Use this tag for questions concerning history of mathematics, historical primacies of results, and evolution of terminology, symbols, and notations.
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1answer
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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 ...
48
votes
10answers
8k views
Results that came out of nowhere.
Most big results in mathematics are built on years and years of groundwork by the author and other mathematicians, such as Wiles' proof of FLT or the classification of finite simple groups. ...
0
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0answers
57 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.
...
7
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3answers
3k views
Indian claims finding new cube root formula
Indian claims finding new cube root formula
It has eluded experts for centuries, but now an Indian, following in the footsteps of Aryabhatt, one of the earliest Indian mathematicians, claims to ...
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 ...
1
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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.
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
32
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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 ...
3
votes
1answer
180 views
What base did Ancient Egyptians use?
I'm wondering if anyone would know anything about Egyptian mathematics in a prehistorical setting. I've been reading mixed answers, with Egyptians using base 10 or base 12, (interestingly, without ...
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 ...
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 ...
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 ...
6
votes
1answer
160 views
Which is the primary source of the Conway base 13 function?
I have been looking for the first appearance of the Conway base 13 function in the literature, but the only thing I have found is the wikipedia article whose unique element in the bibliography I ...
12
votes
2answers
948 views
“L'Hôpital's rule” vs. “L'Hospital's rule”?
I know this is not strictly a mathematical question, and I considered putting it on Linguistics SE, but I decided that seeing as this is most probably a mathematical history question, it would be ...
10
votes
7answers
604 views
What's the hard part of zero?
A lot of textbooks said it was hard for human to accept zero when it was first introduced.
How could it be? It seems to me as natural as positive integer which represent there is no elements at all.
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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 ...
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 ...
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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 ...
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, ...
32
votes
4answers
1k views
Why is a full turn of the circle 360°? Why not any other number?
I was just wondering why we have 90° degrees for a perpendicular angle. Why not 100° or any other number?
What is the significance of 90° for the perpendicular or 360° for a circle?
I didn't ever ...
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 ...
6
votes
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 $$\left|\frac ...
3
votes
1answer
72 views
Historical definition of a group
Wikipedia states that van Dyck (1882) was the first to give the definition of a group in the modern way. Before this, what were some of the original axioms or conditions for groups? I mean, how were ...
4
votes
2answers
77 views
Is the validity of measuring area by approximation an assumption of calculus?
The assumption that if you subdivide an area into more and more sub intervals, the approximation gets better and better. Has this been formally proved, or is it just intuition? Thanks!
33
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3answers
687 views
What are examples of unexpected algebraic numbers of high degree occured in some math problems?
Recently I asked a question about a possible transcendence of the number ...
9
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2answers
50 views
Origin of well-ordering proof of uniqueness in the FToArithmetic
In the Appendix to Ivan Niven's book "Numbers: Rational and Irrational", he proves the Fundamental Theorem of Arithmetic (FToA) without using Euclid's Lemma that if a prime divides a product, then it ...
5
votes
1answer
108 views
How was the normal distribution derived?
Abraham de Moivre, when he came up with this formula, had to assure that the points of inflection were exactly one standard deviation away from the center, and so that it was bell-shaped, as well as ...
4
votes
1answer
81 views
The manuscript Summa Logicae (William of Ockham)
The Summa Logicae (Latin, in English it's the Sum of Logic) is a textbook on logic by William of Ockham. There are articles about the Summa Logicae in Wikipedia and in Logicmuseum.
It was published ...
4
votes
3answers
74 views
A proof for this series?
The summation, $$\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 ...
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 ...
3
votes
3answers
316 views
Is there a text that provides the proof of Fermat's Last Theorem?
I know that professor Andrew Wiles discovered his proof of Fermat's Last Theorem in 1995. One of my friends is looking for a text which provides his proof. I know that the proof is very complicated ...
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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 $e$.
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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?
...
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 ...
15
votes
1answer
248 views
Does there exist a copy of Euclid's Elements with modern notation and no figures?
I am working through Euclid's Elements for fun, but I find the propositions difficult to understand without referencing the provided figures. Unfortunately, the figures usually give away the proofs, ...
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:
...
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 ...
-1
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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 ...
95
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15answers
5k views
In the history of mathematics, has there ever been a mistake?
I was just wondering whether or not there have been mistakes in mathematics. Not a conjecture that ended up being false, but a theorem which had a proof that was accepted for a nontrivial amount of ...
65
votes
8answers
6k views
Are half of all numbers odd?
Plato puts the following words in Socrates' mouth in the Phaedo dialogue:
I mean, for instance, the number three, and there are many other examples. Take the case of three; do you not think it may ...
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 ...
1
vote
3answers
300 views
On the Origin and Precise Definition of the Term 'Surd'
So, in the course of last week's class work, I ran across the Maple function surd() that takes the real part of an nth root. However, conversation with my professor ...
2
votes
3answers
185 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
votes
1answer
63 views
Square root principle value convention
Why is the principal square root of a complex number defined as
$\sqrt z = \sqrt r e^{-i \varphi / 2}$
for $\varphi \in (-\pi, \pi]$ ?
Wouldn't it be more natural to let $\varphi \in [0, 2\pi)$ as it ...
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
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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
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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 ...
