1. Overview
Mary Ellen Rudin (Mary Ellen Estill Rudinˈmɛəriː ˈɛlən ˈɛstɪl ˈruːdɪnEnglish; December 7, 1924 - March 18, 2013) was an American mathematician renowned for her significant contributions to set-theoretic topology and general topology. She was an emeritus professor at the University of Wisconsin-Madison. Her lasting impact on the field was recognized when Elsevier established the Mary Ellen Rudin Young Researcher Award in 2013 in her honor, awarded annually to promising young researchers in topology.
2. Early Life and Education
Mary Ellen Rudin's early life and academic pursuits laid the foundation for her distinguished career in mathematics, characterized by a strong familial emphasis on education and exceptional academic performance from an early age.
2.1. Birth and Family Background
Mary Ellen Estill Rudin was born on December 7, 1924, in Hillsboro, Texas. Her father, Joe Jefferson Estill, was a civil engineer, and her mother, Irene (Shook) Estill, had been an English teacher before her marriage and subsequent retirement. The family moved frequently due to her father's work, but Mary Ellen spent a considerable portion of her childhood around Leakey, Texas. She had one younger brother. Rudin noted in an interview the strong emphasis her family placed on education, particularly mentioning her two maternal grandmothers who had attended Mary Sharp College near Winchester, Tennessee.
2.2. Academic Journey
Rudin attended the University of Texas at Austin, where she demonstrated remarkable academic prowess by completing her Bachelor of Arts degree in just three years in 1944. She then continued her studies in the graduate program in mathematics, working under the supervision of Robert Lee Moore, a prominent topologist known for his rigorous teaching methods. Her graduate thesis notably presented a counterexample to one of "Moore's axioms," a significant early achievement that hinted at her future contributions. She earned her Ph.D. in 1949. During her undergraduate years, Rudin was an active participant in campus life, being a member of the Phi Mu Women's Fraternity and earning induction into the prestigious Phi Beta Kappa society, which recognized her outstanding academic excellence.
3. Personal Life
In 1953, Mary Ellen Estill married fellow mathematician Walter Rudin, whom she had met while teaching at Duke University. They had four children together, building a family life alongside their demanding academic careers. The Rudin family resided in Madison, Wisconsin, in the distinctive Walter Rudin House, a residence specifically designed by the renowned architect Frank Lloyd Wright.
4. Career and Academic Contributions
Mary Ellen Rudin's professional career was marked by distinguished teaching positions and groundbreaking academic achievements that profoundly influenced the field of mathematics, particularly in topology.
4.1. Professorial and Administrative Roles
At the beginning of her career, Rudin held teaching positions at Duke University and the University of Rochester. In 1959, she joined the University of Wisconsin-Madison as a lecturer, where her talents were quickly recognized, leading to her promotion to Professor of Mathematics in 1971. After her retirement in 1991, she continued to serve as a Professor Emerita, maintaining her connection to the academic community. She was also recognized as the first Grace Chisholm Young Professor of Mathematics and held the Hilidale Professorship. Rudin's influence extended beyond her university roles; she was an Invited Speaker at the International Congress of Mathematicians in Vancouver in 1974, a testament to her global recognition. From 1980 to 1981, she served as the Vice-President of the American Mathematical Society, a leadership position within a major professional organization. In 1984, she was chosen as a Noether Lecturer, an esteemed honor recognizing women who have made fundamental contributions to mathematics. She was also made an honorary member of the Hungarian Academy of Sciences in 1995. Her significant contributions were further acknowledged in 2012 when she was named a fellow of the American Mathematical Society.
4.2. Major Contributions to Topology
Rudin is widely recognized in topology for her innovative constructions of counterexamples to prominent conjectures that had long baffled mathematicians, as well as for her significant proofs of other complex mathematical problems.
4.2.1. Construction of Key Counterexamples
In 1958, she made a notable early contribution by discovering an unshellable triangulation of a tetrahedron. Her most celebrated achievement occurred in 1971 when she successfully constructed the first Dowker space. This pivotal construction disproved a long-standing conjecture by Clifford Hugh Dowker, which had been a driving force in topological research for more than two decades. Her ground-breaking example spurred further investigation into "small" ZFC Dowker spaces.
4.2.2. Other Significant Proofs and Theories
Beyond her counterexamples, Rudin also made crucial advancements in proving several conjectures. She successfully proved the first of the Morita conjectures and a restricted version of the second. Her last major result was a definitive proof of Nikiel's conjecture. Additionally, she provided an elementary proof demonstrating the paracompactness of metric spaces, which simplified previous, more complex proofs. Reflecting on the depth of her work, mathematician Steve Watson remarked, "Reading the articles of Mary Ellen Rudin, studying them until there is no mystery takes hours and hours; but those hours are rewarded, the student obtains power to which few have access. They are not hard to read, they are just hard mathematics, that's all."
5. Major Publications
Mary Ellen Rudin authored several influential academic works that became standard references in set-theoretic topology and advanced the understanding of complex mathematical concepts. Her key publications include:
- Lectures on set theoretic topology (1975), published by the American Mathematical Society. This book provided an accessible introduction to the complex field of set-theoretic topology, reflecting her expertise and clarity in explanation.
- Dowker spaces, which appeared in the Handbook of set-theoretic topology (1984), offering a detailed exposition on the topic where she made her most famous discovery and providing foundational insights for subsequent research.
6. Legacy
Mary Ellen Rudin's contributions continue to influence the mathematical community through academic initiatives established in her honor and lasting commemorations that celebrate her enduring impact.
6.1. Mary Ellen Rudin Young Researcher Award
The Mary Ellen Rudin Young Researcher Award is an annual prize established by Elsevier in 2013 on behalf of the journal Topology and its Applications. It is dedicated to young researchers making significant contributions primarily in general topology and related fields. The award amounts to 15.00 K USD and is allocated for the awardee's professional development: 5.00 K USD is designated for attending three major conferences in topology, another 5.00 K USD for visiting a research center, and the remaining 5.00 K USD serves as an unrestricted cash prize. The award was named in honor of Mary Ellen Rudin, one of the 20th century's most prominent topologists. Rudin herself granted permission for her name to be used for the award, though she passed away before the first prize was conferred.
6.1.1. List of awardees
| Year | Name | Institution | Awarded at | Area of contribution |
|---|---|---|---|---|
| 2019 | James Hyde | H.C. Wang Assistant Professor, Cornell University | Due to the COVID-19 pandemic, not formally awarded. | Homeomorphism groups |
| 2018 | Osvaldo Guzmán | Postdoc, University of Toronto | 53rd Spring Topology and Dynamical Systems Conference, University of Alabama at Birmingham, March 14-16, 2019 | Almost disjoint families, set theory |
| 2017 | Balázs Strenner | Hale Visiting Assistant Professor, Georgia Tech | 52nd Spring Topology and Dynamical Systems Conference, Auburn University, Auburn, Alabama, USA, March 15, 2018 | Pseudo-Anosov homeomorphisms |
| 2016 | Kathryn Mann | Morrey Visiting Assistant Professor, University of California, Berkeley | 51st Spring Topology and Dynamical Systems Conference, New Jersey City University, March 8-11, 2017 | Homeomorphism groups of manifolds |
| 2015 | Yinhe Peng | Postdoc, Chinese Academy of Sciences | 1st Pan Pacific International Conference on Topology and Applications, Zhangzhou, China, November 25-30, 2015 | Base problem for topological spaces |
| 2014 | Yash Lodha | Ph.D. candidate, Cornell University | 60 years of Dow conference, Cornell University, December 6-9, 2014 | Groups of homeomorphisms of low dimensional manifolds |
| 2013 | Logan C. Hoehn | Assistant Professor, Department of Computer Science & Mathematics, Nipissing University | International Conference on Topology and Geometry, Shimane University, Matsue City, Japan, September 2013 | Solution of Lelek's problem |
6.2. Continued Influence and Commemoration
Mary Ellen Rudin's profound mathematical work continues to inspire subsequent researchers and her legacy is celebrated in various forms. Her deep connections within the mathematical community are further highlighted by her Erdos number of 1, indicating a direct collaborative link with the highly prolific mathematician Paul Erdos. Beyond academic recognition, she is also commemorated through her inclusion in a deck of playing cards featuring notable women mathematicians, published by the Association of Women in Mathematics, further cementing her place among influential figures in the field and inspiring future generations of mathematicians.
7. Death
Mary Ellen Rudin passed away at the age of 88 on March 18, 2013, in Madison, Wisconsin, the city where she had resided for many years.