Math PhD (Nonlinear Programming) switching to Data Science? I am a math Ph.D. student who is interested in going to the industry as a Data Scientist after graduation. I will briefly give some background on my education before posing my question, so that it is better understood: 

Maths Coursework:

This has been mostly in pure maths: topology, functional analysis, etc, but also include more applied ones(on which I have specialized for the dissertation): convex optimization, nonlinear programming, numerical analysis, linear programming, multiobjective optimization. In addition, I have right now 0 knowledge of inferential stat, but I am confident in probability theory. 

Programming: 

I just took a year-long course in the Bachelor, but it was mostly Mathematica and some Java, of which I remember nothing honestly. In this course, the content did not include anything of data structures or design and analysis of algorithms, nor databases management systems. I also learned Matlab on my own for implementing algorithms in the bachelor thesis.

The above background was during the Bachelor and Master's program. Now, during the Ph.D. program, I discovered that Machine Learning is the perfect mix (for me) between Nonlinear Optimization, Programming and applications in the real world, i.e, it is both theoretically interesting and application-oriented. This is the reason why I became so excited to go to industry. Hence, I started learning things on my own(in my little free time) during the last 3 years. 

Short summary of things learned:


Python: I am comfortable implementing optimization algorithms, work with jupyter notebooks and the numpy library (in fact, I had to do this for the dissertation), and doing basic data manipulations and cleaning tasks in pandas. This I learned online, in a platform called dataquest (https://app.dataquest.io). However, I don't think I have enough knowledge to pass an interview in data structures and algorithms(see above).
Machine Learning: I took a master level course in the topic at the uni (since I am in Germany, we don't have courses in the Ph.D., so this was all in my personal time), which I really enjoyed. Topics included: k-NN, PCA, SVM, NN, etc.
Taking a course in Databases this semester, which focuses on SQL.
Taking Deep Learning specialization on Coursera this semester. 


Finally, I want to say that I feel totally capable of learning the topics. In fact, with time I intend to take more graduate-level courses available online(for example, Stanford CS231N, CS234, etc) because, in my opinion, online courses may not be rigorous enough. Hopefully, after the defense, I will be able to focus full time on this.

Hence the questions:


Can I still get hired at this point (I mean, after finishing this semester with the knowledge described above)? I honestly think I am not ready, but I feel confident that I  can get decent in a year.
Am I being too naive in thinking a company would give me a chance? 
What should I do to become more hirable in any case?
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.