|Born||October 5, 1898|
|Died||January 27, 1965 66) (aged|
|Known for||Franklin graph|
|Doctoral advisor||Oswald Veblen|
|Doctoral students||Alan Perlis|
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. 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. in 1920 and Ph.D. in 1921 both from Princeton University. His dissertation, The Four Color Problem, was supervised by Oswald Veblen. After teaching for one year at Princeton and two years at Harvard University (as the Benjamin Peirce Instructor), Franklin joined the Massachusetts Institute of Technology 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 functions (now known as "Franklin's system").
In 1934, Franklin disproved the Heawood conjecture 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 now known as the Franklin graph.
Franklin also worked with Jay W. Forrester on Project Whirlwind at the Office of Naval Research (ONR).
Franklin was editor of the MIT Journal of Mathematics and Physics from 1929.
In 1940 his comprehensive textbook 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.
In mathematics, a conjecture is a conclusion or a proposition which is suspected to be true due to preliminary supporting evidence, but for which no proof or disproof has yet been found. Some conjectures, such as the Riemann hypothesis or Fermat's Last Theorem, have shaped much of mathematical history as new areas of mathematics are developed in order to prove them.
In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color. Adjacent means that two regions share a common boundary curve segment, not merely a corner where three or more regions meet. It was the first major theorem to be proved using a computer. Initially, this proof was not accepted by all mathematicians because the computer-assisted proof was infeasible for a human to check by hand. Since then the proof has gained wide acceptance, although some doubters remain.
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In the mathematical field of graph theory, the Franklin graph is a 3-regular graph with 12 vertices and 18 edges.
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