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History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.
13
votes
3
answers
2k
views
Gauss' posthumous publications?
I'm looking for any information about the posthumous publication of Gauss' mathematical correspondence and notebooks.
When did these become widely available, and how did it affect progress in mathema …
11
votes
1
answer
1k
views
History of Sylvester's resultant?
Suppose that we have two polynomials that split:
$$\begin{align*}
f(x)=\sum_{k=0}^d a_{d-k}x^k&=\prod_{i=1}^d (x-\lambda_i),\\
g(x)=\sum_{k=0}^e b_{e-k}x^k&=\prod_{j=1}^e (x-\mu_j).\\
\end{align*}$$
T …
15
votes
1
answer
1k
views
History of Study's Lemma?
The following theorem is usually attributed to Eduard Study:
Let $f(x,y)$ and $g(x,y)$ be polynomials in two variables over a field, with $f$ irreducible. If $f\nmid g$ then the curves $C_f:f=0$ and …
11
votes
2
answers
1k
views
History of the Frobenius Endomorphism?
The existence of the Frobenius endomorphism probably goes back to Euler's proof of Fermat's little theorem. But why is it named after Frobenius? Who gave it this name? When was it first stated in full …
8
votes
2
answers
983
views
History of the kernel of a homomorphism?
This previous question traces the notion of group homomorphism to Jordan (1870) and the term "homomorphic" to Fricke and Klein (1897) and to earlier lectures of Klein:
Whence “homomorphism” and “homo …
8
votes
1
answer
482
views
Earliest use of the term "Galois extension"?
Does anyone know the earliest use of the term "Galois extension"? I thought it might be in Emil Artin's Notre Dame lectures but I couldn't find it there. (He does use the terms "normal" and "separable …
19
votes
2
answers
990
views
Who originated the standard symbols for Lie groups GL, SL, SU, etc.?
Who was first to use symbols GL, SL, O, SO, U, SU, Sp and their projective versions, and how did this notation become standard?
The notation appears in fairly modern form in Weyl's "The Classical Gro …
5
votes
1
answer
685
views
English translation of Steinitz 1910?
Does there exist an English translation of Steinitz' 1910 work "Algebraische Theorie der Körper"?
http://www.digizeitschriften.de/dms/img/?PPN=GDZPPN002167042
7
votes
3
answers
2k
views
"Mächtigkeit" versus "Kardinalität"?
In Cantor's set theory, is there any difference between the terms Mächtigkeit and Kardinalität ?
10
votes
1
answer
626
views
Whence "Durchschnitt" and "Vereinigung"?
Today the set-theoretic operations of intersection $\cap$ [German: Durchschnitt] and union $\cup$ [German: Vereinigung] are standard.
The modern notations are present in the first edition of van der …
9
votes
1
answer
349
views
Origin of the concept of "homomorphism"? [duplicate]
When was the concept of a "homomorphism" of algebraic structures first introduced?
Steinitz' 1910 paper Algebraic Theory of Fields is often pointed to as the first true work of abstract algebra, yet …
11
votes
2
answers
2k
views
History of Jordan Canonical Form?
Can anyone suggest a reference that discusses the history of the Jordan canonical form? In particular, I am interested in:
When and how was it first stated? (I understand it was independently stated …
10
votes
1
answer
733
views
Analogy between Lagrange's Theorem and Rank-Nullity Theorem?
One can view view Lagrange's Theorem $$|G/H|=|G|/|H|$$ and the Rank-Nullity Theorem $$\dim(V/U)=\dim(V)-\dim(U)$$ as directly analogous. Does anyone know a high-level explanation of this analogy? I su …
24
votes
2
answers
4k
views
To what extent can fields be classified?
The study of algebraic geometry usually begins with the choice of a base field $k$. In practice, this is usually one of the prime fields $\mathbb{Q}$ or $\mathbb{F}_p$, or topological completions and …
4
votes
1
answer
562
views
Historical precursor for Peano's axioms of a linear space?
Peano is typically credited with giving the first abstract definition of a vector space (1888):
http://www-history.mcs.st-and.ac.uk/HistTopics/Abstract_linear_spaces.html
Apparently, Peano credits M …