Walter Helbig Gottschalk (November 3, 1918 – February 15, 2004) was an American mathematician, one of the founders of topological dynamics.

Gottschalk was born in Lynchburg, Virginia, on November 3, 1918, and moved to Salem, Virginia as a child.^[1][2] His father, Carl Gottschalk, was a German immigrant who worked as a machinist and later owned several small businesses in Salem; his younger brother, Carl W. Gottschalk, became a notable medical researcher.^[3]

Gottschalk did both his undergraduate studies and graduate studies at the University of Virginia, finishing with a Ph.D. in 1944 under the supervision of Gustav A. Hedlund.^[1][2][4] After graduating, he joined the faculty of the University of Pennsylvania, and was chair of the Pennsylvania mathematics department from 1954 to 1958.^[1][2][5] In the academic year 1947/1948 he was a visiting scholar at the Institute for Advanced Study.^[6] At Pennsylvania, his doctoral students included Philip Rabinowitz, who became known for his work in numerical analysis, and Robert Ellis, who became known for his work on topological dynamics.^[4] Gottschalk moved to Wesleyan University in 1963; at Wesleyan, he also served two terms as chair before retiring in 1982.^[1][2] He died on February 15, 2004, in Providence, Rhode Island, where he had lived since his retirement.^[1]

Gottschalk and his advisor Gustav Hedlund wrote the 1955 monograph Topological Dynamics.^[1][7][8] Other research contributions of Gottschalk include the first study of surjunctive groups^[9] and a short proof of the De Bruijn–Erdős theorem on coloring infinite graphs.^[10]

As well as being a research mathematician, Gottschalk also put on two exhibits of mathematical sculptures in the 1960s.^[1]

Gottschalk was a fellow of the American Association for the Advancement of Science.^[1]

• Gottschalk, W. H. (1951), "Choice functions and Tychonoff's theorem", Proceedings of the American Mathematical Society, 2 (1): 172, doi:10.2307/2032641, JSTOR 2032641, MR 0040376.
• Gottschalk, Walter Helbig; Hedlund, Gustav Arnold (1955), Topological dynamics, American Mathematical Society Colloquium Publications, vol. 36, Providence, R. I.: American Mathematical Society, ISBN 9780821874691, MR 0074810.
• Gottschalk, Walter (1973), "Some general dynamical notions", Recent Advances in Topological Dynamics (Proc. Conf. Topological Dynamics, Yale Univ., New Haven, Conn., 1972; in honor of Gustav Arnold Hedlund), Lecture Notes in Math., vol. 318, Berlin, New York: Springer-Verlag, pp. 120–125, doi:10.1007/BFb0061728, ISBN 978-3-540-06187-8, MR 0407821.