I am looking for summer internships this year. I originally wanted to try Wolfram but they require people who know computer programming or mathematica(which I would have to enroll into their summer camp to learn more about) so this seems to be out of the question. I wonder if I could shadow a lecturer or researcher at a University(Cambridge is obviously too ambitious because, let's face it, who would want a lower 6th student bothering them for days?) I have had brief interactions with Professor Imre Leader from Cambridge though - should I ask him whether there will be any slight chance that I might be able to get an internship or would it be just a waste of effort? Where else would be good places to get mathematics work experience? If this helps, my favorite branch in mathematics is abstract algebra.