Use this tag for questions concerning history of mathematics, historical primacies of results, and evolution of terminology, symbols, and notations. Consider if History of Science and Mathematics Stack Exchange is a better place to ask your question.

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Lasker-Noether Theorem and Kummer-Dedekind

I would like to know about the relations between Ernst Kummer's invention of complex ideal numbers (and Dedekind's development of them into what is now called ideals) regarding the unique ...
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1answer
51 views

Why did mathematicians name a functional that assigns number to function as a “distribution”?

Why did people name it as a "distribution"? I don't see the reason. My instructor told us don't bother with this strange name, but I guess maybe I will have a better understanding if I know the ...
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120 views

History of differential and integral calculus

My math teacher told me that the research in differential calculus and integral calculus began on two separate tracks.Apparently people didn't know there was a relation between the two until some ...
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47 views

Kronecker's 1870 paper on finite Abelian Groups??

Could anyone please provide me with the exact bibliographic reference for Kronecker's 1870 work on finite Abelian groups? If you could provide me with his exact formulation (or even with a acanned ...
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67 views

Notations for interior product

There are two symbols in the Unicode "Supplementary Mathematical Operators" range whose names intrigue me 2A3C: INTERIOR PRODUCT: ⨼ (like $\lnot$ upside down) 2A3D: RIGHTHAND INTERIOR PRODUCT: ⨽ (...
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123 views

What really is inductive reasoning?

I am looking for concrete information on "induction" in the old sense of the word. Now it is used to refer to proof by "mathematical induction"; however, I am aware that it also means inductive ...
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64 views

History of Dihedral Groups?

I'm trying to write a brief historical outline for a project concerning Dihedral Groups, but It has been to hard for me to find information about the first time these groups appeared on literature. If ...
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52 views

Apolonius' definition of a parabola

I need help understanding what apollnius did when he defined a parabola and what he proved. "First let the diameter PM of the section be parallel to one of the sides of the axial triangle as AC, and ...
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82 views

Chi-square or chi-squared?

The $\chi^2$ test/distribution is referred to as either "chi-square" (more frequently) or else "chi-squared" (less frequently). What is the history behind the name? Footnote 2 in this paper by Peter ...
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55 views

In which years in the prefaces to mathematical books thanks to secretaries for typing text books have disappeared?

In which years in the prefaces to mathematical books thanks to secretaries for typing text books have disappeared? Just interesting. When latex won?
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37 views

A finite generalization of differentials?

So basically, in trying to make sense of a certain math aspect of a thermodynamic problem (how to manipulate differentials) I end up reading this http://www.tau.ac.il/~corry/teaching/toldot/download/...
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41 views

Did Hamilton have a proof that $\mathbb{R}^3$ is cannot be turned into an $\mathbb{R}$-division algebra?

It is well-known that $\mathbb{R}^n$ cannot be made into a non-commutative $\mathbb{R}$-division algebra if $n\ne 4$. My question is whether there is a (slick) proof of this for $n=3$; in particular, ...
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42 views

Different proofs for two squares theorem for primes

There is a proof of two squares theorem for primes of form $4k+1$ from quadratic forms and there is a proof from Bolyai using Gaussian integers. I am reasonably sure such a nice simple statement has ...
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41 views

The name of $fusc$ (Calkin-Wilf sequence)

I was just wondering where $fusc$ got its name (where $fusc(2n) = fusc(n), fusc(2n + 1) = fusc(n) + fusc(n + 1)$, seeds: $fusc(0) = 0, fusc(1) = 1$). The function is of some importance in the Calkin-...
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50 views

Are there any functions which were proposed as elementary by mathematicians but not considered elementary now?

Are there any functions which were proposed by various mathematicians to be included in the set of elementary functions because of their properties but not considered elementary as of now?
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91 views

In Whitehead & Russell's PM, if $P$ is an infinite well-ordered series, can $P$ have a last term?

If I'm not mistaken, $B‘\overset{\smile}{P}$ is the last term of $P$. If it does not exist, there is no need to put ~$(B‘\overset{\smile}{P}) \in C‘∇‘P $ in the hypothesis. Chances are I missed ...
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109 views

Hard-to-put-together but easy-to-prove results

What are the most important examples of theorems and definitions which are post factum obvious, i.e., hard to put together but easy to understand and use (and prove, in the case of theorems) once you ...
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1answer
44 views

In Whitehead&Russell's PM, What is $\max_p$'s converse domain?

Here is the definition of upper limit. If I'm not mistaken, $\max_P$'s converse domain is the universal set $V$. The definition appears to be limiting the converse domain of $\operatorname{seq}_P$ ...
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47 views

first example of backwards induction?

In Mathematics Magazine 28(1954/55), 21-46, Richard Bellman presents a proof for the theorem which says that the geometric mean of $n$ numbers is always not greater than the arithmetic mean: the proof ...
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62 views

recommend me some texts on the history of the non-western mathematics

I would like to self study the detailed history of the non-western mathematics. I have started the literature of Barton (7th Ed.) but it primarily concentrated on Western and American Mathematics. ...
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56 views

In Whitehead and Russell's PM, are homogenous relations the only ones that have relation numbers?

Given the definition of ordinal similarity: ✳151.01 $P \overline{smor} Q = \hat{S}\{ S\in 1\rightarrow 1. C‘Q=ConverseD‘S. P=S^;Q\}$ Df. $Q$ has to be homogeneous, otherwise $C‘Q$ is meaningless. ...
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70 views

Why are frames called “frames”?

Definition: A frame $F$ is a suplattice such that for any $x_{i}, y\in F$ (for $i\in I$, $I$ a set), we have $$y\wedge\left(\bigvee_{i\in I}x_i\right)=\bigvee_{i\in I}(y\wedge x_i).$$ Why are ...
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75 views

Historical study of dynamical system

I am currently doing a historical study on my school project 'study of ODE' which slowly shift to the study of dynamical system as I am interested in pursuing my study of ode from linear system, phase ...
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76 views

How did Fourier find the formula for the fourier series coefficients?

The modern proof use the dot product but did he use that ?
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53 views

Indecomposable groups vs. indecomposable objects

An object $X$ in a category $\cal C$ with an initial object is called indecomposable if $X$ is not the initial object and $X$ is not isomorphic to a coproduct of two noninitial objects. A group $G$ ...
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129 views

Who invented the standard construction of finite fields (and field extensions)?

The title says it all, but just to be clear I mean the construction of taking $k[x]$ modulo an irreducible polynomial of suitable degree. Was it an open problem for any considerable amount of time, ...
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56 views

The “enabler” of Maxwell's equations

Is it possible to point to a specific development in mathematics that allowed Maxwell's equations to happen? Similarly to Newton's laws of physics that depended on the invention of calculus? And ...
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51 views

pierre simon laplace and his knowledge of the (Laplacian) matrices

so as we all know, there is a graph matrix called the Laplacian that is used in some eigenvalue/eigenvector/graph theory/spectral theory problems. i'm wondering if the name of this matrix is ...
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47 views

Is there a source linking Robinson's work in wing theory with his theory of infinitesimals?

Abraham Robinson worked in applied mathematics for several decades. MathSciNet lists 12 articles by Robinson in wing theory. His production included the book Robinson, A.; Laurmann, J. A. Wing theory....
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57 views

Historical question about irrationals.

Which beliefs of the Pythagoreans were invalidated by the discovery of irrationals?
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1answer
133 views

Probability of World Series - Using Pascal and Fermat “Problem of Points”

This is a question I have for a history of math class, but I can't figure it out. I need to use the three method that Pascal and Fermat used on their problem of points, and it doesn't seem to work ...
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32 views

Pascals first method

So pascals first method was to first solve a simple problem,this was before the pascal triangle. This is in relation to De Meres problem: Each player stakes $32$ pistoles. One player has 1 round ...
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89 views

Weierstrass and Borel summation

In the Wikipedia article on Borel summation, there is the following quote attributed to Gösta Mittag-Leffler: Borel, then an unknown young man, discovered that his summation method gave the '...
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199 views

Historical reason to define a matrix vector product the way it is

What is the reason why we defined a matrix vector product (a transformation) this way: $$\begin{pmatrix} a_1 & a_2 \\ a_3 & a_4 \\ \end{pmatrix}\cdot ...
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146 views

Mathematical foundation crisis and the RSA

I am currently in my last year of high school and I am writing a report on cryptography from a idea historical and mathematical perspective. I am including a few of the subjects: Cantor's diagonal ...
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190 views

What are the historical roots of cryptarithmetic?

A typical cryptarithmetic is: S E N D 9 5 6 7 + M O R E + 1 0 8 5 ----------- ----------- = M O N E Y = 1 0 6 5 2 On the internet it is said: "The invention of ...
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71 views

what is a connection between two simple yet important economics and math formula: elasticity

what makes it interesing to define them in mathematics? what is a connection between two simple yet important economics and math formula: elasticity? Something interesting to read: http://en....
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57 views

Motivation for Kervaire's seminal paper

Let DIFF denote the category of smooth manifolds, TOP the category of topological manifolds and PL the category of piecewise linear manifolds. In Kervaire 1960 it is shown for the first time that ...
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68 views

History of ' low-dimensional geometry '

I want to have a brief history about the low-dimensional manifolds and geometric structures on manifolds specially on low-dimensional manifolds .where I can read about thus ?
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83 views

How were trigonometrical functions and its inverses discovered?

Imagine you just did a circle. Some functions are just definitions, like $\sin$,$\cos$ and $\tan$ but how do you derive a formula to get the $\sin$ from an angle in radians (maybe by Taylor series, ...
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114 views

Ptolemy's Theorem corollary: Chord(2\alpha+2\beta)=BC and more.

So I've got this problem that is making me go a little insane, I'm not sure if I'm just missing simple identities or what. I'll put the problem on imgur, since it has diagrams. http://i.imgur.com/...
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106 views

How was the isoperimetric inequality formulated?

I'm tyring to understand how the isoperimetric inequality came into existence. It seems like finding the region which yields maximum area when enclosed by a curve of fixed length is an old problem. ...
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39 views

History: continuously differentiable groups over the real numbers

Continuously differentiable groups over the real numbers are all isomorphic to addition, as is well-known, but who proved it and when?
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135 views

Etymology of algebra (as k-algebra)?

Why algebra (over a field) is called "algebra?" (My random guess is that it's a back-formation of some algebras, chopping adjectives from say Lie algebra or Clifford algebra, etc.) And when was that ...
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160 views

History of calculus-based optimization

I would like to know: - who started with calculus-based optimization problems and when it was, - if there is a book focusing on history of ellipses/ conic sections - if someone ever tried to ...
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250 views

Who found this example of continuous nowhere differentiable function?

In many books from mathematical analysis (for example in Rudin) is presented the following example of continuous nowhere differentiable function: $$f(x)=\sum_{n=1}^\infty (\frac{3}{4})^n g(4^n x) \...
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159 views

History of operator precendence

I have seen a lot of debates over operator precedence but what is the history of operator precedence and how it evolved over time? Why multiplication precedes addition; Is it just to be definitive? ...
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96 views

Historical relation between computer science and the theory of dynamical systems

I wonder if there is any historical relation between the fields of Dynamical systems (and related fields such as Optimal control) and (theoretical) Computer science. The reason for which I ask this ...
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131 views

Reference: Wittgenstein teaching mathematics

Can anyone give me any reference concerning L.Wittgenstein teaching school kids mathematics? I have been wondering what kind of mathematics he taught and how he lectured the material.
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114 views

Opinions attributed to Gauss

In this article, Armand Borel writes the following: [...] In fact, during the next quarter century, we experienced a tremendous development of pure mathematics, bringing solutions of one ...