Indeed, if I could find one phrase that would sum up my wishes for you on this occasion, I think it would be devoted to convincing you of the futility of living too much by the advice of others.
What can I say to you that will not contravene this conviction? … It is this: that you should never cease to be aware that all aspects of the learning you have acquired, and will acquire, are possible because of their relationship with negation – with that which is not, or which appears not to be.
The trouble begins when we start to be so impressed by the strategies of our systematized thought that we forget that it does relate to an obverse, that is hewn from negation … And when that happens, when we forget these things, all sorts of mechanical failures begin to disrupt the function of human personality. When people who practice an art like music become captives of those positive assumptions of the system, when they forget to credit that happening against negation which system is, and when they become disrespectful of the immensity of negation compared to system – then they put themselves out of reach of that replenishment of invention upon which creative ideas depend, because invention is, in fact, a cautious dipping into the negation that lies outside system from a position firmly ensconced in a system …
It would seem to me that your success as teachers would very much depend upon the degree to which the singularity, the uniqueness, of the confrontation between yourself and each one of your students is permitted to determine your approach to them. The moment that boredom, or fatigue, the ennui of the passing years, overcomes the specific ingenuity with which you apply yourself to every problem, then you will be menaced by that overreliance upon the susceptibly positive attributes of system.
from “Advice to a Graduation,” in The Glenn Gould Reader, pp. 3-5.
You can check out the whole speech from the Library and Archives Canada.