The Best Journals in Mathematics
by Scott Williams

This article is re-printed and updated, with permission from the author, the author's article published in the NAM Quarterly Newsletter 32.3 Fall 2001.

When I was a graduate student, my advisor would go to the common room and read/scan each journal as it arrived. In those days I would guess this took up about seven to ten hours a week. Now there are too many journals to read. Even the sub-sub-disciplines have two or three journals of their own. Every area of mathematics has journals where their strongest articles appear. Each of us should read are own, however, what general journals should we open? Is there a "best mathematics journal?"

A journal fitting this description would have every article, no matter the field, important and extremely strong. If attention is limited to the U.S., then I would claim that such a journal exists, and it is The Annals of Mathematics published by Princeton. I can say from personal experience, its standards of publication are extremely high. So high that upon occasions very good important articles are rejected. Please note that Acta Mathematica (there are several journals by this name) published by the The Royal Swedish Academy of Sciences' Mittag-Leffler Institut is at the same level. It is questionable whether there are others in the world at this class, even the oldest mathematics journal, known as Crelles Journal, is not so lofty.

Which of us has published in these journals? Not me. I only know of a few papers published in these journals by people of African descent. There are three by David Blackwell, two by each of W. W. Schliefelin Claytor (after whom NAM's Claytor Lecture is named), Atlanta University's J. Ernest Wilkins and Georgia Tech's Wilfrid Gangbo and one by UCSD's Katherine Okikiolu. I list them above & below:

  1. Schiefelin Claytor, Topological Immersion of Peanian Continua in a Spherical Surface, The Annals of Mathematics, 2nd Ser. 35 (1934), 809-835
  2. Schieffelin Claytor, Peanian Continua Not Imbeddable in a Spherical Surface, The Annals of Mathematics, 2nd Ser. 38 (1937), 631-646.
  3. Blackwell, David, Idempotent Markoff chains, The Annals of Mathematics, 2nd Ser. 43, (1942). 560--567.
  4. Wilkins, J. Ernest, Jr. Multiple integral problems in parametric form in the calculus of variations. The Annals of Mathematics (2) 45, (1944). 312--334.
  5. Blackwell, David, Finite non-homogeneous chains, The Annals of Mathematics, 2nd Ser. 46, (1945). 594--599.
  6. Wilkins, J. Ernest, Jr. A note on the general summability of functions. The Annals of Mathematics (2) 49, (1948). 189--199.
  7. Bellman, Richard; Blackwell, David On moment spaces. The Annals of Mathematics, 2nd Ser. 54, (1951). 272--274.
  8. Kevin Corlette. Archimedean superrigidity and hyperbolic geometry. Annals of Mathematics 2nd Series 135 (1992), no. 1, 165-182
  9. Gangbo, Wilfrid; McCann, Robert J. The geometry of optimal transportation. Acta Mathematica 177 (1996), no. 2, 113--161.
  10. Okikiolu, Katherine. Critical metrics for the determinant of the Laplacian in odd dimensions. The Annals of Mathematics, 2nd Ser. 153 (2001), no. 2, 471--531.
  11. E. A Carlen and W. Gangbo. Constrained steepest descent in the 2-Wassertein metric, Annals of Math. 157, May (2003)


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