Options have only been around for 49 years??!! Starting in 1973?? I thought it originated way earlier than that.
I did my undergrad "thesis" on the Black-Scholes Options Pricing Model. It took me a while to try and solve the non-linear partial differential equation that arouse from that -- this was in 1990. My Numerical Analysis class came in handy. I believe that's how RC Merton solved it originally. Even in 1990 Numerical Analysis was fairly new.