How to be persistent in a polite way? Recently I contacted an important researcher in my field, and he offered me a collaboration with his group. He told me to email him a proposal. Moreover, he recognized that he was usually very busy and received a lot of email, so I should be persistent. He even gave me his personal phone number.

I sent him the proposal, and alerted him by an SMS. He replied that he would look at it. It's been a couple of weeks, so I SMS him again, and he replied that he hadn't had the time yet to look at the proposal, but that he would soon.

This is a very important and unique opportunity for me. In view of his advice to be persistent, and the fact that he is very busy, I want to do what I can to remind him of this, until he acts on it.

What is the most polite way to insist? What time window should I wait before reminding him again?
Having worked in sales and academia, I have often come across the "how often do I contact this person" question. The answer heavily depends on the situation and the person whom you wish to contact.

You have contacted him twice thus far, and he encouraged your being persistent. I would think he would have no problem in you checking back with him every two weeks. Going to his office may even be suggested after several attempts had been made.

Try to approach the professor in your emails with courtesy, but also with urgency. Always thank him for his time, but also stress that you would like to get your research plans finalized, so if he could respond by such and such date it would be helpful.