Dear Maya, I am sorry to hear about this frustrating situation.
I do think that the above mentioned post on how to control one's anger
(in a relationship) applies also here insofar as to identify the source
of your anger: is it a threat to your self-image due to his criticism
and now the boss who starts to believe him? Injustice? Lack of control
over the situation? All of the above? Etc.
Sometimes, already getting a better grasp of where the anger is coming
from helps to reduce it. Another tool which helps me significantly to
reduce the anger is to try to understand the other person, genuinely. As Jean was mentioning earlier in the other post about colleagues one can't stand [sidenote: how do I include links to other posts? - it is a bit pathetic that I can't figure this out given that I studied Computer Science ;o), though I didn't see any info on how to do this yet], most people are good, are at least, usually have good intentions. For example, in your story, you mentioned that 'he began doing everything to infuriate me', attributing to him an intention to actually infuriate you. Are you sure it is the case? Given that he is attracted to you as you said, it would be normal that he tries to meet with you as often as he can, not to infuriate you but rather because he likes to be with you. This is still annoying for you, but at least it makes it more bearable than to think that he is actually doing it on purpose, in full knowledge that it will infuriate you (are you sure he knows that it infuriates you, e.g.?). I personnally think that these situations, where one gets angry at someone else because of not just what they do but also because they think the other person does it on purpose (which is rarely the case in my [young and naive] experience), are actually quite common. And separating the what happens vs. what we think the other person's intentions are, can often help to reduce the level of anger.
Finally, about what to do, here are a few questions for you:
1) Do you have to work with this guy, or can you have somebody else supervise him?
2) You said that he is not very talented and unable to learn from mistakes. If this causes a lot of problems in your work environment, do you have objective facts to back this up to bring to your boss so that she could get a more realistic picture of the situation rather than just his sweet talk? Don't make it personal, but rather put it in concrete terms, as what you are trying to achieve with your job and what are the difficulties you are facing because of him.
Just some initial food for thoughts...