Eckhardt never finished his PhD in mathematics, claiming that he left graduate school for the trading pits after an unexpected change of thesis advisors.
Despite leaving academia prematurely, Eckhardt has published several papers in academic journals.
In 1993, Eckhardt's article "Probability Theory and the Doomsday Argument" was published in the philosophical journal Mind.
[1] His follow-up article, "A Shooting-Room view of Doomsday" was published in The Journal of Philosophy in 1997.
In 2006, he published "Causal time asymmetry" in the journal Studies In History and Philosophy of Modern Physics.