How can the Quran be written by man?

It wasn't. The angel Gabriel would bring revelations to Prophet Muhammad(pbuh) through God. It was also never written down in his time. His followers were made to memorise the verses, or write them down on barks of trees or stone slabs. After the death of the prophet(saw), dispute arose over the verses, and they were then collected and compiled into what is now known as the Quran. And yes, the prophet(saw) was intelligent, but illiterate, possibly because he was born in a very poor family/tribe.