Changing research topic I am a Master's student doing a research internship. I do not have to defend the results of my research at the end of the internship; however, I would ideally get a publication out of this. 

I am working with a well-respected professor in applied mathematics. When he suggested a research topic, I quickly agreed. At first I found the topic a little bit strange and uninteresting, but I thought that I didn't understand it well. It seemed like he had not thought about the topic a lot, but he seemed enthusiastic about it.

After learning more, I confirmed my initial impressions. This problem has been studied extensively before, and my special case doesn't seem all that special. I reported my findings to the prof and he seemed to agree. Yet he suggested that I perform several numeric experiments to further investigate. I did so, but didn't get any definitive results. My supervisor had said that if the experiments failed, we would change the topic. But now he just keeps suggesting new ones. 

I do not like the topic and would like to change topics as quickly as possible. However, I do not want to be seen as one who just jumps from topic to topic when something doesn't work. During our last meeting I attempted to "corner" the professor, asking for the interpretation of the possible outcome of the experiment in advance. Also, I was seemingly displeased by the idea of more experiments because I was arguing about their meaninglessness. The supervisor said something like "you seem to be looking for the excuse to not do the job." I definitely want to do the work as I want to get results. Yet, I think our current efforts will be fruitless.

What should I do?
First, negative results are useful too: for instance if you can show that the method is inapplicable by trying every reasonable option to make it work, this is a result by itself and it might be worth publication. Since your intuition is that this method cannot work, why not try to prove it? It doesn't really matter that your supervisor doesn't share this intuition.

It's not very surprising that your supervisor insists on continuing in this direction since it was what you agreed to at the start. Now if this is not something you want to do, then you have no choice: you need to talk to them about switching to a different topic. Mind that it's not always feasible to switch to a completely different topic during the course of a research internship.

Without knowing the details, my impression is that it's probably in your interest to finish the work that has been started rather than restart something from scratch (I assume that it's only for a few months). The important lesson here is: don't accept a topic that you don't like in the first place. Keep this in mind if you choose to do a PhD later ;)