sibley (05/13/82)
"Mathematics is what mathematicians do." Mathematicians do not solve differential equations or spend their time evaluating really tough integrals. In fact, the best people at doing this sort of thing are engineers and physicists. Neither do mathematicians search for bigger and better trig identities. They prove theorems. They prove intersting theorems, but 'interesting' is hard to define. Hence, the definition above. As a mathematician myself, I can tell you that what I do bears no resemblance to Dijkstra's suggested approach to programming. Certainly theorems do not 'prove themselves' the way he implies that programs 'write themselves'. (I don't think programs write themselves either.) When I start thinking about a potential theorem I don't even have any assurance that it is true. This makes it very different from programming. A programmer always (well, almost always) knows that what he or she wants to do is possible. The problem is 'how'. After I decide that a theorem is true, i.e., have a convincing sketch of a proof, begins the tedious part -- writing down a detailed and correct proof and then going through the hassles of publication. My experience is that this part might be a little like programming. In fact, when I start thinking about something, often I don't have even a potential theorem in mind. I'm just trying to understand how something 'works'. The important insights become theorems. This seems entirely unrelated to writing programs. 'Proofs of programs', BTW, come under the heading of 'uninteresting' above. Proving a program does what you claim is just boring. It may be important, but it's still boring and not mathematics. I might accept 'mathematical' in the sense that it resembles mathematics without being part of it. Note, however, that theories about how programs might be proved may very well be mathematics. Just doing it is not. I guess this means that what Dijkstra does may be mathematics, but what he suggests programmers should do is not. Dave Sibley Department of Mathematics Penn State Univ. psuvax!sibley