Judith Sally

Judith Sally (née Donovan) was born in New York on March 23, 1937. After going to high school at the Convent of the Sacred Heart in New York, she attended Barnard (BA 1958), and then began her graduate studies in mathematics at Brandeis (MA 1960). While at Brandeis, Judith met Paul Sally, who was already in the Brandeis doctoral program in mathematics; they were married in November 1959.

Judith postponed her career while they had three sons (David, Stephen, and Paul III). In 1965, Paul completed his dissertation at Brandeis and joined the department of mathematics at the University of Chicago. Judith entered Chicago’s doctoral program in mathematics in 1968, and was awarded her PhD in 1971, working under Irving Kaplansky, her thesis on a topic in commutative algebra (published in the Transactions of the AMS in 1972). Judith then spent the year 1971–1972 as a postdoc at Rutgers University (while Paul was at the nearby Institute for Advanced Study).

Judith joined the department of mathematics at Northwestern University in 1972, where she remained until her retirement in 2002. Initially hired by Northwestern as a visiting assistant professor (1972–1974), she was appointed assistant professor in 1974, and then promoted to associate professor in 1977 and professor in 1982. Judith was the second woman to be appointed a professor in mathematics at Northwestern. (Alexandra Bellow had been the first, in 1968. Earlier, Lois Wilfred Griffiths had been promoted to associate professor in mathematics in 1938, and Helen M. Clark had been promoted from lecturer to assistant professor in mathematics in 1959.)

Figure 1.

Judith lecturing in Lunt Hall.

Judith was a highly active researcher during her thirty years at Northwestern. Her curriculum vitae for 1999 lists 37 papers, including ones in the Proceedings and Bulletin of the AMS, Mathematische Annalen, Journal of the London Mathematical Society, Proceedings of the Cambridge Philosophical Society, American Journal of Mathematics, Journal of Algebra, and Journal of Pure and Applied Algebra. She also wrote one book (Numbers of Generators of Ideals in Local Rings, 1978) and translated Dieudonné’s History of Algebraic Geometry (1985) into English. In recognition of her research accomplishments, Judith was invited in 1995 to give the Association for Women in Mathematics Noether Lecture, an honor “for fundamental and sustained contributions to the mathematical science.” The AWM summarized her research thus:

Sally’s research is in Commutative Algebra, one of the fields in which Emmy Noether’s work had such impact. Her main interests lie in the study of Noetherian local rings and graded rings with emphasis on Hilbert functions and birational extensions. These concepts play an important role in ascertaining the nature of singularities in applications in algebraic geometry. The Hilbert function of a local ring at a point on a variety is a very good measure of how bad the singularity is at the point. One of the themes in Sally’s research is the interaction between the local ring and its associated graded ring. This interaction plays a critical role in understanding and computing the Hilbert function. She has also worked on birational blowing up of ideals, the extention of valuations and other concepts in the algebra involved in the resolution of singularities.

Judith’s main research centered upon the passage of properties between a Noetherian local ring $R$ with maximal ideal $\mathfrak{m}$, and its tangent cone, the ring $G = R/\mathfrak{m}\oplus \mathfrak{m}/\mathfrak{m}^2\oplus \mathfrak{m}^2/\mathfrak{m}^3 + \dots$. General deformation arguments can be used to show that good properties of $G$ force the same properties for $R$; Sally’s results and conjectures concerned the other direction. She famously proved that if $R$ is either Cohen-Macaulay with minimal multiplicity or Gorenstein with almost minimal multiplicity, then the Hilbert series and Poincaré series are completely determined; she passes to $G$ and its study to prove these results. She made striking conjectures extending her work, including the Sally conjecture (posed in 1983, but only proved thirteen years later, independently by Rossi and Valla in 1996 and Wang in 1997). The Italian group studying Judith’s questions used her techniques so much they dubbed her methods the “Sally machine.” The relationship between the tangent cone and the Rees algebra led her to concentrate on birational maps from $R$ to various affine blowups, through study of the Rees algebra and Sally modules, named in her honor. Her introduction of the core of an ideal with David Rees led to an explosion of work on this topic.

Figure 2.

Son David Sally’s wedding in 1986. Left to right, Paul III, Serena Yoon, David, Judith, Paul, and Stephen.

During her time at Northwestern, Judith was awarded the National Science Foundation Visiting Professorship for women for the 1988–1989 academic year, during which she traveled to Purdue University in West Lafayette, Indiana. She also won a Bunting Fellowship at the Mary Ingraham Institute at Radcliffe College, an Alfred P. Sloan Foundation Fellowship, and a Northwestern College of Arts and Sciences Teaching Award.

Judith directed the dissertations of four students at Northwestern (Young Hyun Hong, 1981, John Gately, 1995, Petra Constapel, 1995, and Kewen Yao, 1997), and served as director of undergraduate studies (although this had a different title back then) for mathematics in 1982–1984 and 1990–1991. In later years Judith and her husband Paul developed an interest in mathematical pedagogy and outreach. This included teaching mathematics courses for four summers at the University of Chicago for historically underrepresented groups preparing to take the MCAT, and teaching geometry courses and seminars for four years for elementary school teachers. They wrote four books together: TriMathlon: A Workout Beyond the School Curriculum, Peters, 2003, Roots to Research, AMS, 2007, Geometry: A Guide for Teachers, AMS, 2011, and Integers, Fractions and Arithmetic: A Guide for Teachers, AMS, 2012.

Judith’s service at the national, university, and departmental levels was exemplary: she was on the editorial board of the Transactions of the AMS for four years (1990–1993), and her 1999 CV shows her serving on four AMS committees and panels; fifteen university committees, boards, and panels (including the 1996 Search Committee for the WCAS Dean); and eleven department committees, including twice chairing both the Undergraduate and Personnel committees.

One aspect of Judith’s life that many of her colleagues were unaware of was that for some 15 years she was a serious marathon runner. She ran her first marathon in 1981 in New York City, finishing in under 3 hours 40 minutes, placing 56th in her age group; she also ran in a number of Chicago marathons completing her last one in 1995, and in the intervening fourteen years she ran in many local 5k and 10k races, often finishing first in her age group. She was also an avid reader, frequently making notes about the books she read on 3 x 5 index cards; the comments on these could be appreciative, perceptive, amusing, or acerbic (“don’t waste my time!”), depending.

Judith died on January 28, 2024 in Chicago, at the age of 86. She leaves three children, eight grandchildren, and two siblings; her husband Paul died ten years earlier. Judith will be remembered as a remarkable mathematician, and a wonderful friend and colleague.