Doron, I think your Opinion merits some discussion on the semantic meaning of the words "trivial", "deep" and "interesting". You criticize Hardy's statement that chess is trivial, and offer your own opinion that chess is both much deeper and more interesting than the Riemann Hypothesis. The Oxford English Dictionary (http://www.oed.com) gives several definitions for the word "trivial", of which the ones which seem pertinent are 1. Of small acount, little esteemed, paltry, poor; trifling, inconsiderable, unimportant, slight. 2. (math.) Of no consequence or interest, e.g. because equal to zero. "Deep" is defined in various ways, among others as 1. Hard to fathom or get to the bottom of; penetrating far into a subject, profound. 2. Said of actions, processes, etc. in which the mind is profoundly absorbed. As for "interesting", I won't bother defining it, except to recall the Hebrew saying "al ta'am ve'al reach ein le'hitvakeach" (which I find more evocative than the English equivalent "different strokes for different folks"). What you explain about why you find chess deeper and more interesting than the RH, is that the problem of determining if White has a winning move is more difficult than RH (I agree), will probably never be solved (I agree), and a solution, should one ever be found, will occupy more space than a solution of the RH (I agree). What I think Hardy meant when he used the word "trivial" with regards to chess - and it is clear he meant to use it in a belittling sense, no matter what dictionary he consulted - is that chess, being in some sense an arbitrary problem dependent on human culture and history, is less worthy of consideration as a mathematical problem. And this, regardless of any issues of applicability - I'm sure Hardy, purist that he was, would not find that the present-day uses of the Riemann Hypothesis in questions of cryptography detract in any way from its beauty. Hardy, and I think most present-day mathematicians, myself included, had a tendency to assign a value to mathematical problems, based on criteria of elegance, beauty, intrinsic interest, and most importantly, some elusive concept of "naturality". You may find chess of more intrinsic interest than the RH - it's really pointless arguing about interest. But I think even you would be hard-pressed to argue that chess is a more natural problem. When I say natural, I mean something such as: would intelligent beings on some remote planet also come up with this problem? And even if they were living in a different physical universe than ours, would they still come up with this problem? I believe the answer is "yes" for the RH, and "most probably not" for chess (though they may come up with quite similar-looking problems to chess). To summarize, I claim that there is really no disagreement between you and Hardy! You two simply enjoy different aspects of the practice of mathematics - you have different utility functions, one might say. You may be in it for the pure fun of it, the joy of taking a problem, no matter where it came from, and attacking it with all you've got. Hardy, as you correctly observed, had an almost religious sense concerning which problems were the most important, and got an extra kick from the "added value" of thinking about the problems which seemed to possess some kind of transcendence or nobility. And to conclude on an optimistic note, I think it's great that there are people like you out there, and also people like Hardy! This shows that there are all sorts of ways of viewing and doing mathematics. Why be so dogmatic about your own personal way of thinking? There is room for everybody, don't you think?
Although I agree fully with all you say there, I think there is a point where it may need some revising, not to be unfair to that old Queen of Number Theory, as Uncle Petros, in an angry moment, called G. H. Hardy. You say that he says 'chess is trivial', which is indeed an amazing statement, if he made it. Although I have not a copy of the Apology here, I did some looking-up on the internet and I think that the only connection he makes between chess and triviality is in the sentence "A chess problem is genuine mathematics, but it is in some way 'trivial' mathematics..." And of course a chess problem, of the type he means (mate in 2 or 3 moves) is rather trivial mathematically, but this is altogether a different kind of statement than saying 'chess is trivial'. I just thought I'll tell you this, so you could check it -- maybe I'm wrong and he actually says 'chess is trivial' somewhere but, if not, the statement about problems itself is. I'm sure you'll agree, not the ideal target for your (justified) rage . But I think the main point of your Opinion can still be validly made, with a small amendation, because the amazing thing (or perhaps not so amazing in pre-Alan Turing times) is that Hardy does not think of chess as mathematics (too messy, too complex, too inelegant I'm sure) although he calls chess-problems the 'hymn-tunes' of mathematics, trivial ones of course! And his not considering chess to be mathematics, but only the 'trivial' chess problems, is perhaps as amazing, or more, than saying it is trivial mathematics.
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