360 



R.D. Anderson 

 Appendix J""e 7, 1985 



TWENTIETH CENTURY MATHEMATICS IN THE UNITED STATES 



Until the second world war, American mathematicians lived in 

 the shadow of Western Europeans. With the possible exception of G.D. 

 Birkhoff of Harvard and Norbert Wiener of MIT, the "giants" of the era 

 were Europeans. Even in the United States, many of the important 

 mathematicians were from Europe. Some were attracted by economic and 

 academic opportunities in the United States, others were refugees from 

 Hitler's Germany. 



In the U.S. almost all major departments had senior faculty 

 who were trained abroad. Indeed, as late as 1950 at Princeton 

 University, (then, as now, considered to have one of the strongest 

 mathematics departments in the country) half of the full professors 

 of mathematics had been born in Europe. At the nearby Institute for 

 Advanced Study, developed in the thirties into a major continuing 

 force in world mathematics, the majority of the mathematics faculty 

 were Europeans. The mathematicians who came to our shores were from 

 various parts of Europe. They came not only from Germany, France, and 

 England, but from many smaller countries as well, with those from 

 Hungary and Poland being particularly noteworthy. 



In the post-war era, mathematics made a massive forward surge, 

 with computing and modern applications in this country and classical 

 mathematics in France leading the way. As evidence of the French 

 influence in traditional areas, we cite the awards of the Fields 

 Medals given at the International Congresses, the most prestigious 

 awards in mathematics. Of the six medals given in the fifties, three 

 were awarded to Frenchmen, with one each to a Norwegian, a Japanese 

 and an Englishman. 



But the fifties was a time when the United States mathematics 

 community was coming of age. Of the nineteen medals given since 1960, 

 eight have been awarded to mathematicians from the States, with two 

 more to Japanese and Chinese mathematicians who took doctorates here 

 and who currently hold faculty positions in the U.S. Concurrently, 

 the United States was leading the world in the rapid development of 

 the computer and information sciences and of modern applications of 

 mathematics to real world problems. While traditionally most research 

 mathematicians in the U.S. have been in academe, there is now a 

 growing presence in the private sector. This arises from major groups 

 at Bell Labs and IBM, but also from smaller groups in nearly 500 

 business, industrial and government installations, and private 

 consulting firms, which extend the use of mathematical methods to many 

 facets of our society. 



The past few years have been particularly exciting for the 

 mathematicians in both the theoretical and applied areas. Some famous 

 old problems have been solved, and an entirely unexpected phcno.Tienon 

 has been discovered in four dimensional space. On the practical side, 

 a new method for solving large linear programming problems has been 

 discovered which promises to greatly reduce computing time and to 

 bring much larger problems within the range of our computers. 



