cgk said:
Are you all sure that you are not overdoing it? I knew plenty of people in my teens who solved previously unsolved problems routinely. And he is not exactly claiming to have proven the Riemann hypothesis.
I don't think so. This problem is listed in the Wikipedia entry "
List of unsolved problems in mathematics", which means its one of the ~200 most interesting/challenging/difficult (pick your favorite word here) problems. This problem has remained unsolved for over a century, and despite making some headway was unsolved by Ramanujan and Eordos. Do you know plenty of people in their teens who have solved such problems? That seems somewhat improbable.
For the OP to progress, he needs to have an accurate picture of where he is. Possibility A: he's another Ramanujan, someone who has made a great deal of progress without formal education. Indeed, he's
better than Ramanujan, because he's done in 16 years what Ramanujan failed to do in 32. This is a person who can "explain" mathematics to professors who have studied this material for years or even decades. Possibility B: we have someone who is excited, but hasn't gone through the decade-long process to become a mathematician, and as such has made an error that he doesn't see.
What are the odds of Possibility A? Well, there have been perhaps 100 billion people who ever lived, and the number of people who are better mathematicians than Ramanujan might be around ten. On the other hand, the number of people who have made a mistake in mathematics is close to that 100 billion, so a sensible Baysean prior might be 10
-10 or so. Now, we have one piece of evidence: the response of the journal. How often do journal editors make mistakes of this magnitude? Surely not 10% of the time - they'd be fired. Probably 0.1%, but let's be generous and say 1%. That gets is to P of about 10
-12.
So, with P = 0.0000000001% , the OP is justified in pushing ahead.
On the other hand, with P = 99.99999999999% he has made a mistake and should devote his energies to learning more mathematics. In short, to listen more and to read more. I mentioned earlier than scientific journals are a dialog and publishing in a journal you don't read is tantamount to talking without wanting to listen. That's a strategy that is valid - impolite, but valid - 0.0000000001% of the time. The other 99.99999999999% it's still impolite, but no longer valid.