Sokal's research lies in mathematical physics and combinatorics. In particular, he studies the interplay between these fields based on questions arising in statistical mechanics and quantum field theory. This includes work on the chromatic polynomial and the Tutte polynomial, which appear both in algebraic graph theory and in the study of phase transitions in statistical mechanics. His interests include computational physics and algorithms, such as Markov chain Monte Carlo algorithms for problems in statistical physics. He also co-authored a book on quantum triviality. In 2013 Sokal co-authored a paper with Nicholas Brown and Harris Friedman, rejecting the Losada Line, a concept popular in positive psychology. Named after its proposer, Marcial Losada, it refers to a critical range for an individual's ratio of positive to negative emotions, outside of which the individual will tend to have poorer life and occupational outcomes. This concept of a critical positivity ratio was highly cited and popularised by psychologists such as Barbara Fredrickson. The trio's paper, published in American Psychologist, contended that the ratio was based on faulty mathematical reasoning and therefore invalid.
Sokal affair
In 1996, Sokal was curious to see whether the then-non-peer-reviewed postmoderncultural studies journal Social Text would publish a submission which "flattered the editors' ideological preconceptions". Sokal submitted a grand-sounding but completely nonsensical paper titled "Transgressing the Boundaries: Toward a Transformative Hermeneutics of Quantum Gravity." After holding the article back from earlier issues due to Sokal's refusal to consider revisions, the staff published it in the "Science Wars" issue as a relevant contribution. Soon thereafter, Sokal then revealed that the article was a hoax in the journal Lingua Franca, arguing that the left and social science would be better served by intellectual underpinnings based on reason. The affair was front-page news in The New York Times on May 18, 1996. Sokal responded to leftist and postmodernist criticism of the deception by asserting that his motivation was to "defend the Left from a trendy segment of itself". The affair, together with Paul R. Gross and Norman Levitt's 1994 book Higher Superstition, can be considered to be a part of the so-called science wars. Sokal followed up in 1997 by co-authoring the book Impostures Intellectuelles with physicist and philosopher of scienceJean Bricmont . The book accuses some social sciences academics of using scientific and mathematical terms incorrectly and criticizes proponents of the "strong program" of the sociology of science for denying the value of truth. The book had contrasted reviews, with some lauding the effort, and some more reserved. In 2008, Sokal revisited the Sokal affair and its implications in Beyond the Hoax.