[dandermotj]

The straight forward answer you'll get is to study a pure/applied science in university up to MS or PhD level. This is probably half of the answer. The other half is being voraciously curious in many many areas and actively self teaching (deliberately or not) through reading, practicing and generally immersing yourself in whatever you're interested in. Working on "big problems" requires experts across fields with unique perspectives and knowledge. Getting a PhD for XYZ might mean your smart, but not necessarily unique.