Worry about stealing of research ideas
You need to consider what role you want the math professor to take: are you looking for a co-author, a collaborator, a consultant, or a service provider.

Since you lack background in one area and are working in a place that does not prioritize publications, I would consider bring the individual on as a co-author. If that is your decision you need to provide the co-author with everything you are planning on doing so that he/she can make an informed decision. This obviously puts you at risk of being scooped. This then leads to the question of how to minimize the chances of being scooped. The first thing to remember is most researchers do not want to get into a publish first race. Scooping tends to be accidental and a result of two people independently starting the same/similar projects. You can minimize your chances by contacting an established person who is known to play "nice". The second thing you can do is to bring the research along as far as you can without the collaborator. This means they will be starting from so far back that it is unwise to enter the race.