About publishing and children

The problem with children, particularly non-academic ones is that they think that one is brilliant if he or she has published some stuff. They may be even try to publish even unpublished stuff. In my opinion most of the published stuff is rubbish. But it is a process which keeps certain activities alive out of which worthwhile and some dangerous things also come out. Recently one of the children asked me why I am not working on one of the millennium problems. Once I accidentally did for a couple of days and even got my name mentioned in a book ( Poincaré's Prize by George Szpiro) for that effort. Except for exceptioptional people, the way esearch happens is that you may be interested in some general area where you have done well in university and want to do research in that general area. You look around, find schools where such research is done and try to join one of them. Once you join one of them, there are specialists in some of the topics in that area, who tell you what to read to get to what sort of problems in which they may be able to help you. Often it is an industry to publish papers because number of publications are important for survival in the current academic job market. In better places somewhat better things happen but it is very rare to have research places where number of publication do not matter. As usual there are exceptions both among institutions and people. Anyway, the research one does is often determined by this entry point and we often do not get to big problems. But even good places which have entry points to big problems like millennium problems have not really succeeded so far. The one who solved Poincaré conjecture was an outsider.
The reason I looked at PC for a couple of days was this. I did not enter mathematics in a standard fashion. I did not want to be guided and wanted to study topology. In my days there was only one in that area in TIFR and he was abroad. But the institute encouraged me and Raghunathan and Ramanan went out of their way to learn some topology to help me. But their directions were more sophisticated than my interests and I continued my way and Poincaré conjecture was one of the big problems in that area I chose. I did not get any ideas and I knew lot of brilliant people spent years on it without getting anywhere. One of them was C.D. Papakyriakopoulos. He published a long paper on his efforts. One day when I was idly browsing it, I noticed I can reduce it a more accessible one. It did not take much time and I wrote of a short paper and sent it off which was accepted almost immediately. Then I noticed that it could not work. But the paper was accepted , I was young and could do with some publications and I kept quiet. Somebody immediately published a counterexample and since C.D.P. was famous, my name was mentioned as one of those who showed the famous mathematician's attempt did not work. To this day nobody mentioned the absurdity of it that I noticed soon after. That was my one two-day attempt at a big problem.
P.S. The absurdity of CDP's approach as far as I remember: if it worked, it would have shown that a hologram three sphere is a real three sphere which is patently absurd. But to see this, one has to look at his paper and the argument there.