Thomas Hakon Gronwall (1877–1932) was a Swedish-American mathematician with a broad range of interests in mathematical analysis, physics, and engineering. Though he was primarly known for his results in pure mathematics, his career as a “consulting mathematician” in America from 1912 to his death in 1932 provides a backdrop against which one can discuss contemporary issues involved in the increasing application of mathematics to engineering, industrial, and scientific problems. This paper attempts a summary of his major mathematical contributions to industrial, governmental, and academic institutions while relating his often difficult life during these years. He decided to leave Sweden and enroll in the corresponding school in Germany, the Charlottenburg Technische Hochschule in Berlin, where he received a degree in civil engineering in 1902. He practiced this vocation in Berlin until deciding to move to America in 1904.