Is Kim Jong-il (or the dear leader) right about math?

The mindcrime liberty show discusses the philosophy of mathematics using a statement made by the "dear leader" of North Korea.  In a statement during a school class of whether 1+1=2 the "dear leader" purportedly  stated that it doesn't always equal 2 rather that sometimes it can equal 1. If you take one drop of water plus another drop of water do you get 1 big drop?  The statement made by the dear leader is obvious alarming propaganda representing an Orwellian nightmarish state, nonetheless, we use this as an inroad to discuss various philosophical issues relating to math. 

Do numbers exist? Are numbers merely a useful fiction or do they have some platonic or abstract existence. We  discuss the different numbering systems including the roman system which arguably is more intuitive as Herbert Spencer argues.    We finally end with a  discussion of  the dearth of "philosophy of mathematics" training or interest from professional mathematicians who tend to treat math as something that just exists and isn't to be questioned.  Why is that the case? Does math need to be knocked off its perch a few levels?