Gudeman was born the eldest of four children. No later than 1865, the family had moved to New York. When his father went to Cuba and did not return, the stepfather Solomon Zickel took over the care of the family. Zickel had come from Germany to New York and was so successful that he was able to buy a house located near Dresden, where he spent his retirement with the publication of German weeklies.
Gudeman studied Classical Philology at Columbia University and went to his bachelor's degree in 1883 at the University of Berlin in order to deepen his studies with Hermann Diels. From 1890 to 1893 he was a lecturer at Johns Hopkins University, 1893-1902 Professor at the University of Pennsylvania. In 1902 he moved to the Chair of the Cornell University. In 1904 he was appointed as the only American scientists to the Thesaurus Linguae Latinae to Munich. His three sisters established themselves in Germany. Gudeman married a German and not even returned for a visit to the United States. In 1917 he received the German citizenship.
Even after the seizure of power by the National Socialists Gudeman remained in the German Reich. The problems of the Hitler era are reflected in his correspondence from the spring of 1935. His son Theodore Gudeman could emigrate in 1937 in the state of Indiana, Gudeman itself is not. He was classified in the camp Theresienstadt deported Jew, where he died on September 9, 1942 at the age of 80 years.
Gudemans research has focused on the Latin literature of antiquity. Among his most important publications include a commentary on Aristotle's Poetics (1934 ), which was preceded by a much used bibliography on this text (along with Lane Cooper, 1928), Latin Literature of the Empire ( 2 volumes, 1898-1899 ), History of Classical Philology (1902 ) and imagines Philologorum (1911 ). Many of his writings were published in the German Reich.