Use this tag for questions concerning history of mathematics, historical primacies of results, and evolution of terminology, symbols, and notations.
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0answers
58 views
Personal results that came out of nowhere. [closed]
This is a modification of a question earlier today that asked
"Results that came out of nowhere".
The question asked if there were
any big mathematical results
that were surprises when they appeared.
...
1
vote
2answers
211 views
What is the Greek version of $\;\cal{quod~erat~demonstrandum}\;$?
What is the Greek version of "quod erat demonstrandum"?
Edit:
I found this in Bridge to Abstract Mathematics, but I was hoping to find something I could actually copy and paste into a tex file.
19
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3answers
2k views
Yitang Zhang: Prime Gaps
Has anybody read Yitang Zhang's paper on prime gaps? Wired reports "$70$ million" at most, but I was wondering if the number was actually more specific.
EDIT$^1$:
Are there any experts here who can ...
2
votes
1answer
85 views
How to calculate large exponents by hand?
How to calculate large exponents by hand like they did in ancient times?
Is it something to do with Prosthaphaeresis? for example calculate $2^{15}$.
3
votes
2answers
105 views
Why demonstrations are important in mathematics?
Good evening, I'm studying math and would like to know how important are mathematical proofs in the world and particularly in a school of mathematics
Thanks for your help
2
votes
0answers
57 views
History of Hindman's Theorem
At this blogpost about Hindman's Theorem, I read the following lines:
'I love the odd history so allow me to digress... etc. '
This sentence made me curious to know what this history looks ...
2
votes
2answers
64 views
Why the terms “unit” and “irreducible”?
I'm trying to understand why in a ring we choose the names unit to an invertible element and irreducible element in this definition
Maybe historical reasons?
For example, I suppose the second ...
0
votes
1answer
55 views
+200
Who was responsible for finding sufficient conditions for functional extrema?
In the calculus of variations, there is a well-known sufficient condition for weak functional extrema, involving conjugate points and the strengthened Legendre condition ($f_{y'y'} > 0$). Who was ...
2
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0answers
24 views
History of odds making in sports betting
Can anyone provide a reference to the history of odds making in sports betting? In many cases, certain odds are set and then adjusted as people make bets. However, I am having difficulty tracing the ...
-2
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0answers
67 views
Best mathematical proofs [closed]
For you wich are the best mathematical proofs?
I can remember Furstenberg´s proof of the infinitude of primes that really amaze me.
I am very interested in this kind of proof that really can ...
37
votes
6answers
4k views
Why do the French count so strangely?
Today I've heard a talk about division rules. The lecturer stated that base 12 has a lot of division rules and was therefore commonly used in trade.
English and German name their numbers like they ...
7
votes
2answers
209 views
Who was V. Viskovatov?
I'd be interested to learn some biographical detail about Vasilii Viskovatov, whose name is associated with a method for converting (a ratio of) power series to a "corresponding" continued fraction, ...
8
votes
0answers
113 views
Hao Wang's $\mathfrak S$ system: a “transfinite type” theory?
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 ...
3
votes
1answer
72 views
Historical definition of a group
Wikipedia states that van Dyck (1882) was the first to give the definition of a group in the modern way. Before this, what were some of the original axioms or conditions for groups? I mean, how were ...
32
votes
1answer
427 views
Unexpected approximations which have led to important mathematical discoveries
One often finds at MSE approximate numerology questions like
Prove $\log_{\frac{1}{4}} \frac{8}{7}> \log_{\frac{1}{5}} \frac{5}{4}$,
Prove $(\dfrac{2}{5})^{\frac{2}{5}}<\ln{2}$,
Comparing ...
4
votes
2answers
77 views
Is the validity of measuring area by approximation an assumption of calculus?
The assumption that if you subdivide an area into more and more sub intervals, the approximation gets better and better. Has this been formally proved, or is it just intuition? Thanks!
6
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0answers
184 views
A curious theorem by Peano
Let $f$ be defined on $[a,b]$ and there differentiable.
Show that for every $ \epsilon>0 $ there exists a partition $\, a=a_0<a_1<...<a_n=b \,$ of $ \,[a,b] \,$ so that $$\left|\frac ...
33
votes
3answers
687 views
What are examples of unexpected algebraic numbers of high degree occured in some math problems?
Recently I asked a question about a possible transcendence of the number ...
9
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2answers
50 views
Origin of well-ordering proof of uniqueness in the FToArithmetic
In the Appendix to Ivan Niven's book "Numbers: Rational and Irrational", he proves the Fundamental Theorem of Arithmetic (FToA) without using Euclid's Lemma that if a prime divides a product, then it ...
4
votes
1answer
81 views
The manuscript Summa Logicae (William of Ockham)
The Summa Logicae (Latin, in English it's the Sum of Logic) is a textbook on logic by William of Ockham. There are articles about the Summa Logicae in Wikipedia and in Logicmuseum.
It was published ...
5
votes
1answer
108 views
How was the normal distribution derived?
Abraham de Moivre, when he came up with this formula, had to assure that the points of inflection were exactly one standard deviation away from the center, and so that it was bell-shaped, as well as ...
4
votes
3answers
74 views
A proof for this series?
The summation, $$\sum_{i=1}i^2=n(n+1)(2n+1)/6$$ However, how could you prove this? All of the proofs I've seen already assume knowledge of the formula, but how do you prove this without first knowing ...
1
vote
0answers
43 views
Is Risch's algorithm powerful enough to determine any integral of a function have a closed form or not?
Is Risch's algorithm powerful enough to determine any integral of a function have a closed form or not?
Is there a historic piece of reference that support your answer?
...
1
vote
3answers
159 views
How did Euler and Bernoulli prove this limit?
Prove that the lim as x approaches infinity of $(1+1/x)^x$ exists, and prove this without assuming any prior knowledge of $e$.
0
votes
2answers
39 views
What is the initial reason to define the evolute of a curve?
The evolute of a curve is defined as the envelope of the normals or as the locus of the center of the osculating circle.
What is exactly "the envelope of the normals" ?
What is the reason to ...
0
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0answers
27 views
What is the reason of the naming of the “simplex method”?
What is the reason of the naming of the "simplex method"?
Is there any method other than simplex? Or it has any other cause?
4
votes
1answer
47 views
Is the Knuth arrowup notation defined for non-natural exponents?
I recently found out about Knuth's arrowup notation. Wikipedia, among other websites, only shows a definition for $a \uparrow^n b$ where $n \in \Bbb{N}_0, a \in \Bbb{R}, b \in \Bbb{N}$ as following:
...
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votes
0answers
88 views
Math is a young man's game? [closed]
Do you agree with this quote from Hardy? Supposedly someone is in their prime between ages 18-25.I don't think I agree with this, since most of the people doing research and advancing math are ...
1
vote
0answers
66 views
Gray's “Plato's Ghost” - a curious mistake
I am currently reading Jeremy Gray's "Plato's Ghost", and I run into the following passage (Chapter 5, page 332). The point is, it seems to me that it contains two very elementary mistakes that feel ...
3
votes
2answers
163 views
Isn't seven bridges problem trivial? [closed]
What was the actual actual problem that led Euler to graph theory?
By looking even at non-simplified map like this
It is obvious that, if a landmass is connected by odd number of bridges, it ...
2
votes
3answers
186 views
why is variance so famous that it appears in almost half of the probability textbook? [closed]
why is variance so famous that it appears in almost half of the probability textbook?
What is its significant history so that a statistical model would appear in such textbooks and what does it help ...
4
votes
1answer
60 views
The 633 reducible configurations of the 4 color Theorem
Ken Appel died a few days ago, and I wanted to see how long it took to perform the four color theorem proof now, with modern systems. At the Four Color Theorem page, there is a link given for the ...
0
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0answers
15 views
Information of paraproduct
I am studying paraproduct nowadays, mostly the interplay(or application) with Fourier transform and as a tool to formulate some integrals(Young's, stochastic one,etc.).
As mentioned in this notice, ...
2
votes
1answer
93 views
Carl Friedrich Gauss and the 'useless' FFT in 1805
This is a history question, so you need to know something about math history to answer it.
There's a rumour that says that Carl Friedrich Gauss knew the FFT in 1805, but he thought it was useless, ...
4
votes
3answers
97 views
Where can I find a good comprehensive read about the history of Mathematics?
I'm doing a Bachelor of Pure Mathematics in Unisversity, and while reading through the book that outlines the course selections, I found one that is listed as "rarely offered", which the department ...
1
vote
0answers
39 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 ?
32
votes
2answers
998 views
On a 500 page proof
On wikipedia there is a claim that the Abel–Ruffini theorem was nearly proved by Paolo Ruffini, and that his proof spanned over $500$ pages, is this really true? I don't really know any abstract ...
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3answers
255 views
What have been some of the most revolutionary philosophical shifts in perspective in mathematics?
Often times, great revolutions in mathematics come from shifts in philosophical perspective. The shift from extrinsic to intrinsic geometry yields manifolds (and much else). The shift in focus from ...
10
votes
1answer
114 views
Any branch of math can be expressed within set theory, is the reverse true?
Set theory seems to have the property of being "universal", in the sense that any branch of math can be expressed on its language. Is there any other branch of math with this property?
I am asking ...
4
votes
2answers
120 views
Disjunction: Why did the inclusive “OR” become the convention?
In How to Prove it by Velleman, for defining disjunctions, he gives the difference between exclusive "OR", and inclusive "OR."
Given two events $P$ and $Q$, the disjunction is defined for them as:
...
2
votes
1answer
107 views
How do we know $\pi$ is a constant? [duplicate]
How did the ancient Greeks discover that the ratio of a circle's circumference to its diameter is constant? It does not seem so intuitive. Thanks!
5
votes
1answer
94 views
Mathematics for Pleasure of a Beginner
I've just read "The Music of the Primes" by Marcus du Sautoy, it is worth a read. I'm not from a maths background, but I'd like to develop a deeper understanding of the concepts. The poetry of math is ...
5
votes
2answers
72 views
Why the SVD is named so…
The SVD stands for Singular Value Decomposition. After decomposing a data matrix X using SVD, it results three matrices, two singular vactors U and V, and one singular value matrix whose diagonal ...
3
votes
3answers
176 views
What do these old symbols from set theory mean? (Large E, $\cdot$ and $+$ for sets, and $\ \bar{\!\bar X}\,non\!\geqslant\frak n$)
So, I'm trying to prove the theorems in this paper by Tarski:
On Well-ordered Subsets of any Set, Fundamenta Mathematicae, vol.32 (1939), pp.176-183
but it is from 1939, and I don't recognize a few ...
7
votes
1answer
65 views
Why is logistic equation called “logistic”?
The logistic function solves the logistic ODE which is the continuous version of the logistic map.
However, I was not able to find why any of these things are called "logistic".
6
votes
0answers
154 views
Priority of the content of a note by Lebesgue from 1905
I refer to a note by Lebesgue Remarques sur la définition de l'intégrale, Bull.Sci.Math. 29 (1905) 272-275 not very known (see pdf for an exposition in English).
It is a pedagogical note containing a ...
7
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0answers
118 views
Why did Arnold say: “Mathematics is divided into cryptography, hydrodynamics and celestial mechanics.” [closed]
On V. I. Arnold's website you can find
the following text:
All mathematics is divided into three parts: cryptography (paid for by CIA,
KGB and the like), hydrodynamics (supported by ...
3
votes
0answers
146 views
Which theorem did Poincaré prove?
Two related elementary facts in group theory are sometimes called Poincaré's theorems.
If $H\lneq G$ and $[G:H]<\infty$, then there is $N\leq H$, $N\lhd G$ such that $[G:N]<\infty$.
The ...
14
votes
0answers
109 views
Hilbert's original proof of basis theorem
Does anyone know Hilbert's original proof of his basis theorem--the non-constructive version that caused all the controversy? I know this was circa 1890, and he would have proved it for ...
1
vote
2answers
42 views
Diadics and tensors. The motivation for diadics. Nonionic form. Reddy's “Continuum Mechanics.”
I'm taking a course in continuum mechanics. Our book is Continuum Mechanics by Reddy, a Cambridge edition. In the second chapter he introduces tensors and defines them to be polyadics. He is ...
