Philip Franklin (October 5, 1898 – January 27, 1965) was an American mathematician and professor whose work was primarily focused in analysis. Dr. Franklin received a

B.S. A Bachelor of Science (BS, BSc, SB, or ScB; from the Latin ') is a bachelor's degree awarded for programs that generally last three to five years. The first university to admit a student to the degree of Bachelor of Science was the University ...

in 1918 from City College of New York (who later awarded him its Townsend Harris Medal for the alumnus who achieved notable postgraduate distinction). He received his

M.A. A Master of Arts ( la, Magister Artium or ''Artium Magister''; abbreviated MA, M.A., AM, or A.M.) is the holder of a master's degree awarded by universities in many countries. The degree is usually contrasted with that of Master of Science. Tho ...

in 1920 and

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

in 1921 both from

Princeton University Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ...

. His dissertation, ''The Four Color Problem'', was supervised by

Oswald Veblen Oswald Veblen (June 24, 1880 – August 10, 1960) was an American mathematician, geometer and topologist, whose work found application in atomic physics and the theory of relativity. He proved the Jordan curve theorem in 1905; while this was lon ...

. After teaching for one year at Princeton and two years at

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of high ...

(as the

Benjamin Peirce Benjamin Peirce (; April 4, 1809 – October 6, 1880) was an American mathematician who taught at Harvard University for approximately 50 years. He made contributions to celestial mechanics, statistics, number theory, algebra, and the philoso ...

Instructor), Franklin joined the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...

Department of Mathematics, where he stayed until his 1964 retirement. In 1922, Franklin gave the first proof that all planar graphs with at most 25 vertices can be four-colored. In 1928, Franklin gave the first description of an

orthonormal In linear algebra, two vectors in an inner product space are orthonormal if they are orthogonal (or perpendicular along a line) unit vectors. A set of vectors form an orthonormal set if all vectors in the set are mutually orthogonal and all of un ...

basis for ''L''²( ,1 consisting of continuous functions (now known as " Franklin's system"). In 1934, Franklin disproved the

Heawood conjecture In graph theory, the Heawood conjecture or Ringel–Youngs theorem gives a lower bound for the number of colors that are necessary for graph coloring on a surface of a given genus. For surfaces of genus 0, 1, 2, 3, 4, 5, 6, 7, ..., the required ...

for the Klein bottle by showing that any map drawn on the Klein bottle can be coloured with at most six colours. An example which shows that six colours may be needed is the 12-vertex

cubic graph In the mathematical field of graph theory, a cubic graph is a graph in which all vertices have degree three. In other words, a cubic graph is a 3-regular graph. Cubic graphs are also called trivalent graphs. A bicubic graph is a cubic bi ...

now known as the

Franklin graph In the mathematical field of graph theory, the Franklin graph is a 3-regular graph with 12 vertices and 18 edges. The Franklin graph is named after Philip Franklin, who disproved the Heawood conjecture on the number of colors needed when a two ...

. Franklin also worked with Jay W. Forrester on

Project Whirlwind Whirlwind I was a Cold War-era vacuum tube computer developed by the MIT Servomechanisms Laboratory for the U.S. Navy. Operational in 1951, it was among the first digital electronic computers that operated in real-time for output, and the firs ...

at the Office of Naval Research (ONR). Franklin was editor of the

MIT Journal of Mathematics and Physics The journal ''Studies in Applied Mathematics'' is published by Wiley–Blackwell on behalf of the Massachusetts Institute of Technology. It features scholarly articles on mathematical applications in allied fields, notably computer science, ...

from 1929. In 1940 his comprehensive

textbook A textbook is a book containing a comprehensive compilation of content in a branch of study with the intention of explaining it. Textbooks are produced to meet the needs of educators, usually at educational institutions. Schoolbooks are textbook ...

br>''A Treatise on Advanced Calculus''
was first published. Franklin was married to Norbert Wiener's sister Constance. Their son-in-law is Václav E. Beneš.

Books

* ** * * * * ** * * *

References

External links

* * {{DEFAULTSORT:Franklin, Philip 1898 births 1965 deaths City College of New York alumni Princeton University alumni Princeton University faculty Harvard University faculty Massachusetts Institute of Technology School of Science faculty Mathematical analysts 20th-century American mathematicians Mathematicians from New York (state) Scientists from New York City