Many mathematicians have been notable not just for their contributions to mathematics, but also for helping teach the next generation of mathematicians. A number of important mathematicians have tutored and helped other important mathematicians progress in their careers. Here are a few such mathematicians.
Paul Erdős - Paul Erdős was a notable mathematician who lived an eccentric and mathematically productive lifestyle. He was known for collaborating with many other mathematicians, so many that his collaborating spawned the concept of the Erdős number, which measures how far away mathematicians are from citing some of Erdős's work. Erdős also influenced younger mathematicians, such as the Fields Medalist Terence Tao.
Ernst Kummer - Ernst Kummer was a notable mathematician who made important contributions to mathematics in fields such as geometry and number theory. He also helped educate people in mathematics, one example being that he trained german officers in ballistics. He also was the advisor of several notable students and helped inspire Leopold Kronecker to pursue a career in mathematics.
David Hilbert - David Hilbert was a very prominent mathematician who created the list of Hilbert's problems; a list of 23 unsolved (at the time) and important problems in mathematics. Hilbert helped make the University of Göttingen a leading institution in mathematics. Hilbert also had many doctoral students; at the University of Göttingen Hilbert had 69 doctoral students.
George Pólya - George Pólya was another prominent Hungarian mathematician like Paul Erdős. He wrote numerous books about problem solving, which served to help many students problem solve in mathematics. One of his more popular books, How to Solve It, has sold more than one million copies and discusses strategies for approaching/solving problems.
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