On Thu, 25 Sep 2003, Richard Schroeppel wrote:
JHC remarks that he wouldn't trust a numerical geometric proof.
I'll ask: Why not? It's a packing problem, and computer calculations might well provide a proof. I assume even John accepts computer searches for error correcting codes and similar packing problems as valid.
I've no objection to proofs of any kind, provided they are correct; it's just that I doubt very much whether anyone can find a correct proof of this kind for this theorem, whether they use a computer or not (such a proof would probably be better if it used a computer than not, since it would be more likely to be reliable then). Such a proof would probably involve an enormous case discussion, and the unreliable part would be the division into cases rather than the discussion of each case. The latter is the part that's easiest to computerise, and so probably the former wouldn't be. The point is now moot, since Dan tells us that fortunately the proof is of the second, much more reliable, kind. [It sounds exactly like the Sloane-Bannai proof I mentioned.] Please don't regard this as a prejudice of mine. My guess is that this proof will only be a few pages long, and that those pages will be easy to follow and check. That's why I believe it's probably correct. John Conway