How to prepare for the job market during a (pure math) PhD First of all, I apologise if a similar question has been asked before, I did some research but couldn't find a satisfying answer.

I'm a second-year pure math PhD-student (in EU, if that matters) in a field with relatively few real-world applications (low-dimensional topology). I am already determined that I won't pursue an academic career after the PhD, so I will have to transition into the job market at some point. However, this frightens me because my field has no real-world applications, and I think that it might be a good idea to start expanding my knowledge to a different field (say, computer science or economy). This brings up the following question: How do you do this during a PhD?

To be more precise, let's say I am interested in financial markets and would like to steer towards a job in quantitative finance. What is the best way to prepare for this during my PhD studies? The following options come to my mind:


Reading books and self-study. However, do employers value knowledge purely gained from self-studying (without any degree behind it)?
Participating in relevant courses at my university. However, does that make sense if I'm not a registered student and therefore won't get grades?
Participating in online courses (such as Coursera, for example). However, do employers value the participation in such courses?
Not doing anything, focus on my PhD and start looking for internships afterwards (to get knowledge).


I am aware that in almost any case mentioned above, I will still lack any sort of actual work experience (which is probably going to be the biggest problem in finding a job). However, I believe that I still might be in a better position if I already have some theoretical knowledge about a job's broader field rather than no knowledge. Of course, if there are any other options that I didn't mention above please let me know.

I would highly appreciate any advice, guidance or personal experience on this topic. Thanks!
Here are a few things that might benefit both your PhD and your preparation for the job search:


Communicate with your advisor. Setting goals and making plans with your advisor will help align how you measure the success of your graduate experience. You can also report to your advisor about your progress towards these goals; accountability goes a long way. Finally, your advisor can help you prepare for and find a job in industry, but only if they know that's what you want to do!
Code and compute. If you don't know how to code, take some courses and learn how. If you do know how to code, keep improving your abilities. Computing is a valuable skill for research, since examples will help you make sense of new ideas and constructions. In industry, computing will be invaluable. As a mathematician, employers will want to hire you for your analytical skills. These skills will be much more useful to them if you are comfortable gathering, producing, analyzing, and communicating data that they care about.
Connect. If you have the opportunity, do an internship in industry. You may find things that you like or dislike about working outside academia, and you may gain new insights into your academic work. You should also try networking. For better or worse, who you know makes a big difference in finding jobs. Your advisor might have some contacts in industry, or your university might have an employment center that can help you with this.


As an aside, even low-dimensional topology might not be as far removed from applications as you might think. Differential geometry and algebraic topology both have applications to data analytics and machine learning. Depending on your exact specialty, topological data analysis could be an opportunity for you to apply ideas from your PhD to finance or whatever industry you decide to join.