As a post-doc, should I pursue incremental research or revolutionary research? I've recently finished my PhD (the field almost doesn't matter, but applied mathematics if it helps), and begun a 3 year grant-funded postdoc with a heavy but very flexible research emphasis, in the same general area as my dissertation.  At their request, I sent my doctoral adviser (a super senior/recently emeritus professor) a list of the papers I'm currently working on/close to submitting, and my ideas for approximately the next 6 months to a year.   

All the papers I'm currently working on represent incremental progress on projects that either developed from my dissertation, or formed as collaborations with others.  I didn't outline any wide-eyed ideas, because all the wide-eyed ideas I have will take several years and a long list of incremental progress to come to fruition. In my opinion (formed in part by reading science philosophers like Kuhn), this is how science progresses: incremental progress as long as it yields fruit.

My adviser responded with an alarming level of "concern" (to put it gently) that my current projects are not ambitious enough and he feels they don't match his expectations of me nor do they sufficiently challenge the status quo.  I got the impression that he seemed to think that by publishing works that are only a slight improvement on the existing literature, I won't amount to anything, which I took to mean I won't be able to get myself a "real" job once my 3 year postdoc is up.

Oh, and by the way, he suggested a solution, which is essentially to drop everything I'm doing and spend more time working on a particular idea that he thinks will revolutionize a particular area of science.  I'm always skeptical any time someone says that, no matter how good the idea, so I pushed back and said no, I'm going to pursue an array of topics, some of which are pretty mainstream, in order to build up a good publication record and good relationships with people in my field.    

Ignoring the complexities of funding (my funding is flexible enough to permit me to work on a wide array of sub-topics), am I right to think that an early career academic doesn't really have the political (or emotional!) capital built up to make a "bold move" into an unproven field, which inevitably might involve trying to convince many experts they're doing it wrong?  It seems to me like "challenging the status quo" is a dangerous game that can only be played by those with Tenure. 

Or do I have it backwards?  Is academic science so competitive that one can only progress, career-wise, by challenging the status quo?  If so, aren't we just chasing each other around in circles, scientifically speaking?
Consider that he may be correct.

There may not be an upper bound, but there is certainly a lower bound to the 'boldness' of work that will move you to the next level. 

Indeed, while progress is usually incremental, few good faculty positions go to individuals that produce 'usual' work. Your senior advisor has certainly had time to feel out what is likely to succeed.