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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 (as the Benjamin Peirce Instructor), Franklin joined the MIT 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 ''L''²(()) 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, P. "A Six Color Problem." J. Math. Phys. 13, 363-379, 1934. 〕 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. Franklin was married to Norbert Wiener's sister Constance. Their son-in-law is Václav E. Beneš.〔http://www-history.mcs.st-and.ac.uk/Biographies/Franklin.html〕 ==References== 〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Philip Franklin」の詳細全文を読む スポンサード リンク
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