Philip Franklin attended the College of the City of New York receiving his B.S. in 1918, the year after Post. After graduating Franklin went to the Princeton University to undertake doctoral studies. He was awarded his Ph.D. in 1921 for a thesis The Four Color Problem written under Veblen's supervision.
On completing his doctorate Franklin remained at Princeton where he was an instructor in mathematics 1921-22. Then in 1922 he went to Harvard where he was Benjamin Peirce Instructor until 1924.
In 1924 Franklin was appointed Instructor in Mathematics at Massachusetts Institute of Technology. He was to remain at MIT, being promoted to assistant professor in 1925. Then, during 1927-28 he held a Guggenheim Fellowship, befor being promoted to associate professor in 1930 and full professor seven years later.
He worked on the four colour problem and also published books on calculus, differential equations, complex variable and Fourier series. In particular he wrote Differential equations for electrical engineers (1933), Treatise on advanced calculus (1940), The four colour problem (1941), Methods of advanced calculus (1944), Fourier methods (1949), Differential and integral calculus (1953), Functions of a complex variable (1958) and Compact calculus (1963).
In addition to this impressive collection of books, Franklin was editor of the Journal of Mathematics and Physics from 1929. In 1943 he was honoured by his old College where the College of the City of New York awarded him the Townsend Harris Medal.