In US and Canada, lawyers, dentists and doctors are all from different backgounds. As far as I know, one Norbel Economics winner (his name seems to be Lucus, now teaching at UofChicago) used to be a sociology master student and do not have any training on maths. But this guy excells. Strengths and weakness are fuzzy concepts. Sticking with existing path sometimes means dead-end, Why not try to walk around?