I recommend making sure you are good with Guesstimation to start (The book of that name by Weinstein and Adams). Be sure to create your own questions and attemp

I recommend making sure you are good with Guesstimation to start (The book of that name by Weinstein and Adams). Be sure to create your own questions and attempt to answer them. Watch some TED talks and try to use mathematical skepticism to criticize them. Doing all this should make you comfortable using mathematics as a tool. Once you are in that frame of mind, you can explore and have fun with the other topics as ably listed in the other comments on this page. Think of math as a faithful toolkit to explore the world. Once you start to try to describe the world in mathematical language, the more proper tools of mathematics will make much more sense. Also, keep in mind that pretending things are lines is really useful. See the secant method.