Mathematician Peter Loeb had a stroke of genius one day 30 years ago while swimming in the pool at the home he and his wife owned at the time in Champaign. The idea, which was the solution to a long-standing problem regarding the use of probability theories and infinitesimals, so surprised Loeb with its strangeness that, “I had to go to the edge and hang on,” Loeb said. A colleague later said, “I’m surprised you didn’t drown.”
Since then, the eponymous “Loeb spaces” have been applied not only to probability theory but to mathematical physics and ordinary number theory. Loeb spaces also have been applied in Loeb’s ongoing work with his former graduate student Yeneng Sun on the purification of measure-valued maps, mathematical economics and game theory.
Loeb and Sun recently finished three research projects; the results from the latest of these will appear in the proceedings of the American Mathematical Society.
Loeb, who retired last August after 40 years on the UI faculty, is still active on campus. For the spring semester 2009 he is teaching a graduate course in real analysis, working with a graduate student on the student’s thesis, and reviewing papers written by people in his field for the journal Logic and Analysis as a member of the journal’s board. Loeb also remains active in the Urbana-Champaign Senate as a member of the University Statutes and Senate Procedures committee, although his term expires in 2009.
For about 15 of the 20 or so years Loeb was involved with the senate, he rallied for support of an amendment to the University Statutes that required at least two of the three campus senates to agree on the exact wording of any amendment. That amendment came about as a result of another amendment – which established the severe sanctions short of dismissal for faculty members – which was nearly passed on to the university’s president by the University Senates Conference without many of the safeguards that the three campus senates had proposed.
“That made it clear to me that the process for amending the statutes was flawed, and that we could have something go through that didn’t have the agreement of any of the senates,” Loeb said. “So I started pushing for an amendment on how the statutes could be amended, and for a while, it was a fairly lonely business.”
Although the two amendments had long, slow tortuous paths clearing all the legislative hurdles, each of them was placed in the statutes after many years of debate and editing.
For more than 30 years, Loeb has dabbled as an amateur photographer and in December he judged a contest for a local camera club, as he has done in the past.
In October, Loeb, who enjoys photographing landscapes, took a trip to Mexico with his wife, Jane, a professor emerita of educational psychology, and found some interesting landscapes that they had not counted on when the second major hurricane of the season, Hurricane Norbert, struck Mexico’s west coast.
“When the hurricane went through where we were, it wasn’t very much; trees were bending to the wind but that was about it,” Loeb said. “When we crossed the Sea of Cortez, the power went out for a while, so the telephone lines and the ATMs were down. For a while we couldn’t use credit cards or get cash from the ATMs. Until the situation was resolved, we were highly motivated bargainers.”
This spring and summer, Loeb plans to travel to England and perhaps to China for professional meetings. The China trip will mark the third time that the Loebs have tried to visit China; their first trip in 1989 was derailed by the rioting that occurred in Tiananmen Square, and Jane’s sudden illness forced them to cancel their plans the second time.
Beyond the professional meetings in England and China, Loeb said that he’d also like to travel to Australia and to Singapore, which he has visited several times, to visit a former student who is now his co-author. Beyond that, Loeb said that he’s enjoying retirement and taking it “one year at a time.”
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