When I encountered difficult problems

In this talk , I describe briefly my research experience when I encountered very difficult problems and how I responded, right or wrong. For this purpose, I have chosen the difficulties into four subjects:

(a) when theorists seemed to encounter a deadlock for a long time,
(b) when there is a well-accepted theory, but there seemed to exist a seriously contradicting observed fact,
(c) when there was a generally accepted morphology of a phenomenon, which does not seem agree with my observations,
(d) when a single theoretical approach or theory has prevailed on a problem.

Most researchers must have encountered some of these or similar problems.