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Results tagged with ho.history-overview
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user 2384
History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.
16
votes
Accepted
Modular forms and "too many symmetries"
My interpretation of Mazur's quote was in terms of the history of the discovery of modular forms. Of course trigonometric functions came first, and then a whole variety of other special functions in t …
- 85.6k
9
votes
Certain notations in Cayley's work
Some of the symbols used in that time would be tricky to type in Latex, so instead of writing an explanation here, I hope it is okay to just give a reference. There are two books by Florian Cajori, "A …
- 85.6k
5
votes
Hall's treatment of algebraic operations
I haven't checked Hall's book so I'm not entirely sure that this is exactly what he talks about, but there are quite a few generalizations of groups by allowing multivalued operations. I mention some …
- 85.6k
21
votes
Accepted
What's tropical about tropical algebra?
A lot of sources mention that the adjective "tropical" is given in honor of Imre Simon, but it seems hard to find who precisely coined the term. I found some sources which attribute this to some Frenc …
- 85.6k
43
votes
whence commutative diagrams?
An excerpt from Mac Lane's Categories for the Working Mathematician (p29, Notes on Chapter 1):
The fundamental idea of representing a function by an arrow first appeared in topology about 1940, proba …
- 85.6k
13
votes
Accepted
Biography of Felix Hausdorff
There is the "Hausdorff edition" project (E. Brieskorn, F. Hirzebruch, W. Purkert, R. Remmert and E. Scholz) which will entail all collected works and is supposed to have a decent biography as well. O …
- 85.6k
8
votes
Accepted
Why were plane partitions invented?
MacMahon invented a technique which he called partition analysis to determine (multivariable) generating functions for many combinatorial objects and as a computational method for solving combinatoria …
- 85.6k
23
votes
A gamma function identity
A proof of the statement has already been given, so I will just add a small historical remark.
The left hand side of your identity is the Veneziano amplitude in the case of four identical scalar parti …
- 85.6k
4
votes
Birkhoff's theorem about doubly stochastic matrices
From Schneider's "The Birkhoff-Egervary-Konig theorem for matrices over lattice ordered abelian groups" after the following theorem is presented
Let $G$ be a lattice ordered abelian group. Every g …
- 85.6k
6
votes
Why do we teach calculus students the derivative as a limit?
It's funny that actually many students believe that the symbiosis is always the other way around, i.e. derivatives are used to compute limits (l'Hopital etc.). My favorite example of an elegant calcul …
16
votes
Accepted
What are hypergroups and hyperrings good for?
While I don't know much about hyperstructures other than hypergroups, I know it is hard to study the history behind them because of the non-consistent terminology attributed to these objects by differ …
- 85.6k
22
votes
Accepted
What was Galois theory like before Emil Artin?
The development of Galois theory from Lagrange to Artin by B. Melvin Kiernan, is a history of pre-Artin Galois theory.
- 85.6k
25
votes
Accepted
Why are parabolic subgroups called "parabolic subgroups"?
It appears that neither of the answers is fully correct. There is a great book, "Essays in the history of Lie groups and algebraic groups" by Armand Borel, when it comes to references of this type. To …
- 85.6k
19
votes
Accepted
Motivation for strong law of large numbers
Here is a nice post of T. Tao on SLLN. In the comments section he is asked a very similar question to which he answers the following: (I hope it's ok to reproduce it here, since it is buried down in t …
- 85.6k
23
votes
Accepted
Newton and Newton polygon
The Newton polygon and Newton's method are closely related. The following theorem was first proven by Puiseux:
if $K$ is an algebraically closed field of characteristic zero, then the field of Pui …
- 85.6k