Among the world’s wealthiest individuals, especially those over 50, there seems to be a growing shared passion for discovering the elixir of life. Billionaires including Jeff Bezos, Bill Gates, Larry Page and Michael Bloomberg have all invested personal wealth in biotech startups that research everything from cancer cures to cell reprogramming. Elon Musk, the richest of them all, is a notable exception. Although his main business endeavors—doing away with fossil fuel on Earth and colonizing Mars—have time horizons spanning decades and even centuries, the entrepreneur himself isn’t that interested in immortality.

In a podcast interview with Peter Diamandis, the founder of the nonprofit XPrize Foundation, that........

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