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2answers
66 views

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

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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1answer
94 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
121 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 ...
8
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0answers
99 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-$p$ ...
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2answers
58 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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1answer
37 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 ...
0
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1answer
115 views

Why are some branches of mathematics called 'theory' and others not?

We say: graph theory , group theory, number theory , set theory, what is definition of theory? We also say abstract algebra, real analysis, but why we do not say abstract algebra theory or real ...
2
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0answers
61 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".