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

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2answers
34 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 ...
67
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12answers
12k 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
61 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
32 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
514 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
158 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 ...
15
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1answer
206 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 ...
18
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1answer
4k 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
64 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 ...
5
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1answer
88 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
117 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
96 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-$p$ ...
0
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2answers
55 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 ...
1
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1answer
32 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
109 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".
2
votes
2answers
65 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 ...
6
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3answers
186 views

Why is the Gamma function off by 1 from the factorial? [duplicate]

Why didn't they define it as $$ \tilde \Gamma(x) = \int_0^\infty t^x e^{-t} \, dt ?$$ Then the definition would have two less characters than the standard definition of $\Gamma(x)$, and we would have ...
1
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0answers
54 views

Is our Arabic number system based on a geometric design counting corners? [duplicate]

The following writer asserts that our system of Arabic numerals is a geometric design where the number of corners corresponds to the number represented: My question is: Is our Arabic number system ...
3
votes
1answer
29 views

Does “data” in Cauchy data come before or after the coinage of data in computer science

Is the usage of data as in Cauchy data (i.e. initial conditions) borrowed or came before the usage of data in computer science and do both usages mean roughly the same thing (data ~ information)?
10
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1answer
169 views

Estimating the “size” of the mathematical research literature

The other day I was telling one of my friends that mathematics, as a living science, possesses quite an extensive research literature. How extensive then, she asked. Unfortunately, I didn't have ...
14
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2answers
2k views

Why is it called Sylvester's Law of Inertia?

By "Sylvester's Law of Inertia," I mean: http://en.wikipedia.org/wiki/Sylvester%27s_law_of_inertia How does the name "Law of Inertia" fit with the statement of the theorem? I guess it's from ...
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0answers
46 views

Proofs that relied on paradoxical sentences

Graham Priest's Logic of Paradox is a modification of classical logic where the principle of explosion does not hold, so that there are inconsistent theories which are not automatically trivial. ...
4
votes
1answer
63 views

History of inner products and texts on it?

Where does the inner product originate from, was it defined in term of the dual or was it defined from just two copies of the space? I.e $(*,*) : V \times V \rightarrow scalar $ or $(*,*) : V \times ...
1
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1answer
46 views

Solving quartic equation using substitution

We are learning a lot about the history of our famous mathematicians and this specific one is stumping me. They want us to solve a problem a specific way and I can't seem to figure out how to do it. ...
7
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0answers
323 views

Ramanujan and sum of four cubes

This is more a question on History than proof itself. About a decade ago, a college professor and a Math coach told us about this beautiful theorem: Every multiple of 6 can be written as a sum of ...
6
votes
5answers
1k views

Pythagorean theorem expressed without roots in an old Tamilian (Indian) statement

There's an old Tamil statement that predicts the hypotenuse of a right angle triangle to a reasonable level of accuracy considering it doesn't involve roots. This is how it goes: “Odum Neelam ...
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1answer
36 views

Euler and differentials

Did Euler have juxtaposition of $dx$ to $f'(x)$ to denote multiplication of a "very small quantity" to $f'(x)$ to obtain another "very small quantity" $dy$? This seems to imply that $\frac{dy}{dx}$ is ...
12
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1answer
2k views

Proof of Euler's Theorem without abstract algebra?

Every proof I've seen of Euler's Theorem (that $\gcd(a,m) = 1 \implies a^{\phi(m)} \equiv 1 \pmod m$) involves the fact that the units of $\mathbb{Z}/m\mathbb{Z}$ form a group of order $\phi(m)$. ...
3
votes
4answers
241 views

Theorems in number theory whose first proofs were long and difficult

What are the examples of important theorems of number theory that has been shown to have surprisingly simple proofs though their first demonstration wasn't at all simple enough. Now simple proof is an ...
7
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0answers
77 views

What primes were “pending” at the time of Wiles's proof of FLT?

I would like to know what instances of Fermat's Last Theorem were pending at the time of Wiles's proof. More specifically: what families of irregular primes had been discarded as possible ...
8
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0answers
65 views

Why do people prefer cosine to sine when speaking of harmonic oscillation?

In almost all of the physics textbooks I have ever read, the author will write the oscillating function as $$x(t)=\cos\left(\omega t+\phi\right)$$ My question is that, is there any practical or ...
1
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3answers
65 views

History of convolution

Let $f, g\in L^{1}(\mathbb R),$ we may define the convolution of $f$ and $g$ as follows: $f\ast g(x)= \int_{\mathbb R} f(x-y)g(y) dy, (x\in \mathbb R).$ It is well known that it can be defined on ...
0
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0answers
45 views

Difference between infinitesimal motion and finite motion

I was reading an article about back ground of Killing's work by Thomas Hawkins from Historia mathematica 1980.In it Hawkin's says that,Killing was trying to generalise all types of space ...
-1
votes
2answers
45 views

Question about the existence of points and lines.

Say we draw a point on a graph. If the point should not take up any area than how come we could see it. Say we graph $y=x^2$, we obviously could see it. However, because $y=x^2$ is a function made up ...
26
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6answers
2k views

Where did mathematicians learn how to do truth tables?

I'm trying to find out who invented truth-tables. Here is what I have so far. Leibniz 'invented' binary arithmetic, or at least is the first one recognized to have codified and explained a base 2 ...
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0answers
39 views

Why do we call a linear mapping “linear mapping”? [migrated]

What are the historical reasons that created the term "linear mapping"?
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2answers
163 views

Understanding the concepts of division and fractions

$\require{cancel}$ I'm having some issues regarding division so I will start by asking how this concept was developed throughout the ages: What was the first civilization to introduce the idea of ...
1
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3answers
118 views

Improving Mathmatical Skill [closed]

I am a student of computer science and engineering. My understanding of mathematics is not very good. I am getting very hard time studying subject that require a background on mathematics. So, I ...
8
votes
4answers
1k views

What's the idea behind the Taylor series?

I understand that they are viewed as approximations, but was that Taylor's original hope? Assuming that a function can be written as a power series seems to me to be a wild assumption, without some ...
2
votes
0answers
47 views

Alternative proof for the equality of two angles in an isosceles triangle.

From the answers of my previous question, I got an idea to prove equality of two angles in an isosceles triangle. In that question the equality of two angles in a right-angled-isosceles triangle was ...
5
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2answers
311 views

On the original Riemann-Roch theorem

I think Riemann first stated and proved a part of the Rieman-Roch theorem on a compact Riemann surface. And later Roch supplemented it. I wonder what the original statements of the R-R theorem by ...
-1
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1answer
91 views

How values of the constants are derived mathematically? [closed]

As said by Jan regarding constant value $\pi$ ,Imagine you have a circle and you are able to measure its circumference "c". Then, you can also find out what its diameter "d" is. When you divide ...
4
votes
1answer
53 views

Right modules Vs Left modules.

I have been reading Frobenius Algebras, Volume 1 By Andrzej Skowroński, Kunio Yamagata. On page 18 I came across the following paragraph, and I founded interesting, I will quote it and then ask my ...
3
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2answers
160 views

Why is the observation that proof of the Fundamental Theorem of Algebra requires some topology not tautological?

I have heard it mentioned as an interesting fact that the Fundamental Theorem of Algebra cannot be proven without some results from topology. I think I first heard this in my middle school math ...
3
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0answers
40 views

$\tau$-ists and the History of Radian Measure?

Recently, I have been reading about the $\tau$ vs $\pi$ debate. One of the arguments for $\tau$ was that $1\tau$ radian is the whole circle, thus fractions of $\tau$ correspond to the fractions of the ...
3
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0answers
51 views

When was the unit circle formalised

I am wondering about the origins of the Unit Circle. Of course it is part of trigonometry, which goes back many centuries. But since it uses Cartesian coordinates, it should be after Descartes. So, ...
2
votes
2answers
152 views

Is the decimal notation the “right” notation for arithmetic?

I am considering here the pre-decimal notations such as Roman numerals, Egyptian numerals etc. It seems reasonable that these must all be equivalent. And it seems that decimal notation (i.e. ...