If the above post is talking about the actual compilation of cryptographic information, Cryptonomicon, I don't have much to say other than I am sure that it will have more than enough information regarding the subject.
On the other hand, if he's talking about the recent book by Neal Stevenson, I highly recommend that you check it out. It isn't exactly a reference book on cryptography, but it is an extraordinary, complicated and page-turning book about the applicationns of cryptography (or at least the essence thereof) in three different settings: the events surrounding the struggle to decipher German codes during WWII, the travails of a special military detatchment in the same war, and modern efforts to establish a data-haven in South-East Asia. It is probably too long to be useful to a school project and, because it is fiction, probably not useable as a source, but if you get into cryptography, I hope you'll check it out.
Before too many intelligent minds fall to the task of disproving Goldbach's conjecture, let me suggest the likely purpose to the proposed contest:
Goldbach's conjecture is very probably true; mathematicians and number theorists don't need to be reminded of that and likewise don't need to be bothered by "amateurs" (really, lay-people without formal education in number theory) who suggest that the conjecture is false. In all matters of fact, while I am sure that Faber and his erudite associates would be happy to be presented with a valid counter-example, said mathematicians probably aren't losing any sleep over the possibility. What Tony Faber is looking for and what's worth $1m to him is not the labors of the unitiated towards a hopeless cause but is instead the establishment of the conjecture's logical truth by means of established principles of number theory -- he wants to know how this elegantly simple and ostensibly true statement may be derived from postulates and previous proofs, not, regrettably, whether or not it is true.
There has been some grumbling over the apparent fact that Faber is trying to keep the proof of Goldbach's conjecture within the mathematical community. If the conjecture is proved, it will be through the collaborative efforts of the professional mathematic community -- I simply can't see someone without extensive background in number theory really having a chance of winning the contest. Remember that the proof of Fermat's theorem was by no stretch of the imagination simple and elegant. If there were an elegant proof to Goldbach's conjecture, it would almost certainly have already been realized by mathematicians who are just as intelligent and, if anything, better-versed in matters of number theory than folks like you and me, and if there is a proof, I suggest that its development will not be a feat accomplishable by anyone who doesn't make their living in mathematics.
And before anyone tries to make this proof a black&white, true/false issue (too late?), let us remember the work of mathematician Kurt Gödel:
Gödel's most famous contribution was the proof that some statements about natural numbers are true but unprovable.... [his] proof demonstrated that the axioms of number theory are incomplete. That is, there are true statements about the natural numbers that cannot be proved by those axioms. (J. W. Dawson, Jr., Scientific American - June 1999)
Do I underrate the ingenuity of the human mind? I hope so; however, I would like to think I am merely being realistic. It seems to me that blind beginner's luck has been drastically overrated in response to the proposed contest.
To those of you interested by the prospect of testing every reasonably-large even number to find a counter-example and thus disprove the conjecture, and especially to those of you who have suggested that the resources of distributed.net be used in so doing, please refer back to sela, 3/19. I'm afraid you'll be wasting your time.
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On the other hand, if he's talking about the recent book by Neal Stevenson, I highly recommend that you check it out. It isn't exactly a reference book on cryptography, but it is an extraordinary, complicated and page-turning book about the applicationns of cryptography (or at least the essence thereof) in three different settings: the events surrounding the struggle to decipher German codes during WWII, the travails of a special military detatchment in the same war, and modern efforts to establish a data-haven in South-East Asia. It is probably too long to be useful to a school project and, because it is fiction, probably not useable as a source, but if you get into cryptography, I hope you'll check it out.
Goldbach's conjecture is very probably true; mathematicians and number theorists don't need to be reminded of that and likewise don't need to be bothered by "amateurs" (really, lay-people without formal education in number theory) who suggest that the conjecture is false. In all matters of fact, while I am sure that Faber and his erudite associates would be happy to be presented with a valid counter-example, said mathematicians probably aren't losing any sleep over the possibility. What Tony Faber is looking for and what's worth $1m to him is not the labors of the unitiated towards a hopeless cause but is instead the establishment of the conjecture's logical truth by means of established principles of number theory -- he wants to know how this elegantly simple and ostensibly true statement may be derived from postulates and previous proofs, not, regrettably, whether or not it is true.
There has been some grumbling over the apparent fact that Faber is trying to keep the proof of Goldbach's conjecture within the mathematical community. If the conjecture is proved, it will be through the collaborative efforts of the professional mathematic community -- I simply can't see someone without extensive background in number theory really having a chance of winning the contest. Remember that the proof of Fermat's theorem was by no stretch of the imagination simple and elegant. If there were an elegant proof to Goldbach's conjecture, it would almost certainly have already been realized by mathematicians who are just as intelligent and, if anything, better-versed in matters of number theory than folks like you and me, and if there is a proof, I suggest that its development will not be a feat accomplishable by anyone who doesn't make their living in mathematics.
And before anyone tries to make this proof a black&white, true/false issue (too late?), let us remember the work of mathematician Kurt Gödel:
Do I underrate the ingenuity of the human mind? I hope so; however, I would like to think I am merely being realistic. It seems to me that blind beginner's luck has been drastically overrated in response to the proposed contest.
To those of you interested by the prospect of testing every reasonably-large even number to find a counter-example and thus disprove the conjecture, and especially to those of you who have suggested that the resources of distributed.net be used in so doing, please refer back to sela, 3/19. I'm afraid you'll be wasting your time.