I am just wondering why Mathematics is often defined as The study of Structures, Logic and Numbers which I can concur with but still retain various questions in mind.

I am a postgraduate student of Financial Mathematics now and have loved it even when at bachelor's. Unfortunately, I fail (at the many times I have tried) to give specific reasons for my love for Mathematics.

I am now thinking of what my next step in life might be. I don't feel like sitting down in an office doing Quant work just for the sake of money (I did this program because I thought being a quant was more paying). I have resolved to continue with what I love but I am having problems getting answers to some questions.

I would love to continue doing Mathematics because I think it can literally answer any single question in life. I am particularly interested in number theory (basic knowledge) and functional analysis. I am wondering and asking my self these three questions below;

(i) Are there any common real-life activities that employ Mathematics just at their surface. Rephrasing it would mean I say; How can I do mathematics and explain even sophisticated University mathematics to a minor or non-mathematician and get them loving it?

(ii) Talk about phenomena like robbery, drug abuse, domestic violence. Is there any good mathematics exploring or even explaining these areas of life, leave alone social science?

(iii) What good books can I read about Mathematics in Real life? A google search yielded nearly nothing.

Could someone advise? Thanks very much in advance.