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what is the origin of the proof via peaks?

What is the history of the proof of the existence of a monotone subsequence via peaks as found for example here as well as in problem 6, page 4 here (where they are called "giants" instead of "peaks")?...
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45 views

Deriving the wave equation in 3 dimensions and the history of it

I'm trying to find how the wave equation was derived in 3 dimensions. Surprisingly, there isn't much information available on this apart from wikipedia of all places https://en.wikipedia.org/wiki/...
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On non-modular lattices and orto-modularity

I would like to have a definition for non-modular lattices which clearly sets them appart from their modular counterparts, thereby focusing on their main distinctive feature. Besides, I would be very ...
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28 views

On a curve every point of which is a point of ramification

The title of my post is the same as the title of a known article written by Sierpinski where he introduced its famous triangle. In the book Handbook of the history of general topology by Lowen said ...
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41 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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42 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 \frac{dn}{\...
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121 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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66 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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58 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 ...
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68 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. ...
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66 views

Generlization of Riesz Representation Theorem until now

I am writing on Riesz Representation Theorem. How this theorem was motivated and what further generalizations were done while it was on its way to where it is now. Starting from the begining, ...
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44 views

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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52 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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133 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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1answer
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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69 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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62 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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130 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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67 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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93 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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110 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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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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77 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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130 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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52 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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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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92 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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1answer
201 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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192 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 ...