[FOM] 827: Tangible Incompleteness Restarted/1

[José Manuel Rodríguez Caballero]

Lasse wrote:
>
>  I think it is dangerous to discuss and speculate about ?general
> attitudes? on the basis of a single anecdotal comment. Of course in
> mathematics, as in any field, people may hold some very strong opinions.
> Speaking as a mathematician not working in discrete mathematics or
> foundations, I can only say that I hold graph theory in very high esteem,
> and certainly consider it (or, at least, aspects of it) very much part of
> mathematics. I believe that the majority of my colleagues would feel the
> same ? including Fields Medalists.


There is a group of mathematicians (school of Gabriel) who prefer to
substitute the word GRAPH by the word QUIVER. According to [1], a quiver is
a collection of edges which may stretch between (ordered) pairs of points,
called vertices. Hence a quiver is a kind of graph, often called a directed
graph. So, a mathematician may say: I do not know what a directed graph [2]
is, I work with quivers [3]. Why Gabriel did not use the word GRAPH? In
[4], Bourbaki and Alain Connes talk about the books of Gabriel's school
(Serre was the advisor of Gabriel).

All the best,
Jose M.


[1] P. Gabriel, Unzerlegbare Darstellungen. I, Manuscripta Mathematica 6:
71–103, (1972)
link: https://link.springer.com/article/10.1007/BF01298413

[2] https://en.wikipedia.org/wiki/Directed_graph

[3] https://en.wikipedia.org/wiki/Quiver_(mathematics)

[4] https://youtu.be/QqR459KxDVU?t=3319
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