There are plenty of mathematicians that don't program very well. Keep in mind, there are many "programmers" that are not really the sort of programmers Dijkstra is talking about. He's not talking about whipping together WP sites with a little JQuery to make dynamic menus.
What looks the most like traditional mathematics in computing is the η-conversion in the lambda calculus.
The η-conversion is any operation on expressions that yields an equivalent expression, on the condition that it is not just a rename, because that would amount to an α-conversion. It is also called mathematical derivation or what other people incorrectly call mathematical "proof".
Without denying the merits of being proficient at showing that expressions are equivalent through η-conversion, we can easily see that quite a few mathematicians only use this method to show that the one meaningless and useless expression is equivalent to another not more meaningful one.
I'm not sure what this has to do with anything. I suppose you're trying to refute the notion that computing is related to mathematics because of this one trivial and somewhat strange example you bring up, which I suppose is to mean that you think this is really the only thing in computer science that resembles mathematics. I would just say that that is pretty odd.
Well, the mathematical method is pretty much typified by its propensity to engage in derivation of equivalent statements. This is simply what people do when they construct a "proof", which is of course not a proof, but that is another issue altogether. Alonzo Church says that derivation can entirely be done by (1) renaming (=alpha) (2) application (=beta) and (3) substitution (=eta). I think that Alonso Church is right. That summarizes the only technique that pure mathematicians seem to be capable of, which is indeed a bit poor. So, I agree with Dijkstra: don't go into computing if that is all you can do.
Just like an artist only has the techniques: move pencil horizontally, move pencil vertically, move pencil toward or away from the paper. The art comes from knowing what to draw and how to combine these steps based on a vision in your head. And the real part of pure mathematics is envisioning new structures and new relations that nobody has used before, at which point the proof itself can become a detail. IT's not through lack of trying that formal computer proof systems haven't been able to touch a milli-part of modern mathematics
> We are all taught that “proof” is the central feature
of mathematics, and Euclidean geometry with its careful array of axioms and propositions has provided
the essential framework for modern thought since
the Renaissance. Mathematicians pride themselves on
absolute certainty, in comparison with the tentative
steps of natural scientists, let alone the woolly thinking
of other areas.
> It is true that, since Gödel, absolute certainty has
been undermined, and the more mundane assault of
computer proofs of interminable length has induced
some humility. Despite all this, proof retains its cardinal role in mathematics, and a serious gap in your
argument will lead to your paper being rejected.
> However, it is a mistake to identify research in mathematics with the process of producing proofs. In fact,
one could say that all the really creative aspects of
mathematical research precede the proof stage. To take
the metaphor of the “stage” further, you have to start
with the idea, develop the plot, write the dialogue, and
provide the theatrical instructions. The actual production can be viewed as the “proof”: the implementation
of an idea.
> In mathematics, ideas and concepts come first, then
come questions and problems. At this stage the search
for solutions begins, one looks for a method or strategy. Once you have convinced yourself that the problem has been well-posed, and that you have the right
tools for the job, you then begin to think hard about
the technicalities of the proof"
