Philip Franklin was an American mathematician and professor whose work was primarily focused in analysis.

Dr. Franklin received a B.S. in 1918 from City College of New York

City College of New York

The City College of the City University of New York is a senior college of the City University of New York , in New York City. It is also the oldest of the City University's twenty-three institutions of higher learning...

 (who later awarded him its Townsend Harris Medal for the alumnus who achieved notable postgraduate distinction). He received his M.A.

Master of Arts (postgraduate)

A Master of Arts from the Latin Magister Artium, is a type of Master's degree awarded by universities in many countries. The M.A. is usually contrasted with the M.S. or M.Sc. degrees...

 in 1920 and Ph.D.

Ph.D.

A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...

 in 1921 both from Princeton University

Princeton University

Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....

. His dissertation, The Four Color Problem, was supervised by Oswald Veblen

Oswald Veblen

Oswald Veblen 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.-Life:...

. After teaching for one year at Princeton

Princeton University

Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....

 and two years at Harvard

Harvard University

Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...

 (as the Benjamin Peirce

Benjamin Peirce

Benjamin Peirce 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 philosophy of mathematics....

 Instructor), Franklin joined the MIT

Massachusetts Institute of Technology

The Massachusetts Institute of Technology is a private research university located in Cambridge, Massachusetts. MIT has five schools and one college, containing a total of 32 academic departments, with a strong emphasis on scientific and technological education and research.Founded in 1861 in...

 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 basis for L²([0,1]) consisting of continuous function

Continuous function

In mathematics, a continuous function is a function for which, intuitively, "small" changes in the input result in "small" changes in the output. Otherwise, a function is said to be "discontinuous". A continuous function with a continuous inverse function is called "bicontinuous".Continuity of...

s (now known as "Franklin's system").

In 1934, Franklin published a counterexample to the Heawood conjecture

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. It was proven in 1968 by Gerhard Ringel and John W. T. Youngs. One case, the non-orientable Klein bottle, proved an...

, this 12-vertex cubic graph

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....

 is now known as the Franklin graph

Franklin graph

In the mathematical field of graph theory, the Franklin graph 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-dimensional surface is partitioned into cells by a graph...

.

Franklin also worked with Jay W. Forrester

Jay Wright Forrester

Jay Wright Forrester is a pioneer American computer engineer, systems scientist and was a professor at the MIT Sloan School of Management. Forrester is known as the founder of System Dynamics, which deals with the simulation of interactions between objects in dynamic systems.- Biography :Forrester...

 on Project Whirlwind at the Office of Naval Research

Office of Naval Research

The Office of Naval Research , headquartered in Arlington, Virginia , is the office within the United States Department of the Navy that coordinates, executes, and promotes the science and technology programs of the U.S...

 (ONR).

Franklin was editor of the Journal of Mathematics and Physics from 1929.

Franklin was married to Norbert Wiener

Norbert Wiener

Norbert Wiener was an American mathematician.A famous child prodigy, Wiener later became an early researcher in stochastic and noise processes, contributing work relevant to electronic engineering, electronic communication, and control systems.Wiener is regarded as the originator of cybernetics, a...

's sister Constance.