A well-known point of agreement amoung mathematicians is an often sigted discussion by Tim Gowers, namely “Two cultures of mathematics“.

It has, however, been argued that there are other, perhaps more accurate, divisions of mathematicians. I sight Peter Cameron’s view that “those who delve
deep and those who range more widely.” This is, of course, not entirely incompatable, but it does rais several questions. If these two cultures both eist ae they entirely independent, ie is it more sensible to classify mathematicians as points on aplane, rather like the well known political compass? Or it simply the case that one is right and the other not, or worse that neither is right? If neither are right, then what is right? Is this case division a help or a hinderece? (I suspect the latter.)

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