On paul turán's influence on graph theory

One of those few people from whom I learned a great deal in mathematics, Paul Turin, died on the 26th of September, 1976, after being ill for several years. In this paper, written in his memory, I will endeavor to give a picture of his influence on graph theory as well as his views on mathematics. Today most mathematicians specialize in one narrow field of mathematics. Perhaps the most evident reason for this is that only the best can excel in more than one branch. Turin was one of these. His ideas and results deeply influenced the development of graph theory. However, his main work, his most important results, concern other topics of mathematics, primarily number theory, interpolation and approximation theory, the theory of polynomials and algebraic equations, complex analysis, and Fourier analysis. And one additional item should be mentioned: Turin discovered (created) a new method in analysis, called the method of power sums, which gave results interesting in themselves and applicable in many branches of mathematics, for instance, number theory, numerical analysis, and stability problems in the theory of differential equations. Hence the picture given here is just a fragment of the whole picture, reflecting Paul TurBn’s personality in some cases but not in other ones. The deep knowledge and great proof power of TurBn, for example, is reflected more in his theorems and proofs from analysis and number theory. On the other hand, I hope that the survey given hzre on Turin’s graph theoretical work and on the theory developed around his work will clearly show that Turin had a very good eye for finding interesting mathematical problems and could create starting points for mathematical theories.