The answer is complex and depends on what you mean by "write."
What we know:
* No historical evidence exists to confirm Homer's existence. We have no contemporary accounts of his life, no writings by him besides the epics, and no confirmed archeological findings.
* The poems were likely transmitted orally for centuries before being written down. The style and content suggest a long oral tradition.
* The poems were attributed to Homer by ancient Greeks. But this attribution may be a later development.
Arguments for Homer's authorship:
* The poems display a remarkable consistency in language, style, and theme. This suggests a single author, though some argue it could be a group of poets working over time.
* The epics are full of rich detail about ancient Greece. This suggests the author had firsthand knowledge of the culture and society.
Arguments against Homer's authorship:
* The poems contain inconsistencies and contradictions. This suggests multiple authors or a long process of oral transmission.
* The language and meter of the poems are remarkably consistent, which is unusual for oral poetry. This raises questions about the authenticity of the written texts.
* The epics contain references to events and places that were unknown in Homer's supposed time. This suggests the poems were written or edited centuries later.
Conclusion:
While we cannot definitively prove or disprove Homer's authorship, most scholars now believe he was a product of a long oral tradition rather than a single individual.
The poems were likely passed down through generations of poets, with each adding their own verses and embellishments. Eventually, they were written down and attributed to Homer, who may have been a real person or a mythical figure.
The important thing is that the poems are powerful works of literature that have resonated with readers for centuries, regardless of their origins.