Hoo, boy! Where to begin?...
I think Dr. A covered some of my points pretty well. Gernsback should never, ever, EVER be on anyone's list of Great Writers of anything -- period! I do not in any way wish to detract from Gernsback's importance to the field, but he was an absolutely atrocious writer, and even though a bad writer may have an enormous influence on a field through their ideas ... his book did not. (Seriously, the only reasons to ever read that novel is if you are a dyed-in-the-wool sf completist where the period is concerned, or out of academic rigor -- or if you're a serious glutton for punishment. It's a very brief book, but it seems interminable. The man couldn't write his way out of a pay toilet, I believe is the phrase....
One point, though: Mary Shelley has been considered in this position for a long time, by several of the Golden Age writers, as well, including Asimov, Heinlein, Clarke, and others. So it's not just the fashionable thing now. This is an idea that has been pretty current since the 1920s at least. And Asimov's robot stories were in large part (according to his own essays on the subject) a reaction to Frankenstein; not to mention his coining of the term "The Frankenstein Complex" used in many of those stories.... She also wrote The Last Man, a post-apocalyptic novel that is certainly sf, and several short stories and novellas that would qualify for inclusion in the field. Her prose in Frankenstein is indeed a bit wonky -- it was her first novel, written originally when she was in her teens, after all -- but in her later work, her prose is not only eloquent, but elegant and precise' however much it may seem to ramble, it isn't -- like Lovecraft, she's going for an extreme precision in thought and nuance, and she does it quite well. But putting her as the greatest SF writer is simply completely off the beam.
Wells definitely deserves serious consideration, not only because his work continues to sell quite well, entertain, and enlighten even today, but because he remains a strong influence, and for a considerable time set a high-water mark in the field. So a contender, definitely. The same can be said for Verne.
Lovecraft... I am a very intense fan of HPL. I admire him and his work tremendously, and the more I learn of each, the more my appreciation grows. But he was not an sf writer; and he would have seen red had he been termed such. He had contempt (deservedly) for the vast bulk of sf of his time, with only such rare exceptions as Stanley G. Weinbaum (who should certainly be on the list, by the way, being a pre-Campbell Campbell writer -- that is, one who wrote exactly the sort of thing Campbell was trying to initiate -- better science, better writing, and genuine science fiction rather than adventure stories dressed up with pseudoscientific jargon -- before Campbell ever began his revolution). While several things HPL wrote may well be classed as either sf or proto-sf, it is more by accident than anything else.
Asimov. Again, I'm very fond of Isaac; but his style wobbled seriously at times, and while he wrote some of the most important works in the genre, they are neither the best nor the most influential. His vision was individual and unique, and no one really attempted to copy Isaac much; he was seen as a solid writer, a good storyteller, but not an innovator where fiction was concerned; thus he really doesn't belong on the list, either. Wyndham, again, falls somewhat into this category: a damned good writer, a solid storyteller for 30-40 years, wrote classics in the field, but not generally speaking either an innovator, nor a huge influence, nor are his books (for all their excellence) anywhere near the best in the field.
As has been said, Heinlein should definitely be on the list under just about any criteria. His influence on the field, his popularity, the variety of types of tales he wrote (from hard sf to fantasy, humorous to starkly tragic, puritanical to bawdy, etc.) ... all argue for him being there no matter how you define your terms. (This may be a good or a bad thing; some would argue either way, and with some justice on each side.) Clarke was an enormous influence on the field because of the rigor of his science and his ability to convey the sense of being "out there", perhaps more than any writer. Plus, he has had several classics in the field, and a great number of his books have been immensely popular; so he should be on the list.
If we're talking "classic" as in "Golden Age", then C. M. Kornbluth, and the team of Henry Kuttner and C. L. Moore should definitely be on the list; Fritz Leiber should be there, regardless, as his works were not only quite popular, but he was one of the best prose stylists the field ever produced, he was incredibly versatile, won more awards than you can shake a lucas at. Sturgeon should definitely be included, as well. There are many others that are due for consideration in this case.
If we're going beyond the Campbell years, then the number of writers who are due for consideration proliferates enormously. Yes, Dick deserves serious thought here. So does Harlan Ellison who did write sf (though he's primarily a fantasiste -- not of the faux-mediaeval school, but contemporary fantasy or "science fantasy") and has won so many awards you'd need a warehouse for them all; he's also had an enormous influence on the field both through his pyrotechnic, emotionally intense, and immensely popular writing, and for his various projects as editor, including Dangerous Visions and Again, Dangerous Visions, and for his various fights to protect writers rights where their material are concerned. Robert Silverberg deserves strong consideration for being one of the most erudite and eloquent writers in the field; Michael Moorcock for his influence via initiating the New Wave and presenting its malleable template, Jerry Cornelius, as well as promulgating the idea of the multiverse and many of the ideas that are now seen as part of Chaos theory as well, through his various writings; he is both enormously popular, unbelievably prolific, and often quite influential with his ideas and (in his later writing especially) his abilities with the language and in broadening the definition of science fiction.
J. G. Ballard is certainly due for consideration, as well, for his unique, disturbing, and highly artistic tales that have both delighted and influriated people for half a century now. He has been both adored and villified by numerous writers, readers, and editors, and his work is most assuredly among the most literate prose sf has produced; and he's had his imitators, as well.
And that's not even beginning to address a tithe of the writers of the 50s and 60s, let alone tackling those who have come along since!
So, before you go any further, you really do need to define your terms. Set the parameters in your questions (this is what I was addressing in an earlier post to you), because you are leaving this thing so wide open that it may as well not have any boundaries at all! Which is a sure-fire way to end up with muddled thinking and knots that the gods themselves couldn't unwind. So I strongly suggest you sit down, look at what you've got so far, and draw up a plan of what you want to address and how; define your terms; set your parameters (at least initially) on what you wish to cover; and then formulate your questions. Right now, you're producing nothing but the foggiest of conceptions, if the open-endedness of these questions is any indication, and you're going to end up spinning your wheels indefinitely, and find that you've got nowhere at all.
As Dr. A said, the field can always use more academic support, but it really doesn't help if it's not done with the same care and attention that one would expect from an academic thesis on any other branch of or figure in literature.
