the two species of programmers

Along the same lines as that "clash of programming language civilizations" post, I have long had the idea that there are two basic species of programmers. I have no hard evidence for this blurry distinction, but only my own experience and hyperactive generalization. I'm also sure that I'm not the only one to have stumbled upon this. Anyway, in alphabetical order, the two species: linguistic and mathematical.

1. Linguistic. This species spells correctly most of the time. In fact, the linguistic can often be observed lecturing or poking fun at the mathematical's egregious spelling errors. Per its name, the linguistic has excellent language intelligence or aptitude, and perhaps may study little-used languages like Esperanto. The linguistic may be good at abstract algebra, but may not be as quick as the mathematical when it comes to, say, listing the first 23 prime numbers. A program is a series of sentences and clauses for a linguistic. Functional programming may come more naturally to the linguistic than the mathematical. The linguistic may take excessive pleasure in the logical elegance of a program's design. He or she may be more apt to comment "if the computer can't run my beautiful program efficiently, then that's the compiler or interpreter's problem". Top-down or UML-style design may be a preferred mode of operation for the linguistic.
2. Mathematical. This species often has difficulty spelling correctly. But to the mathematical, correct spelling doesn't really matter so long as the idea gets communicated. Per its name, the mathematical has excellent mathematical intelligence or aptitude, and may know practical trivia about timekeeping. The mathematical's intuitive feel for numbers allows for good estimation, such that the mathematical can arrive at an answer but have trouble explaining how he arrived at it. A program is a series of individual calculations for a mathematical. A mathematical would view the statement a = 5 + 2 to be "add 5 to 2 and store the result in a", while a linguistic would view the same statement as "define a to be the evaluation of the expression 5 + 2". Assembly programming may come more naturally to the mathematical than the linguistic. To the mathematical, complex program design is not necessarily a joy; to the contrary, it may be more likely to obscure the real functioning of a program. He or she may be more apt to comment "perfect theroetical purity isn't worth anything if it doesn't adequately solve this particular problem in the real world". Bottom-up or eXtreme Programming may be a preferred more of operation for the mathematical, in which program modularity evolves naturally.

I make no value judgments here about which species is "better". For what it's worth, I identify more with the linguistic species. Of course, my taxonomy is a failure in the sense that any actual programmer may "switch species" in any given situation. For instance, I know that whenever I write a shell script, I do it like a specimen of the mathematical species: look up some quick examples on the Web, use trial-and-error to figure out which utility parameters do what I need, and basically learn as little of the syntax as I must. My two categories also fail in the sense that any actual programmer probably exhibits features of both species. I think it should go without saying, but the best, well-rounded programmer should be a chimera.