How to write a personal statement for a "PhD orientation program" (in mathematics)?
I speculate as I do not know the faculty and their philosophy. 
To my own experiences (PhD 20 years ago, and had some DBA students on my own before I went back to industry), I would suggest you differentiate between research potential and experience against "visiting and orientation". For an orientation program, ...


I would expect people to be open to all directions of learning, in our own as well as in different areas.  
The ability to network, 
ability for out-of-the box thinking, 
ability for telling ideas but also listening. 


Think about onion rings around the exploration of your topics.

How do you show those abilities? Examples from your life?