According to the Guinness World Record (2012), the modern youngest professor in the world is Alia Sabur, who got her Ph.D in Material Science and Engineering at the age of 16, then became a professor at the age of 18 in 2008.
http://en.wikipedia.org/wiki/Alia_Sabur
http://www.huliq.com/62243/world039s-youngest-college-professor-18-years-old
http://zirzameen.com/blog//index.php/2009/10/08/the_youngest_professor_in_the_world?blog=2