Non academic career for maths graduate I'm currently getting towards the end of a PhD in applied maths. My funding runs out in September, and for personal circumstances (kids, security etc) I can't go into a post-doc yet as I don't think I'll be able to submit until January/February. 

I'd like to go into industry and perhaps return to academia later. I have a BSc in maths (more applied) and my research topic has been looking at the topic of optimal transport (numerical method to solving PDE/ computational mathematics) in collaboration with an industrial partner in an application of pattern analysis. I have quite a broad knowledge of for instance: machine learning; image processing; know a few programming languages. But I don't have the formal training of a computer scientist. 

My question is what is the best way to advertise yourself as someone who is trained as a mathematician rather than computer scientist? Looking at the job market, they don't advertise for people 'who like solving problems' :-) The focus is very much on machine learning, data science. I feel at a disadvantage to someone with a CS background.
Looking at the job market, they don't advertise for people 'who like solving problems'


I think you've already found the perfect way to advertise yourself! There are a lot of companies interested in people like yourself. Now, I'm not a mathematician, and I don't know the full details of your background, but it seems to me like there's plenty of problem solving going on in optimization situations. Since you say your background is in applied mathematics, there may be some overlap with econometrics, too.

And also: don't hesitate to contact companies who are searching for computer scientists if you like the vacancy. Ask them if they would be interested in interviewing someone with your skills palette, it never hurts to ask.