Freelancing as Physicist / Mathematician

From my own experience (as a physicist with research experience):

• Data science and Finance seem like obvious choices... however both these fields seem to require a great deal of learning and practice before one becomes competitive and can have an edge due to rigorous training in physics/math.
• Scientific writing or vulgarization (writing about science for laymen) might be good as side jobs, but certainly not as a full-time activity: the time one invests in researching the subject and actually writing is not justified by the earnings.
• Doing homework and final projects for students is an area where contracts are easy to find and carry through, but there is no much money there... and there are obvious moral issues involved.
• Doing actual projects for small companies is good, if you already have some research experience (i.e., for those with postdoc, PhD, or at least Master experience). The clients however are hard to find, although they usually come with long-term contracts.

A third area, in addition to @MichaelLai's first two, might be financial services. But, alas, that would also be lots (and lots) of programming. However, you'd also be developing models requiring lots of math.

I have an ms in physics, but most of my work has been programming models for the financial services industry in New York City. For instance, binomial tree models (e.g., https://en.wikipedia.org/wiki/Binomial_options_pricing_model) to solve the Black-Scholes equation (e.g., https://www.hoadley.net/options/bs.htm) Take a look at those pages, and I think you'll agree that your math background will be put to pretty good use (albeit lots different from C*-algebras, etc:).

Also, my experience is mostly contract programming in New York City, where financial services comprise a large segment of the city's economy. I know nothing about San Diego. And also, although contract programming is typically hourly, I've usually been expected to put in hours that amount to full-time work, or even more hours. However, on various occasions I've had fixed-price contracts, where you agree to deliver a product/project for an agreed-upon fixed price regardless of the hours spent. Then your hours are up to you, although the contract usually has a calendar time-frame for various deliverables leading up to the finished project. And that can be a daunting constraint, depending on how well your experience has prepared you to develop the model.

I think that two of the areas that you can definitely look into would be in the area of AI/machine learning for something more specific, or you can brand yourself as a data scientist if you just want to do general data modelling and analysis of 'big data'.

Most people that I know who are well-trained in the mathematical sciences seem to be picking up work in this area.