Person: Shields, Allen Lowell
Allen Shields was an American mathematician who worked on a wide range of mathematical topics including measure theory, complex functions, functional analysis and operator theory.
Mathematical Profile (Excerpt):
- Shields was an undergraduate at the City College New York where his lecturers included Emil Post and Lee Lorch.
- Despite the fact that Hurewicz was Shields' official supervisor, he was unofficially supervised by Raphaël Salem.
- This became a standing joke between Allen and me, and perhaps it influenced the evolution of his own lecturing style into the model of clarity and vividness that was his hallmark.
- One of my fondest memories from M.I.T. years is running into Allen in the library at ungodly hours of the night.
- Shields' first post was as a Research Instructor in Mathematics at Tulane where he learnt a lot of functional analysis and wrote papers on topological semigroups.
- In 1955, Shields was appointed to the University of Michigan at Ann Arbor, taking up his appointment in the following year, and remained there for the rest of his career except for two years (1959-61) spent in New York.
- On his way from Hildebrandt's office to one of the lecture sessions, George ran into Allen Shields, whom a year earlier he had met at the Summer Meeting at Laramie.
- Allen was cooperative, and George dashed back to report that he had found a substitute and that, after fifteen more minutes the substitute would present a ten-minute paper.
- Young as he was, Allen had already mastered the art of beginning his blackboard work in the upper left-hand corner and ending neatly at the lower right, with one minute to spare.
- Hildebrandt was so impressed that on the spot he offered Allen a one-term appointment.
- Later, the department persuaded both Shields and Hildebrandt to extend the arrangement.
- Soon after George Piranian returned from his leave, he began working with Shields and they published the joint paper The sets of Luzin points of analytic functions (1957).
- Shields worked on a wide range of mathematical topics including measure theory, complex functions, functional analysis and operator theory.
- In 1979 the University of Michigan awarded Allen its Distinguished Faculty Achievement Award.
- J H Shapiro was one of Shields' many PhD students.
- He also notes that Shields advised the greatest number of mathematics PhD theses at the University of Michigan, but as a student was able to give insight into the style of Shields' supervision.
- Allen kept to the sidelines but always made himself available to guide us to the literature, offer opinions, suggest options, lighten the mood with gentle wisecracks, and generally shout encouragement.
- P Duren wrote joint papers with Shields.
- Tragically Shields was struck down with cancer in the summer of 1988.
Born 7 May 1927, New York City, USA. Died 16 September 1989, Ann Arbor, Michigan, USA.
View full biography at MacTutor
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Thank you to the contributors under CC BY-SA 4.0! 
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- @J-J-O'Connor
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References
Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive
