Tilla Klotz Milnor
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Tilla Weinstein (1934–2002, née Savanuck, also published as Tilla Klotz and Tilla K. Milnor) was an American mathematician known for her mentorship of younger women in mathematics. Her research concerned
differential geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...
, including
conformal structure In mathematics, conformal geometry is the study of the set of angle-preserving ( conformal) transformations on a space. In a real two dimensional space, conformal geometry is precisely the geometry of Riemann surfaces. In space higher than two d ...
s,
harmonic map In the mathematical field of differential geometry, a smooth map between Riemannian manifolds is called harmonic if its coordinate representatives satisfy a certain nonlinear partial differential equation. This partial differential equation for ...
s, and
Lorentz surface In mathematics, a Lorentz surface is a surface (topology), two-dimensional oriented manifold, oriented smooth manifold with a conformal equivalence class of Lorentzian metrics. It is the analogue of a Riemann surface in metric signature, indefinite ...
s. She taught for many years at
Rutgers University Rutgers University (; RU), officially Rutgers, The State University of New Jersey, is a Public university, public land-grant research university consisting of four campuses in New Jersey. Chartered in 1766, Rutgers was originally called Queen's ...
, where she headed the mathematics department in the
Douglass Residential College Douglass Residential College, is an undergraduate, non degree granting higher education program of Rutgers University-New Brunswick for women. It succeeded the liberal arts degree-granting Douglass College after it was merged with the other unde ...
.


Early life and education

Weinstein was born as Tilla Savanuck, in 1934. Her father was a Russian immigrant and lawyer in
New York City New York, often called New York City or NYC, is the List of United States cities by population, most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the L ...
; her mother was a legal secretary. She began her undergraduate studies in 1951 as an English major at the
University of Michigan , mottoeng = "Arts, Knowledge, Truth" , former_names = Catholepistemiad, or University of Michigania (1817–1821) , budget = $10.3 billion (2021) , endowment = $17 billion (2021)As o ...
, in part to get away from her parents' rocky marriage and to live near relatives in
Detroit Detroit ( , ; , ) is the largest city in the U.S. state of Michigan. It is also the largest U.S. city on the United States–Canada border, and the seat of government of Wayne County. The City of Detroit had a population of 639,111 at th ...
. There, her courses included calculus from
Hans Samelson Hans Samelson (3 March 1916 – 22 September 2005) was a German-American mathematician who worked in differential geometry, topology and the theory of Lie groups and Lie algebras—important in describing the symmetry of analytical structures. C ...
and a course in the
foundations of mathematics Foundations of mathematics is the study of the philosophy, philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the natu ...
from
Raymond Louis Wilder Raymond Louis Wilder (3 November 1896 in Palmer, Massachusetts – 7 July 1982 in Santa Barbara, California) was an American mathematician, who specialized in topology and gradually acquired philosophical and anthropological interests. Life Wilde ...
. After her first year in Michigan, she became engaged to an English student she knew in New York, and after her second year (in 1953), she married him and returned to New York. Not wishing to repeat her earlier coursework (as she would if she had transferred to the
City College of New York The City College of the City University of New York (also known as the City College of New York, or simply City College or CCNY) is a public university within the City University of New York (CUNY) system in New York City. Founded in 1847, Cit ...
), she became a mathematics undergraduate student at
New York University New York University (NYU) is a private research university in New York City. Chartered in 1831 by the New York State Legislature, NYU was founded by a group of New Yorkers led by then-Secretary of the Treasury Albert Gallatin. In 1832, the ...
. She was the only woman in the program at the time. After her marriage, she used the name Tilla Klotz for her publications, a name she would continue to use until the late 1960s. At NYU, her calculus instructor,
Jean van Heijenoort Jean Louis Maxime van Heijenoort (; July 23, 1912 – March 29, 1986) was a historian of mathematical logic. He was also a personal secretary to Leon Trotsky from 1932 to 1939, and an American Trotskyist until 1947. Life Van Heijenoort was born ...
, noted her ability, encouraged her to participate in the school's team for the
William Lowell Putnam Mathematical Competition The William Lowell Putnam Mathematical Competition, often abbreviated to Putnam Competition, is an annual list of mathematics competitions, mathematics competition for undergraduate college students enrolled at institutions of higher learning in th ...
, and led her to take advanced classes in mathematics, including a class in
complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates Function (mathematics), functions of complex numbers. It is helpful in many branches of mathemati ...
from
Lipman Bers Lipman Bers ( Latvian: ''Lipmans Berss''; May 22, 1914 – October 29, 1993) was a Latvian-American mathematician, born in Riga, who created the theory of pseudoanalytic functions and worked on Riemann surfaces and Kleinian groups. He was also kn ...
. In her first meeting with Bers, she announced her pregnancy, but Bers was supportive and helped her to complete her bachelor's degree "without undue delay", despite opposition from the dean of the school. She completed her Ph.D. in 1959 at NYU. Her dissertation, ''On G. Bol's Proof of Caratheodory's Conjecture'', was supervised by Bers.


Career and later life

Although Bers found a position for Weinstein at the
University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...
, she was unable to find a matching position for her husband, and declined the offer. With the assistance of Bers, she instead became a faculty member at the
University of California, Los Angeles The University of California, Los Angeles (UCLA) is a public land-grant research university in Los Angeles, California. UCLA's academic roots were established in 1881 as a teachers college then known as the southern branch of the California St ...
, and earned tenure there in 1966, the first woman to earn tenure in the mathematics department there. After a "sudden and unexpected" divorce in the late 1960s, she married Princeton mathematician
John Milnor John Willard Milnor (born February 20, 1931) is an American mathematician known for his work in differential topology, algebraic K-theory and low-dimensional holomorphic dynamical systems. Milnor is a distinguished professor at Stony Brook Uni ...
(also recently divorced) in 1968, and changed her name on her publications to Tilla K. Milnor, a name she continued to use until 1991. She moved in 1969 to
Boston College Boston College (BC) is a private Jesuit research university in Chestnut Hill, Massachusetts. Founded in 1863, the university has more than 9,300 full-time undergraduates and nearly 5,000 graduate students. Although Boston College is classifie ...
, in order to be less far from her husband, who was working in
Princeton, New Jersey Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of whi ...
. In 1970, Weinstein was hired by
Rutgers University Rutgers University (; RU), officially Rutgers, The State University of New Jersey, is a Public university, public land-grant research university consisting of four campuses in New Jersey. Chartered in 1766, Rutgers was originally called Queen's ...
to become the chair of the mathematics department in the
Douglass Residential College Douglass Residential College, is an undergraduate, non degree granting higher education program of Rutgers University-New Brunswick for women. It succeeded the liberal arts degree-granting Douglass College after it was merged with the other unde ...
. She served as chair from 1970 to 1973, and a second term from 1978 to 1981, after which that department was merged into the main mathematics department at Rutgers. In 1992, she married Kive Weinstein and changed her name again to Tilla Weinstein. She retired from Rutgers in 2000, and died on January 21, 2002.


Selected publications

* * * * *


Recognition

The Rutgers mathematics department offers an annual award for outstanding undergraduate achievement, the Tilla Weinstein Award, in her honor.


References

{{DEFAULTSORT:Weinstein, Tilla 1934 births 2002 deaths 20th-century American mathematicians American women mathematicians New York University alumni University of California, Los Angeles faculty Boston College faculty Rutgers University faculty 20th-century American women