Sperm whales are very hard to study. We certainly do not, as yet, have the sort of data on them from which we could directly measure their relative intelligence among whales as confidently as we can rank our own intelligence against other primates. Nor do we have much in the way of problem solving anecdotes from which to guess, so I have begun looking for more indirect measures.
We are faced with a situation, rather like global warming, where our historic measures of temperature are insufficient to give a picture sufficient to our needs. For the period before this we have many naturally occurring phenomena that layered down material from which we can extract the true temperature of earlier years, but only if we make many assumptions about other complicating factors not playing too great a role. In the pages below I have assembled some proxies that pertain to intelligence, and for which we do have adequate data on sperm whales. Because these are more indirect indicators of intelligence, I include them below (from the menu) for the purpose of open discussion.