We're all approaching this from the perspective that the correct thing for your friend is to stay in mathematics. Perhaps not. I think of three very talented friends who eventually left mathematics. One left to become a successful orthodontist, another actually got his Ph.D., but decided to become a doctor instead. The third sold all his worldly possessions and took up with the Worker's Party. I have two children in theatre, and I remember the advice they received from faculty at the schools they were considering:"You've got to want this more than anything else." I don 't think mathematics is much different. Once the desire is gone, one can try to get it back, or consider if it might be time to move on. As a mathematician, I hope your friend finds some way to get back in the groove. Time will tell.
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