* Poetry is subjective: What constitutes a poem is open to interpretation. A limerick, a haiku, a free verse poem, and even a song lyric could all be considered poetry.
* Poetry is constantly being written: New poems are being written every single day, in every corner of the world. There's no way to track or predict when the last poem will be written.
* The world is a big place: Even if we could define "poem" definitively, we'd need to know when the last person on Earth died and whether they wrote a final poem before passing.
So, while we can't identify the last ever poem, it's safe to say that poetry, in all its forms, will likely continue to be created long after we're gone!