I don't know at this point if more heads are necessary to solve the various challenges facing humanity today. To some extent, smart minds will be limited by sparse money. Take biomedicinal research for example: scientists are increasingly leaving their fields because NIH's funding has stalled in recent years, and unless you have a pitch to DOE, DARPA, or another organization, you're just going to be fighting over the same pool money as everyone else, and more minds can only increase the competition and decrease the ability of any one person to hold a stable career and investigate risky subjects.

That's true, I hadn't really thought of that. I suppose it's also eminently possible that funding imbalances will skew the relationship between general population growth and growth in a particular sector... But I do still think some level of pop. growth is necessary to maintain our current rates of progress. As different fields get more and more complex, specialization is necessary, which must eventually lead to a need for more laborers.