In my life career, I have only known about three things:
(1)That I like to swim in the ocean.
(2)That I prefer thinking to work.
(3)That it is better to have a lot of money than not.
The first two things led to a PhD in mathematics (title; "Edge Waves on a Beach"). The third led me to applying maths to the stock market (transitionally doing a 'Post Doc' with the Graduate School of Management and then working for trading houses on Collins Street). As a Quantitative Analyst for a trading house you might:
(1) Familiarise yourself with the markets and the house's current problems.
(2) Develop mathematical/statistical/computer solutions.
(3) Teach the fund manager/sales force how to use that solution.
(4) Keep very quiet. Or publish your observations in financial newsletters.
Some of the work was exciting and made big money for the house, but I sometimes found that, while the sales force was always richly rewarded, the support staff were seen as an expense which could be cut in hard times. The alternatives were:
(1) To get on the telephone and sell product to clients.
(2) To build models for the house and trade for the house.
(3) To build models for yourself and trade your own money.
(4) To combine all three, if you are lucky enough to find a house that allows it.
Having worked as a Quantitative-Analyst, Stock Broker and Principal Trader, I have not stopped being fascinated by the incredibly complex game that is the stock market. Mathematics and statistics have given me a huge advantage; particularly in: time series analysis, probability distributions, risk analysis, modelling and arbitrage.