Based upon your website, I thought that you might find this anecdote interesting.
I'm a mathematics undergraduate who is working on various projects to various degrees in various fields. One of them is a problem in categorical algebra proposed to me by a professor. Yesterday, we talked about it for some time (about 2 hours), and we both got fairly tired of it (especially the lack of progress). Hence he asked me what else I've been working on. I mentioned that I'm giving a talk this week at our discrete mathematics colloquium, about Sturmian words and Beatty sequences (my small contribution to a problem of O'Bryant). I proceeded to describe the jist of what I had done, and he looked dismayed.
He then said "There should be a nice diagramatic way to do this," and showed that he didn't really understand what was going on at all. When I tried to explain where he went wrong, he got visably upset, and then said "well, I don't know how, but perhaps you should find it [the nice method]." I told him that I didn't think it fruitful to try and look for a way to visualize the problem in terms of commutative diagrams.
He told me that diagrams force you to look at concepts, and not special cases (derisively implying that that was what I had been looking at). The conversation went on in this vein, and moved to number theory. He said "I think number theorists don't look at numbers correctly; they are equivalence classes of sets. When you look at them on too small a level, you get lost in special cases and coincidences. They don't really know what they're looking at." This shocked and surprised me (as I once intended to be a number theorist, and still hold an intense interest in it). I changed the subject. I still want to work with my professor despite his bigotry.
I really don't understand this. He treated combinatorics and number theory as nothing more than a collection of meaningless special cases and coincidences. I've looked at your website in the past, and always assumed that the discrimination of the mathematical upper class (topologists, etc.) was something which you had exaggerated out of all control. Now I see that it is real, but I can't begin to fathom it. This sort of attitude seems to me to defeat the purpose of mathematics. A problem should be worked on iff it is interesting. I do find algebraic geometry considerably more interesting than graph theory. Yet this is only a matter of personal taste, so it seems unrelated to the importance of the mathematical results.
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