I have an MTech in Industrial Drives and Control (Electrical Eng). After that could not go for any work... After giving some tuition, I came to the conclusion that I am genuinely interested in mathematics... be it to study or to teach. Is it possible for me to do a PhD in mathematics? Or, are there any PhD options in Electrical Eng that are related to mathematics? I am even ready to take time and get a bachelors and masters in mathematics by distance education.
The only real difficulty with joining a doctoral program in CS or mathematics is getting admitted to a graduate program. If you can get admitted you are on your way. In the US admissions committees generally expect that you will have the knowledge in a "typical" undergraduate degree program. The Mathematics Association of America (MAA) has made curriculum recommendations to colleges. You can read those to see whether you have the knowledge background that people will be looking for.
Those recommendations are a guideline, however, and most colleges will deviate from them somewhat. On the other hand, most colleges will teach other, somewhat more advanced, topics to undergraduates. Those get little mention in the recommendations. But each undergraduate program seeks to give a broad look at mathematics.
But if you have the knowledge in most of the recommended areas and can demonstrate it somehow, it will be easier to make your case for admission. Many students move from a BA/BS program directly to doctoral studies but initially there is (in the US) a lot of coursework for such students prior to specializing in a research area. So there is opportunity to make up for topics you aren't familiar with.
Is it possible for me to do a PhD in mathematics?
Yes it is possible - there is no rule that says you have to stick to your undergraduate discipline and engineering is sufficiently quantitative that you probably meet the admissions requirements. However, because you do not come from a pure math background, you might find it challenging to begin with. I did a masters in mathematics after a chemical engineering undergraduate and I had to work quite hard to bridge the gap - for example in functional analysis, which I knew nothing about. I would actually recommend you consider a masters (but not another bachelors!), as it gives you a chance to see if you really would enjoy spending +4 years working in pure mathematics and will likely strength your application to PhD programs.
are there any PhD options in Electrical Eng that are related to mathematics?
Control theory is pretty mathsy.
If you are from India,All your questions will be answered here about going to mathematics after engineering