Math PhD (Nonlinear Programming) switching to Data Science?
Data science jobs cover a wide range of different activities so any answer is likely to be subjective. I'm in academia so my knowledge of the job market is limited, but from what I can see:


The current context is very favorable to data scientists looking for a job, so anybody with some basic knowledge of ML has a chance. You're already above this level so no worries on this front imho. The trend is reasonably likely to continue like this, but nobody knows the future.
Ideally to increase your chances you should be able to demonstrate that you have some hands-on experience: for instance github projects, participation to a ML competition, this kind of thing.
Don't neglect your maths PhD: you seem to have a lot of free time to learn data science, good for you... But make sure the PhD is your top priority, it's going to be a great asset on your resume even if it's not related to data science.