Scientific intuition and funding: that the two rarely coincide:

In science the Apollonian [systematic thinker] tends to develop established lines of perfection, while the Dionysian rather relies on intuition and is more likely to open new, unexpected alleys for research. Nobody knows what “intuition” really is. My guess is that it is a sort of subconscious reasoning, only the end result of which becomes conscious.

These are not merely academic problems. They have the most important corollaries and consequences. The future of mankind depends upon the progress of science, and the progress of science depends on the support it can find. Support mostly takes the form of grants, and the present methods of distributing grants unduly favor the Apollonian….

A discovery must be, by definition, at variance with existing knowledge. During my lifetime, I made two. Both were rejected offhand by the popes of the field. Had I predicted these discoveries in my applications, and had these authorities been my judges, it is evident what their decisions would have been.

Albert Szent-GyörgyiScience, vol. 176, 1976