No Real Proof
Given that the major players in this scenario all died before the theory could be proven, there’s really no way to know for sure that Mildin’s story helped spark Tarzan’s creation. Mildin’s detailed memoirs were only released, as per his will, when his last heir passed away. But that’s not to say that Burroughs couldn’t have known about them. The broader details being stranded in Africa and of his return were known a few decades before Burroughs ever wrote the book.

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The stories were covered in several articles in The London Times and even romanticized in England’s illustrated papers and magazines. And considering the fact that Burroughs was a very well-read man who did tons of research, it’s unlikely that he would never have heard of Mildin and his adventures.