Józef Henryk Przytycki (/ˌjuːsəf pʃəˈtɪski/; Polish: [ˈjuzɛf pʂɨˈtɨt͡ski]; born October 1953 in Warsaw, Poland), is a mathematician specializing in the fields of knot theory and topology.
In 1987, he and Pawel Traczyk published "Invariants of links of Conway type" (Kobe J. Math. 4, 115−139, 1987), which included a description of what is now called the HOMFLY(PT) polynomial. Postal delays prevented Przytycki and Traczyk from receiving full recognition alongside the other six discoverers. Przytycki also introduced skein modules in "Skein modules of 3-manifolds" Bull. Polish Acad. Sci. 39 : 1–2 (1991) pp. 91–100 (written in 1989); see also his text on the arXiv and his entry in the online Encyclopedia of Mathematics.
A native of Poland, Przytycki received a Master of Science degree in mathematics from Warsaw University in 1977 and, after emigrating to the United States, a Ph.D. in mathematics from Columbia University, where his advisor was Joan Birman. He is currently a professor of mathematics at George Washington University in Washington, DC. According to the Mathematics Genealogy Project, he has supervised 9 Ph.D. students (as of 2016). He has authored and co-authored many mathematical publications, including more than 100 research papers, 10 conference proceedings and 2 books.