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

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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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132 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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88 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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66 views

Who made now part of the problem?

Who came up with the meme of putting the current year as a four digit number into exercise problems? Is there a known first historical account?
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1answer
198 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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143 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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186 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: ...
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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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66 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. ...
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104 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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157 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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158 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 ...
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160 views

What was Cayley's formula for the number of invariants? (Lost Formula!?)

I need to find Cayley's formula for the number of linearly independent invariants of homogenous polynomials. This is a combinatorial formula. He is believed to have discovered it in 1854. ...
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1answer
186 views

Expanding squares and simplification of equations

as i'm reading a paper "An Underdetermined Linear System for GPS" By Dan Kalman i understand the paper but when i traced the equations there's something i don't understand ,may be my mathematics is ...
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121 views

When was the term 'ramification' first used in math literature?

In my studies so far, I have had the word 'ramification' come up in Algebraic Number Theory and Complex Analysis. The Wikipedia article tells me that 'ramification' is also used in some other fields. ...
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1answer
56 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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169 views

Galois false solution to the quintic equation

I am looking for the false solution Galois gave to the quintic equation before discovering group theory.
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3answers
223 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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4answers
921 views

What is the definition of a positive integer?

I am reading the book "The Number-System of Algebra (2nd edition)". At the starting of page-4 the author writes: A positive integer is a symbol for the number of things in a group of distinct ...
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2answers
539 views

Mathematics and slavery [closed]

I think that ancient Greek mathematics is a miracle. Think about Euclid. Developing mathematical arguments from a small set of axioms is incredibly modern. And their influence on modern mathematics is ...
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1answer
456 views

Resurrection of my Tamagawa numbers Question, to understand the Formulation of BSD

My previous question was closed very badly for asking the broad and deep things, so I now understand the consequences of asking such questions, so I refrain from asking such questions, so this is not ...
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2answers
133 views

What is the poetry of mathematics? [closed]

In computer science it's often noted, said or agreed on that algorithms are the poetry of computer science. What is considered the poetry of mathematics? Is it statistics? If there is something agreed ...
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2answers
148 views

How to calculate 3x7 by using logarithm?

This is a story about Newton I read once when I was a child. Now that book is lost and I can only tell you what I remember. When Newton was young, he had been already famous in curiosity and ...
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2answers
644 views

Is it to the students' advantage to learn the language of infinitesimals? [closed]

A colleague of mine asked an interesting question reproduced below with his permission. It is reasonable to ask whether it is to the students' advantage to learn the language of infinitesimals - ...
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5answers
81 views

Can we prove that plumb line is vertical to ground?

Using a plumb line to make sure a wall is vertical for instance, is as far as I know one of the most primary tools in the sense that the very-very ancient builders used it as an instrument. I was ...
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2answers
162 views

Does axiom of foundation/regularity protect against Russell-like paradoxes?

In ZF set theory the axiom of regularity (also called axiom of foundation) says that: In all nonempty sets x there is an element y such that x∩y=∅ As I been told that the intention of the axiom ...
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111 views

Why do some sources call calculus, “the calculus”?

No need to cite specific sources since I think it's a fairly common thing to see. What's up with that? Thank you Edit: I've seen it in several places. Here's where I'm currently looking at it at: ...
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65 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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2answers
87 views

What is the meaning of calculating sine of a number?

When we calculate sine/cos/tan etc. of a number what exactly are we doing in terms of elementary mathematical concept, please try to explain in an intuitive and theoretical manner and as much as ...
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1answer
176 views

Johann Bernoulli did not fully understand logarithms?

This wikipedia article makes the claim: "Bernoulli's correspondence with Euler (who also knew the above equation) shows that Bernoulli did not fully understand logarithms." This is found under ...
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131 views

Is there a analysis conjecture proven to be unprovable or a proof is non-existence?

Is there a analysis conjecture proven to be unprovable or a proof is non-existence? So, is it once a math history milestone
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1answer
53 views

What is the origin of the name Hermitian and Unitary matrix?

A matrix $H$ is Hermitian if $H ^\dagger = H$. A matrix $U$ is Unitary if $U^\dagger=U^{-1}$. My question is: Why do we name matrices of such properties Hermitian and Unitary? These names are ...
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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 ...
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232 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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2answers
389 views

What comes after seconds?

Angles can be measured in different ways. For example, one can measure angles in degrees/minutes/seconds. So $1^\circ$ is divded into $60$ min. and $1$ min is divided into $60$ sec. That way a tenth ...
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2answers
361 views

The word “times” for multiplication…? [closed]

The word "times" for multiplication operation which is quite touching to the concept of time (feeling time this way 0*1=0). When was introduced that term? Did any other language have the kind of term ...
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1answer
56 views

Name for LDC: Lebesgue?

Is there also a name associated to the Lebesgue dominated convergence theorem like Beppo-Levi or Fatou? Would Lebesgue be reasonable? Who did originally prove it?
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89 views

Reference on Infinite Dimensional Manifold

I am studying manifold. For comprehension, I read the site http://en.wikipedia.org/wiki/Manifold, and there is some information about infinite dimensional manifold. Now I have two questions or ...
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2answers
141 views

General questions about theorems and laws

I have doubts about the construction of mathematical elements. There are proofs, that are proven using other theorems (corollaries) and/or axioms or definitions, such as Fermat's Last Theorem, the ...
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3answers
249 views

Resource request: history of and interconnections between math and physics

Reading this article I became curious to learn more of (- study more thoroughly and *seriously*$^{\star}$-) the topic. Is / are there some good references - either papers, books and/or other ...