## In Memoriam: Paul T. Bateman

Also see the memorial published in Celebratio Mathematica.

Paul T. Bateman, 93, died Wednesday, December 26, 2012. He was born in Philadelphia in 1919, the son of Anna and Harold Bateman, and grew up in Philadelphia. He attended the University of Pennsylvania as an undergraduate and graduate student, with an interruption of four years during World War II, when, as a conscientious objector, he worked in a mental hospital in Middletown, CT.

Paul received his Ph.D. in 1946 at the University of Pennsylvania under the supervision of Hans Rademacher. The main result of his thesis was the proof of a formula conjectured by G. H. Hardy for the number of representations of a positive integer as the sum of three squares. This was an old and challenging problem that was solved by a delicate analysis. Paul's paper, published in the Transactions of the American Mathematical Society, has been repeatedly cited and has inspired much further study.

After holding two-year postdoctoral positions at Yale University and at the Institute for Advanced Study, he came to the Department of Mathematics at the University of Illinois in 1950. Paul was on the University of Illinois faculty until retiring in 1989, and he remained active until shortly before his death.

From 1965 to 1980, Paul served as Department Head and oversaw major expansion and faculty renewal. His achievements as head were many; in particular, he raised the level of the whole department and built an outstanding number theory group. His energetic leadership had a positive effect on number theory throughout the nation -- he had both good ideas and the drive to carry them out.

Paul was a member of the American Mathematical Society for 71 years. He gave extensive service to the AMS as an Associate Secretary and a member of the Board of Trustees and the Mathematical Reviews Committee. Paul did much of this work during the time of his headship, while still maintaining an active research program and advising graduate students -- he had a great capacity for work.

Paul married Felice Davidson in 1948. Their daughter, Sarah (Sally to all of us) was born in Urbana and lives here with her mother.

The focus of Paul's research was classical analytic number theory and associated analysis. Paul was a walking encyclopedia of mathematical literature. He put this to good use in writing an authoritative appendix for the reprint of Landau's groundbreaking book “Primzahlen.” Paul supervised 20 PhD students and wrote joint articles with 20 mathematicians. He is perhaps best known to the world's number theory community for formulating the Bateman-Horn conjecture on the density of prime number values generated by systems of polynomials. This topic has been discussed in dozens of research papers.

One of Paul's mathematical enthusiasms was problem solving. He inspired generations of students with problems-based courses that he taught, and several books were enriched by problems that he contributed. Shortly after retiring, Paul was appointed coeditor of the Problems Section of the American Mathematical Monthly, where his accomplishments included cleaning up a backlog of unsolved problems and, as he put it, “keeping egg off our faces.”

Paul organized and promoted Illinois Number Theory Conferences, first as regional meetings, and now as a frequent international event. In recognition of this contribution, the department celebrated Paul's 70th birthday and retirement with a three day meeting at the University of Illinois Conference Center at Allerton Park. The proceedings of this conference were published by Birkhäuser.

Paul and Felice enriched both the Illinois Math Department and number theory through their many social events. These included the annual fall cookout with Paul at the grill, parties for visiting speakers, and the popular daily lunches at the Illini Union. Paul maintained a large worldwide network of colleagues, including Hubert Delange from France; John Selfridge from Urbana, Ann Arbor and DeKalb; Paul Erdös from all over; and many former students. Paul and Felice were supportive of the Math Department in other ways. They, along with Selfridge, created a permanent endowment for a prize and a fellowship in the Mathematics Department that are named in Paulʼs honor.

Paul also brought a different kind of support to the department. For example, intramural sports: the P. T. Batsmen softball team and the cross country competition in which the Math runners sported bright orange Math Reviews T-shirts. (The race ended with a chicken dinner at the Batemans' home.) Then there was the coveted departmental award for the most tardy submission of term grades. The "prize" was to buy a round of beer after the first colloquium of the following term. Originally called the Selfridge Award, after its first winner, a victory by Paul led to its being renamed the Bateman-Selfridge Award. Then in honor of the reigning pope, it was re-renamed the John-Paul Award.

Among his outside interests, Paul loved classical music and opera and he enjoyed such outdoor activities as yard work and exploring mountains on foot and back roads by car. The trips, usually connected with mathematics conferences, always included his family.

Paul will be remembered by his colleagues and acquaintances for his guidance, support, encouragement, and friendship. A number theory conference in honor of the Batemans will be held at the U of I in Spring, 2014. Memorial contributions may be made to the Paul T. Bateman Number Theory Fellowship Fund, c/o the University of Illinois Foundation.