Paul Erdös (1913-1996)

On October 18, 1996, hundreds of people, including many mathematicians, gathered at Kerepesi Cemetery in Budapest to pay their last respects to Paul Erdős. If there was one theme suggested by the farewell orations, it was that the world of mathematics had lost a legend, one of its great representatives. On October 21, 1996, in accordance with his last wishes, Paul Erdős’ ashes were buried in his parents’ grave at the Jewish cemetery on Kozma street in Budapest. Paul Erdős was one of this century’s greatest and most prolific mathematicians. He is said to have written about 1500 papers, with almost 500 co-authors. He made fundamental contributions in numerous areas of mathematics. There is a Hungarian saying to the effect that one can forget everything but one’s first love. When considering Erdős and his mathematics, we cannot speak of “first love”, but of “first loves”, and approximation theory was among them. Paul Erdős wrote more than 100 papers that are connected, in one way or another, with the approximation of functions. In these two short reviews, we try to present some of Paul’s fundamental contributions to approximation theory. A list of Paul’s papers in approximation theory is given at the end of this article. These are referenced in this article in the form [ab.n], indicating the n-th item in the year 19ab. This list is a sublist of the official list, of publications by Erdős, in [GN], with a list of additions and corrections available at the website www.acs.oakland.edu/ ∼grossman/erdoshp.html. Other references in this article (such as the reference [GN] just used) are listed just prior to that list of Erdős’ approximation theory papers. Numerous articles and obituaries on Erdős have appeared (see, e.g., the web page www.math.ohio-state.edu/∼nevai/ERDOS/), and more will undoubtedly appear. The interested reader might wish to look at the article by L. Babai which appeared in [Ba]. Acknowledgement The authors are grateful for the editors’ help in coordinating their efforts. This material is based upon work supported by the National Science Foundation under Grant No. DMS–9623156 (T.E.) and by the Hungarian National Foundation for Scientific Research under Grants No. T7570, T22943, and T17425 (P.V.).