Do I still need a PhD to do research if I have double honours in CS and Pure Math?
I can do research sitting at home


Read a few research papers published in highly regarded venues in your field of interest. Are you capable of producing that kind of work at this point in your training? 


Do you know how to identify important and original research questions? 
Do you know how to select an appropriate methodology for answering a particular research question? 
Do you have a "toolbox" of methods you can apply to different research questions as appropriate? 
Are you able to critically evaluate your own and others' work as experts in the field would?


If not: a PhD is an apprenticeship in which you learn how to do the things mentioned above under the guidance of an expert advisor, in an environment that is designed for learning those skills, hopefully with a salary that allows you to focus on improving your research abilities.