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You are at a career stage where it is reasonable to think of your first move and you appear to have a strong academic and work record to attract prospective employers.
If you want to move away from mainframe work, both user and supplier organisations could give you access to a wider range of applications, provided the companies are large enough. However, the change will be smoother if you can apply your current operating system knowledge.
Programming and software engineering are ubiquitous roles that demand the logic and systematic thinking that is implicit in a maths degree. As a mathematician, you might consider working in science-based technologies such as astronomy or aerodynamic modelling. Depending on your experience, you could also look at developing engineering applications in a design function. One consideration is that "deep" mathematical work commonly uses mainframes to some degree.
More generally, numeracy skills are important to any organisation that does large-scale number-crunching. These include market research companies. For job-hunting, the vacancy sections of the trade press are an obvious source, as are recruitment agencies. Try to evaluate all the implications of a particular post and where it will lead you. It is an old adage, but still true, that you should be looking ahead to the job after the next one.
Solution by Jane Standley, E-skills NTO