Although there is no evidence it ever came to fruition, it reflected Mr. Epstein’s longstanding fascination with transhumanism, a modern-day version of eugenics.

Mr. Epstein, who used his wealth to cultivate relationships with a wide range of business, political and scientific luminaries, also claimed to be bankrolling efforts to identify “a mysterious particle that might trigger the feeling that someone is watching you.”

How we know: The Times reviewed public documents and interviewed more than a dozen of Mr. Epstein’s acquaintances, including two award-winning scientists and an adviser to wealthy individuals, who said he had told them about his vision.

What’s next: A federal judge set a tentative trial date for Mr. Epstein for mid-2020 in New York.