One thing for sure, your Maths knowledge is more essential than your software development knowledge. So, if you're interested in that field you should really learn a lot of Mathematics.
> Do I absolutely need to get a degree in this area to participate in this kind of research?
I guess yes (I wish I would say no, really) since it is all about theoretical knowledge it is not easy to validate. Since, it is a research field, domain experts can't spend time in testing your skills so they mainly rely on exams/degree. If you have proved your skills to them at no time, then it is easy to get inside.
> Do I absolutely need to get a degree in this area to participate in this kind of research?
I guess yes (I wish I would say no, really) since it is all about theoretical knowledge it is not easy to validate. Since, it is a research field, domain experts can't spend time in testing your skills so they mainly rely on exams/degree. If you have proved your skills to them at no time, then it is easy to get inside.