Letter to an amateur mathematician making grand claims
- I appreciate your enthusiasm and I'll have a look at your new paper. I think there's little doubt that you have some talent for math and you seem to have the work ethic. Success being 90% perspiration, and 10% inspiration - I think you have the necessary inspiration and willingness to put in the work.
I think that it's fair to say that your efforts have met with either indifference or mild hostility from the people that society generally considers to be "proper" mathematicians and I think that overcoming this will be your biggest obstacle to your progress. Unfortunately for you, the responsibility for changing this lies squarely on your shoulders and you have a lot of work to do.
Regardless of your own opinion of your mathematical abilities, if you are going to succeed in joining the ranks of "proper" mathematicians, you're going in at the bottom and working your way up. The way to gain a better "reputation" and work your way up the ladder is to present modestly and clearly, some interesting and novel mathematical results. Claiming to prove some long sought-after conjecture is attention-seeking behaviour that people will frown on if you can't follow it up. Your last proof attempt failed at an early stage. A "proper" mathematician would consider this a total humiliation and not attempt to claim to have proved an "aliens have landed" level conjecture a few weeks later.
I suggest you go through your "proof" line by line and check that each successive line proceeds logically and clearly from the previous line or from generally accepted theorems.
With your current attitude, there's a disincentive for me or anyone else looking at your work. It looks like you don't have the knowledge or discipline to make a worthwhile contribution to mathematics. It would help you to work through other professional mathematicians' papers in related areas. In order to understand them you will need to educate yourself about the methods they use and the concepts they introduce. These ideas and methods will then be at your disposal for elements of your proof.
You will also learn to appreciate a well-structured and clear paper. It's fair to say that your last paper was intentionally obfuscating some of your intention, presumably in the hope that the sense of "mystery" created would be somehow impressive. It's not.
Until you invest the effort that all "proper" mathematicians, however modest, have made to understand other peoples' work and until you conform to the norms of the mathematical world in terms of what you claim and how you convey your ideas, you will not be taken seriously and you cannot count yourself as a member of their ranks. Unfortunately until you make these changes to your attitude and presentation, you are relegated to a completely separate group of "wanabee" mathematicians whose other characteristics cannot be described positively.
I used to think that "correctness" was the quality most desired in a mathematician but now I think it's "modesty". If one is appropriately modest in one's claims, other mathematicians will not think too much less of you if (and when!) you are found to be wrong. I think that all serious mathematicians have been found to have made at least one mistake somewhere in their career!
Due to the fact that I found a counterexample to one of your basic conjectures I hereby claim authority to revoke your license to claim to have proved noteworthy conjectures, said revocation to endure until a professional mathematician publicly acknowledges that you have proved a novel, non-trivial result. This should not crimp your style and will be good for you and everyone else.