Jean Ellen Taylor, born on September 17, 1944, in San Mateo, California, is an American mathematician whose work on minimal surfaces, soap films, and crystal shapes stands among the major achievements of geometric measure theory in the late twentieth century. She grew up in the Sacramento area as the middle of three children. Her father worked first in banking and later as a lawyer in private practice; her mother was a high school gym teacher who later became a counselor. Nothing in the household pointed toward a scientific career, yet Taylor showed early academic strength and left California for Mount Holyoke College, a women’s college in Massachusetts, having never before been east of the Rocky Mountains.
At Mount Holyoke she studied chemistry and graduated summa cum laude with an A.B. in 1966. She continued in physical chemistry at the University of California, Berkeley, and earned an M.Sc. there. A course in differential geometry changed her direction. Under the mentorship of Shiing-Shen Chern she began to move from chemistry into mathematics. Political turbulence at Berkeley in the late 1960s contributed to a further change of setting. She went to England, completed a second master’s degree in mathematics at the University of Warwick, and there encountered the then-young field of geometric measure theory and the open questions that would define her research. She also met Frederick J. Almgren Jr., who would become both her doctoral advisor and, later, her husband.
Taylor entered the doctoral program at Princeton University in the fall of 1970. Her dissertation, finished in substance by May 1972 and awarded in January 1973, was titled “Regularity of the Singular Set of Two-Dimensional Area-Minimizing Flat Chains Modulo 3 in R3.” The problem is easy to state and hard to solve. Soap films spanning a wire frame often meet along curves where three sheets come together. If the wire is bent, those triple curves bend with it. The question was how wild such a curve could become: could it spiral forever, become fractal, or otherwise fail to be a reasonably smooth one-dimensional set? Using the tools of geometric measure theory, Taylor proved that the singular set remains controlled. The result, published in Inventiones Mathematicae in 1973, settled a long-standing regularity question and marked her as a researcher capable of closing problems that had resisted earlier methods.
In 1973 she joined the mathematics faculty at Rutgers University as an assistant professor. The same year she married Almgren. She remained at Rutgers for her entire regular academic career, rising to full professor and eventually to the rank of Professor II, a distinction reserved for faculty with outstanding national and international recognition. She retired in 2002 as professor emerita and thereafter held a visiting appointment at the Courant Institute of Mathematical Sciences at New York University. She also spent time at the Institute for Advanced Study.
The work that most clearly established her reputation came in the mid-1970s. In the nineteenth century the Belgian physicist Joseph Plateau had described, from experiment, the local geometry of soap-bubble clusters and soap films: surfaces meet in threes along curves at angles of 120 degrees, and those curves meet in fours at the tetrahedral angle of about 109.5 degrees. These rules, known as Plateau’s laws, lacked a mathematical proof. In 1976 Taylor and Almgren published the first proof, a long and technical argument showing that area-minimizing soap-film clusters must obey exactly those singularities and no others. The result is often described as one of the major triumphs of global analysis and geometric measure theory. The same year the two wrote a widely read Scientific American article, “The Geometry of Soap Bubbles and Soap Films,” which brought the subject to a general audience.
From soap films Taylor moved to crystals. Equilibrium crystal shapes are governed by anisotropic surface energy, and the mathematical object that encodes the preferred shape is the Wulff shape. Taylor studied the structure of these shapes, the singularities that can appear on crystal surfaces, and the ways crystals grow, shrink, or rearrange under different physical laws. Her later work treated motion by weighted mean curvature, surface diffusion, surface-attachment-limited kinetics, dendritic growth, and the motion of crystal aggregates in which individual grains can rotate. In 2003 she delivered the Emmy Noether Lecture of the Association for Women in Mathematics under the title “Five Little Crystals and How They Grew,” surveying five distinct modes of crystal evolution. She also used computational methods to explore these models, linking pure geometric measure theory to materials science.
Professional service ran alongside the research. Taylor was president of the Association for Women in Mathematics from 1999 to 2001. She served the American Mathematical Society in several roles, including vice president and, later, trustee, and sat on its council and executive committee. She became a fellow of the American Association for the Advancement of Science, the American Academy of Arts and Sciences (elected 1999), the Association for Women in Mathematics, the American Mathematical Society, and the Society for Industrial and Applied Mathematics. The SIAM fellowship citation recognized her contributions at the interface of mathematics and materials science on crystal growth, optimal crystal shapes, and minimal surfaces. She received an Alfred P. Sloan Research Fellowship and, in 2001, an honorary doctorate of science from Mount Holyoke. She has written and lectured on the status of women in mathematics and has supported organizations committed to broader participation in science.
Her personal life intersected with the mathematical community. She was married three times: first to the mathematician John Guckenheimer, then to Frederick Almgren, and later to William T. Golden, a financier and advocate for science. Accounts of her early career also note interests outside the seminar room, including mountaineering and political and anti-war activity during the years around her graduate study. She is a parent. Colleagues have described a direct style and a willingness to take on problems that looked intractable.
Taylor’s career began when women received only a small fraction of mathematics doctorates in the United States; figures from the early 1970s put that share near six percent. She entered a field whose central objects—soap films, crystals, least-area surfaces—are visible in ordinary experience and whose rigorous theory demands heavy technical machinery. The combination suited her. The 1973 regularity theorem and the 1976 proof of Plateau’s laws remain standard references. Later work on anisotropic energies and crystal growth extended the same geometric ideas into materials science. More than ninety publications and well over a hundred invited lectures record the span of that effort.
In retirement she has continued to be associated with the Courant Institute and with the institutions that recognized her earlier. The problems she chose were old: Plateau formulated his laws in the nineteenth century, and the calculus of variations had asked about least area long before that. The methods she used were new, drawn from the geometric measure theory developed by Almgren, Herbert Federer, and others. The outcome was a precise description of how films and crystals must meet and how they can evolve. That description is now part of the standard picture of minimal surfaces and of the mathematics of materials.