In his many publications, Fortnow has contributed important results to the field of computational complexity. While still a graduate student at MIT, Fortnow showed that there are no perfect zero-knowledge protocols for NP-complete languages unless the polynomial hierarchy collapses. With Michael Sipser, he also demonstrated that relative to a specific oracle there exists a language in co-NP that does not have an interactive protocol. In November 1989, Fortnow received an email from Noam Nisan showing that co-NP had multiple prover interactive proofs. With Carsten Lund and Howard Karloff, he used this result to develop an algebraic technique for the construction of interactive proof systems and prove that every language in the polynomial-time hierarchy has an interactive proof system. Their work was hardly two weeks old when Adi Shamir employed it to prove that IP=PSPACE. Quickly following up on this Fortnow, along with László Babai and Carsten Lund, proved that MIP=NEXP. These algebraic techniques were expanded further by Fortnow, Babai, Leonid Levin, and Mario Szegedy when they presented a new generic mechanism for checking computations. Since this time Fortnow has continued to publish on a variety of topics in the field of computational complexity including derandomization, sparse languages, and oracle machines. Fortnow has also published on quantum computing, game theory, genome sequencing, and economics. Lance Fortnow's work in economics includes work in game theory, optimal strategies, and prediction. With Duke Whang, Fortnow has examined the classic game theory problem of the prisoner's dilemma, extending the problem so that the dilemma is posed sequentially an infinite number of times. They investigated what strategies the players should take given the constraints that they draw their strategies from computationally bounded sets and introduce “grace periods” to prevent the dominance of vengeful strategies. Fortnow also examined the logarithmic market scoring rule with market makers. He helped to show that LMSR pricing is #P-hard and propose an approximation technique for pricing permutation markets. He has also contributed to a study of the behavior of informed traders working with LMSR market makers. Fortnow has also authored a popular science book, titled The Golden Ticket: P, NP and the Search for the Impossible., which was loosely based on an article he previously wrote for CACM in 2009. In his book, Fortnow provides a non-technical introduction to the P versus NP problem and its algorithmic limitations. He further describes his book and illustrates why NP problems are so important on the Data Skeptic podcast.