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I have been studying and doing mathematics for over 40 years, too. I do not mean as a hobby. For the last 20 years (almost), I have been working really hard, and have written a lot.
As to failures, there are three kinds of them in mathematics. Being unable to prove a theorem, or making a mistake and coming up with an erroneous proof, is one thing. Reinventing the wheel, proving something that is already essentially known, is another thing. Being unable to have one's paper accepted at a prestigious journal is something else altogether. The first and second kind of failures I perceive as information about what I did wrong. The third ones, as information about how the peer review system is wrong.
I do not try to adopt my research to fit the preferences of the editors and reviewers of the prestigious journals. In this sense, I disregard the third kind of information altogether. I just bet on the time, or else the afterlife, proving that I was right.
***
This is a nontrivial issue, actually. It is not about errors. Everyone agrees that papers with errors should not be published at all, certainly not before the errors are corrected.
The peer reviewers decide what is significant and what is not, what is important and what is not. What is worthy of publication in a first-rate journal, and what (even though correct) only deserves to be published in a third-rate one.
I disregard their opinion. I follow my own judgement of what is important and what is not.
I have been studying and doing mathematics for over 40 years, too. I do not mean as a hobby. For the last 20 years (almost), I have been working really hard, and have written a lot.
As to failures, there are three kinds of them in mathematics. Being unable to prove a theorem, or making a mistake and coming up with an erroneous proof, is one thing. Reinventing the wheel, proving something that is already essentially known, is another thing. Being unable to have one's paper accepted at a prestigious journal is something else altogether. The first and second kind of failures I perceive as information about what I did wrong. The third ones, as information about how the peer review system is wrong.
I do not try to adopt my research to fit the preferences of the editors and reviewers of the prestigious journals. In this sense, I disregard the third kind of information altogether. I just bet on the time, or else the afterlife, proving that I was right.
***
This is a nontrivial issue, actually. It is not about errors. Everyone agrees that papers with errors should not be published at all, certainly not before the errors are corrected.
The peer reviewers decide what is significant and what is not, what is important and what is not. What is worthy of publication in a first-rate journal, and what (even though correct) only deserves to be published in a third-rate one.
I disregard their opinion. I follow my own judgement of what is important and what is not.
