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In general, what traits do you think may cause people to favor one mathematical field over another?

I have a friend who swears by algebra but hates analysis, and I like analysis better than algebra even though I'm bad at it.

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closed as not a real question by Asaf Karagila, Brian M. Scott, Gerry Myerson, Henning Makholm, Austin Mohr Nov 3 '11 at 23:12

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center. If this question can be reworded to fit the rules in the help center, please edit the question.

Perhaps this question is not a lot deeper than why some people prefer vanilla ice cream over chocolate. –  Weltschmerz Nov 3 '11 at 22:51
Because some people are weird. Which people are which is left as an exercise for the student. More seriously, I’ve voted to close: this isn’t a mathematical question, and it probably has no answer anyway. –  Brian M. Scott Nov 3 '11 at 22:59

1 Answer 1

up vote 17 down vote accepted

I don't know per se if this answers your question, but I think it's heavily related. I have often wondered the same thing. I like algebra and its associates (anything with an algebra prefix: topology, geometry, etc.) and while I don't hate analysis I definitely like it much less than algebra. Why is this? The conclusion I came to is a more general divide, I like "structural" mathematics, things that study the inherent characteristics of given objects. Two more words that I think describe this type of math well are "qualitative" and "adjectival". I would much rather say "I've classified all (adjective) (structures) with (adjective) (quality)" than anything else. Conversely, the things that make analysis unappealing to me are the "quantitative" aspects. I'm not huge on formulas, or equations (although, in the right light, they can look quite nice (e.g. the Peter-Weyl theorem)). I'm not a huge fan of estimating, or perhaps more accurately, it doesn't satisfy me (it can be fun at times).

Thus, put this way, I think what people really say when they go "I hate analysis and love algebra!" or conversely is a statement about whether they like qualitative or quantitative math, opposed to the two broad schools. For example, some types of combinatorics (even algebraic combinatorics) have a much more quantitative feel, and are certainly not always analytical. Conversely, I very much enjoy functional analysis, partly because it is very structural (things like the Gelfand-Naimark theorem).

I hope that makes sense.

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It has been severely linked to in this site (with great justice!), but I shall link to it again: the article about the "two cultures of mathematics" is greatly related, www.dpmms.cam.ac.uk/~wtg10/2cultures.pdf –  lentic catachresis Nov 25 '11 at 22:45
@Alex Interestingly enough, I'm starting to study topology (which I think is amusingly interesting) and I find it's theory strongly related to analisys rather than algebra. –  Pedro Tamaroff Apr 20 '12 at 2:46

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