K.P. Williams was born on August 25, 1887 in Urbana, Ohio. He was the son of John H. and Eva Augusta Powers. He received his A.B. in 1908, and A.M. in 1909 from Indiana University. He then continued on to earn his PhD. from Princeton University in 1913. He married Ellen Laughlin Scott on August 20, 1920.
Williams joined the Department of Mathematics at Indiana University in 1909, becoming Distinguished Service Professor Emeritus of Mathematics by 1957.
Williams served in the Indiana National Guard throughout his entire life. He entered as first lieutenant in the Indiana National Guard serving at the Mexican border in 1916. He also served as a captain of Field Artillery in the U.S. Army with the American Expeditionary Force from 1917-1919, only to be appointed as an officer of Field Artillery for the Indiana National Guard in 1921. He retained that position until 1931, when he was promoted to colonel and chief of staff of the 38th division of the National Guard until 1939. He was then promoted to Colonel and Quartermaster of the Quartermaster corps where he commanded the 113th Quartermaster Regiment, in the 38th division in national service until 1941.
K.P. Williams died on September 25, 1958.