Tagged Questions
8
votes
0answers
111 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 ...
9
votes
2answers
49 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
75 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 ...
0
votes
0answers
25 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?
0
votes
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, ...
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 ...
4
votes
2answers
62 views
Who defined $P$-names?
On reading Cohen's "Set Theory and the Continuum Hypothesis" it occurred to me that it might not have been Cohen himself who first defined $P$-names. In his book on page 113 he defines what he calls a ...
7
votes
0answers
138 views
Citation for subset complement result
Let $S = \{s_1, \ldots, s_n\} \subset \{1, \ldots, 2n\}$. Consider two operations on $S$, unfortunately both called complement in different setting: let $A(S) = \{1, \ldots, 2n\} \setminus S$ (set ...
5
votes
1answer
102 views
Differences in worlds with and without $\aleph_0<|S|<2^{\aleph_0}$
Paul Cohen told us that whether or not there is $S$ with \begin{equation}
\aleph_0<|S|<2^{\aleph_0}
\end{equation} cannot be decided within ZFC, and hence it is reasonable to work in two ...
4
votes
1answer
72 views
Fermat's Little Theorem by Leibniz
The proof for $$a^p \equiv a \pmod p\;,$$
where $p$ is a prime number, is pretty straightforward. But as was characteristic of Fermat, he never provided a proof (not that I know of), from what I ...
2
votes
2answers
53 views
Why is $S/R$ a ring extension?
If $S$ is a ring and $R \subset S$ is a subring it's common to write that $S/R$ is an extension of rings. I frequently find myself writing this and read it quite often in textbooks and lecture notes. ...
15
votes
4answers
626 views
How did the ancients view *infinitesimals*?
With some category/topos theory we can now put infinitesimals on a rigorous ground, as in Bell's A Primer of Infinitesimal Analysis, where the author introduces $\epsilon$ satisfying \begin{equation}
...
1
vote
0answers
32 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?
3
votes
3answers
315 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 ...
12
votes
1answer
229 views
Mendelson's $\mathit{Mathematical\ Logic}$ and the missing Appendix on the consistency of PA
In the first edition of Elliott Mendelson's classic Introduction to Mathematical Logic (1964) there is an appendix, giving a version of Schütte's (1951) variation on Gentzen's proof of the consistency ...
5
votes
2answers
126 views
Books on the history of foundations of mathematics?
Can you point me to some books on the history of the foundations of mathematics? At the moment I'm searching for something light because of my lack of mathematical maturity and also the fact that I'm ...
22
votes
1answer
252 views
Is the Galois group associated to a random polynomial solvable with probability 0?
Choose a random polynomial $P\in\mathbb{Z}[x]$ of degree $n$ and coefficients $\leq n$ and $\geq-n$.
Let $r_1,\ldots,r_n$ be the roots of $P$ and consider ...
15
votes
1answer
243 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, ...
4
votes
2answers
117 views
Plato's Disc of Gold
In the book Mathematical Cranks, Underwood Dudley describes the following problem on page 36:
Dear Archimedes,
Your problem is solved but:-- About twenty years ago he lived on Crete and was ...
8
votes
2answers
147 views
What was Klein working on when he “replaces his Riemann surface by a metallic surface”?
I am reading The Value of Science by Poincare, and the following paragraph from Chapter I seems rather interesting:
Look at Professor Klein: he is studying one of the most abstract questions of ...
40
votes
3answers
893 views
Paul Erdos's Two-Line Functional Analysis Proof
Legends hold that once upon a time, some mathematicians were rather pleased about a 30-ish page result in functional analysis. Paul Erdos, upon learning of the problem, spent ten or so minutes ...
2
votes
1answer
98 views
Earliest proof of completeness for axiomatization of Boolean Algebra
Suppose we define Boolean algebra as the system of algebraic rules (logical equivalences) obeyed by AND, OR, NOT with AND, OR, NOT defined by the usual truth tables. We also have variables, which can ...
2
votes
1answer
67 views
Original Proof of Riesz-Thorin
Wikipedia says that Riesz proved the Riesz-Thorin theorem in 1926 without using any complex methods. Does anyone know where the original proof can be found?
...
29
votes
6answers
712 views
Original works of great mathematicians
In almost every mathematical text there is a line as This was first proved by Gauss or This formula first appeared in a work of Riemann, but for me it's more like My friend told me once that...
For ...
1
vote
0answers
79 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 ...
0
votes
3answers
88 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 ...
1
vote
5answers
108 views
integer constants.
Are there some examples of mathematocal constants which are integer numbers. I know of one that is called Kaprekars constant but thats just a base 10 curiosity. Aret there some more important ...
3
votes
2answers
79 views
Cohen and the axiom of choice
The wikipedia article on Paul Cohen mentions that:
Cohen is noted for developing a mathematical technique called forcing,
which he used to prove that neither the continuum hypothesis (CH), nor
...
5
votes
1answer
139 views
History of Lie algebra notation (in Fraktur)?
Does anyone know how it has become the standard to express Lie algebras in fraktur? I'd also like to know how it's established for each era and region, not only the origin.
It doesn't seem that ...
19
votes
1answer
281 views
When, and by whom, was “$\mathbb{C}$ is algebraically closed” dubbed the “fundamental theorem of algebra”?
Wikipedia has this enigmatic sentence on the page for the fundamental theorem of algebra:
...its name was given at a time when the study of algebra was mainly concerned with the solutions of ...
6
votes
0answers
122 views
Articles on ideas in the history of mathematics notation?
I'm teaching a course this term on the history of scripts (writing systems) and rather than talking interminably about Semitic and Chinese and their spawn, I'd like to give students a more varied ...
13
votes
1answer
259 views
Hilbert's Original Proof of the Nullstellensatz
Does anyone have a link to Hilbert's Original Proof of the Nullstellensatz, or know a book where it's printed? I'd be interested to see what it was like. I only really know the Noether normalisation ...
0
votes
0answers
132 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) ...
3
votes
2answers
168 views
original source for the Borel-Kolmogorov paradox
Does anyone know the original source for the Borel-Kolmogorov paradox? Is it online somewhere? Kolmogorov doesn't give a precise citation. (He does list three works by Borel in his bibliography, ...
2
votes
2answers
492 views
History of Quadratic Formula
My wife is planning a lesson on the quadratic formula for high school students, who have previously learned how to complete the square. It would be nice to open the lesson with some historical ...
12
votes
1answer
399 views
successful absurd formalities
Has anyone published in print or on a web site or elsewhere a compilation of successful illogical formal arguments? By those I mean arguments that follow a form in disregard of the legality of its ...
5
votes
5answers
268 views
Can we decide a conjecture is decidable without knowing a conjecture is correct or false?
Can we decide a conjecture is decidable without knowing a conjecture is correct or false?
I asked this question because I assume that the millenium prize problem is already to be decidable, otherwise ...
15
votes
2answers
333 views
History of Modern Mathematics Available on the Internet
I have been meaning to ask this question for some time, and have been spurred to do so by Georges Elencwajg's fantastic answer to this question and the link contained therein.
In my free time I ...
1
vote
0answers
89 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.
2
votes
1answer
236 views
Reference request for “Weierstrass equation” and “Weierstrass normal form”
I would like to know more about the history of the widely used terms "Weierstrass equation" and "Weierstrass normal form", as they appear in the theory of elliptic curves. When were these terms first ...
3
votes
1answer
307 views
References on the History of Linear Algebra
I have an aggregated understanding of the history of linear algebra compiled from friends, teachers, and coworkers. It may have several errors. It goes something like this:
Even ancient cultures ...
4
votes
0answers
125 views
Clarification: intersection of a finite number of subgroups of finite index and Poincaré
From Scott's book Group Theory
$1.7.10.$ (Poincaré) The intersection of a finite number of subgroups of finite index is of finite index.
My question is: Did Poincaré prove the Theorem as stated ...
3
votes
3answers
341 views
Oldest books on Calculus
What are some of the oldest books available on Calculus? I'm curious to see how the old teaching and explanatory styles compare to modern ones.
6
votes
3answers
291 views
Reference requests: Jitsuro Nagura
I spent some time today looking for any biographical information on Jitsuro Nagura and came up empty-handed. Any suggestions welcome.
Also, the Wiki note on the Chebyshev $\psi$ function says that ...
9
votes
2answers
519 views
Original source for a quote by Lobachevsky
Lobachevsky is quoted in many places to have once written (said?) "There is no branch of mathematics, no matter how abstract, which may not someday be applied to phenomena of the real world." (In the ...
1
vote
5answers
293 views
What is a good book about math history?
Which is a good book on math History?
I want to give it as a gift to a mathematician.
5
votes
4answers
278 views
History of analysis?
Any sites detailing the history of analysis post 1820 (to mid 1900s?) - vis-à-vis Cauchy, Weierstrass, Riemann, Bolzano, ..., Kuratowski, Hilbert?
It's something that appears quite interesting and I ...
8
votes
6answers
445 views
Read old articles instead books.
I'd like to know if there is a site, or maybe a collection of books, where I can read old articles in mathematics in order to study topics directly from the source, instead reading books in the field. ...
2
votes
0answers
147 views
What is the origin of the (nearly obsolete) term “binary decimal”?
What is the origin of the (nearly obsolete) term "binary decimal"?
At least two important publications in the 1930s used this oxymoron to mean what is now ...
6
votes
1answer
110 views
Historical reference request: Young tableaux
I am writing up an article on the RSK correspondence. To this end, I want to understand the history behind the invention of the Young tableaux and how it was introduced into the study of the symmetry ...
