**Philip Franklin** was an American mathematician who worked in analysis and graph theory.

- Philip attended the College of the City of New York receiving his B.S. in 1918, the year after Emil Post.
- After graduating, Franklin spent a year at the U.S. Army Proving Grounds in Aberdeen, Maryland.
- This was to have a very considerable influence on Franklin, mainly because he met and became friendly with Norbert Wiener.
- While he was in the Ordnance Department of the Aberdeen Proving Grounds, Franklin submitted Calculation of the Complex Zeros of the Function P(z) Complementary to the Incomplete Gamma Function to the Annals of Mathematics; it was published in September 1919.
- Franklin had already presented the paper on 26 April 1919 at a meeting of the American Mathematical Society held at New York City.
- On completing his doctorate Franklin remained at Princeton where he was an Instructor in Mathematics during 1921-22.
- While at Princeton, Franklin submitted a number of papers on widely different topics which were published in 1921 and 1922.
- After his year as an instructor at Princeton, in 1922 Franklin went to Harvard University where he was appointed a Benjamin Peirce Instructor.
- We have not yet mentioned one important outcome of Franklin's time at the Aberdeen Proving Grounds.
- In 1924 Franklin was appointed Instructor in Mathematics at the Massachusetts Institute of Technology.
- We have already looked at the titles of some of Franklin's papers up to 1922.
- This is now known as "Franklin's system".
- In A Six Color Problem (1934) Franklin gave a 12-vertex cubic graph whose embedding into the Klein bottle provides the only known counter-example to the Heawood conjecture.
- Franklin's book is an admirable attempt on a much broader scale to combine rigour with completeness in a volume of modest size.
- Four years after publishing this rigorous text, Franklin published another text Methods of advanced calculus on similar material but now with very different students in mind.
- In addition to this impressive collection of books, Franklin was editor of the Journal of Mathematics and Physics from 1929.
- We should mention Franklin's service to the mathematical community through serving on the Board of Governors of the Mathematical Association of America during 1940-42 and again during 1954-56.

Born 5 October 1898, New York, USA. Died 27 January 1965, Belmont, Massachusetts, USA.

View full biography at MacTutor

Analysis, Origin Usa, Puzzles And Problems, Topology

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive