I am become death? Is that really what he said? How is that not grammatically incorrect?

It’s present-perfect tense, an archaic tense found mostly in poetry and old texts. Oppenheimer was quoting old poetry when he spoke it, so that’s why he kept the same tense.

grammarphobia.com/i-am-become-death

The Grammarphobia Blog: Now I am become Death

Why “Now I am become Death" means "Now I have become Death."

Grammarphobia
Thank you for the enlightening response!
No problem! Sorry you got downvotes for a question lol!
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