leichter (05/13/82)
The best definition of mathematics I know is "it's what mathematicians do". To avoid begging the question - how t \\\ To avoid begging the question, here is how you find mathematicians: Ask a good, random sample of people who CALL themselves mathematicians to name the top ten people in mathematics. The top 50 vote receivers win; what they do is mathematics. All of this, of course, answers the question "What is mathematics at a given point in time?" If you look at the history of mathematics, you will find that that's the only meaningful question anyway. Much of what Newton called "natural science" or may even physics is called mathematics today... Does this sound silly? I'm willing to bet that no one comes up with any more concrete definition that will satisfy people...it's as hard as defining "art". By the way, here is a definition of "proof" that is more correct in the real world of mathematics than any formalization: A proof of a fact is something that convinces you the fact is true. Proofs are valid "mathe- matical" proofs when they convince mathematicians. For some excellent discussion of similar ideas, as well as another point of view on CS as mathematics vs. CS as engineering, an article that MUST be read is DeMillo, Perlis, et. al. (I don't remember all the authors) article titled something like "Program Proving and Social Processes", in CACM about two years ago (I'll get the exact reference if people want). (BTW, Dijkstra's comment on the paper begins "I've just read a very ugly paper"; it appeared in, I think, SIGPLAN, about 3 months after the CACM article.) Another interesting comment about mathematicians, from an (excellent) SF book by Edward Llewellyn [sp?] called "The Douglas Convolution": Being good at mathematics involves the ability to see non-obvious relationships amoung abstractions. (Llewellyn is apparently the pen-name of a west-coast physicist or mathematician; as far as I know, this book and one called "The Bright Com- panion" are the only things he has published, and they are EXTREMELY worthwhile.) Anyway...consider how THIS definition of mathematical ability relates to programming... -- Jerry decvax!yale-comix!leichter leichter @ yale