Our existence is solely based on fossil fuel which powers, transports, and fertilizes modern day agriculture. When we head into the down slope of peak oil and inevitably transition into renewable/alternative energy it will be the likes of solar, wind, nuclear, geothermal, and wave. The energy produced will be electricity which will can run our households, and potentially power transportation. However, how do we get food from electricity? I suppose we can desalinate sea water and pump it to product arable lands, but can we create fertilizers and other necessary chemicals that drive our world today?
I think your assumption that fertilizers and other chemicals are critical for 'driving the world'. That being said, yes, I believe we will find other ways to make fertilizer other than using oil. However, if we are smart, it won't be an issue. Oil won't simply stop one day, we will simply be able to produce less and less. During this time we just have to prioritize. Do we want to drive oil powered vehicles or eat
In some ways, we could reduce the need for fertiliser. Instead of growing vast monocultures that require huge amounts of pesticides and growth stimulators, we could rotate crops, plant mutually beneficial crops together, and use more manure and compost.
Algae production for liquid fuels can then be used as fertilizer so there are some good alternatives. Getting rid of subsides for things like corn would also help tremendously.