As an aside, let me ask if graduate students in any other country must compete with the brightest and best from around the world. This policy may work to maintain the strongest mathematical sciences community in the United States, but there may be a cost. Perhaps some American students choose, as a consequence, not to compete or to drop out of graduate school early in the process. The perception may be developing in schools, colleges, and universities that studying mathematics and the sciences is for someone else. Let me acknowledge that the presence of international students and researchers has been a source of strength and vitality for American mathematics in this century and that there would be a real loss if that were changed. However, what has changed during the past two decades is the proportion of students from abroad. It is appropriate to ask whether this change has negatively affected the nature of graduate programs in many cases.
About 5 years ago I chaired a study of doctoral education for the Board on Mathematical Sciences. The findings of our committee were rather dramatic and surprising to many people. Agreement on purpose and the general environment had a substantial effect on the success of students in a graduate program. This was particularly true for women and minority students. These groups are disproportionally affected in programs that adopt a hands-off attitude and subscribe to a "survival of the fittest" philosophy.
In summary, the approach of raising the bar or allowing Darwin to prevail might have several consequences as to who studies mathematics. I think the community must decide how much the composition of the U.S. mathematical sciences community matters. Will it affect mathematics education in the schools, colleges, and universities? Will it affect the public -perception of mathematics? Will it affect public funding of the mathematical sciences?
As I indicated, my goal at the outset was to raise questions, to point out problems. Mathematicians pride themselves on rational thinking and avoiding contradictions. I believe there are some contradictions in our current policies, or at least in our actions. I hope we will work to resolve them.