It is indeed possible to build a perfectly satisfying career in mathematics if one is deeply interested in the subject.
A trained mathematician can be very well employed outside academia. Government departments engaged in space research, defence research, aeronautical research, all employ mathematicians to solve their special problems. Today, cryptology is in vogue (the systems ensuring the safety of your credit card transactions are based on some very sophisticated mathematics). Organisations such as the Defence Research and Development Organisation (DRDO) and the Society for Electronic Transactions and Security (SETS) are interested in mathematicians with training in this area. Financial mathematics is another area that leads to well-paid jobs. Computer giants such as IBM and Microsoft have research departments which have highly paid scientists who are either mathematicians or theoretical computer scientists. (They can, for all practical purposes, be considered as mathematicians). Thus, there is plenty of scope, outside academia, for well-paid jobs for mathematicians.
Having said this, it must be emphasised that the majority of mathematicians will end up in academic jobs, namely, in research and teaching. Read full article here.