Food is not a problem in this very tiny timespan of human existence, because our farming is incredibly inefficient right now.Food is not the problem (until climate change kicks in harder).
Effectively how modern farming works is, you are injecting HUGE amounts of energy into the soil in the form of fertilizer, and you get a fraction of that energy back in the crops you yield. Yes that means that an acre of land will give you 100x its natural production, but at the cost of 1000x the energy (probably an exaggeration but you get the point).
This has two issues:
1) It relies on energy sources that are not inexhaustable. We all know fossil fuels will run out someday, its just a question of when. In theory renewables can make electricity that can be reconverted to create synthetic fertilizers, though there is a transformation cost there as well and you still have to scale up renewable sources, the infrastructure and maintenance are not free.
2) The bigger issue....we are exhausting the land. Slowly and surely, our farmland is experiencing desertification, top soil erodes away, etc. The techniques we are using are simply not sustainable for long term farming.
So yeah, in a very tiny window of human civilization we have made food supplies beyond plentiful. But there is absolutely no guarantee that would last, in fact the lessons of history and nature would suggest that they won't, and mass famine will return to the world at some point....its just a matter of time.