Philip Hanlon's exposure to the National Science Foundation began in 1987 when he received a Presidential Young Investigator (PYI) Award that gave him the recognition – and the resources – to pursue mathematical research in depth and unencumbered by the restraints of time or money.

To Hanlon, a PYI – followed by a five-year NSF "creativity award" – provided what he sees as the basic level of support for his work today: the application of combinatorics to the design of effective computational methods. Combinatorics is the arrangement, operation, and selection of mathematical elements within finite sets and configurations.

With such awards given early in his academic career, Hanlon was able to do significant work on the Macdonald Conjectures, a series of mathematical formulae developed in the early 1980s by the British mathematician, Ian Macdonald. Hanlon ended up pioneering a framework that interpreted the formula in terms of Lie algebra homology.

"By providing me with long periods of guaranteed support, the NSF allowed me the flexibility to study deeper, more challenging mathematical problems and to move into new scholarly areas," says Hanlon. "The five-year time window allowed much more flexibility to engage in riskier research – either deeper or of an interdisciplinary nature – than does a two- or three-year award."

Hanlon, Arthur F. Thurnau Professor of Mathematics, is one of many researchers whose NSF support began with a PYI and has continued. "The NSF has consistently – even sometimes proactively – supported my efforts to broaden the scope of my research and teaching," says Hanlon. For example, the NSF funded the purchase of a series of computers to support his work.

Today, Hanlon is engaged in three sponsored projects. He is continuing his work on new facets of the Macdonald Conjectures, and is working on the identification of epistatic (multi-gene) effects in a research project conducted with UM Medical School professors David Burke and Richard Miller.

In addition, Hanlon is part of a multi-university team study of self-optimizing software, sponsored by NSF and the Defense Advanced Research Projects Agency (DARPA). Hanlon's work focuses on analytical cache modeling. "It is inconceivable that this team would have been put together without the intervention of the NSF and DARPA," says Hanlon. "This program has been very successful exactly because of the blending of the expertise on the team, which points out the important role that NSF plays as a multidisciplinary funding agency."

In 1991, Hanlon received another significant NSF award that has had a profound direct impact of future mathematicians here at Michigan: a curriculum development award for Math 175, a freshman honors course on cryptology and discrete mathematics, with emphasizes problem-solving skills. "I don't know of any course as ambitious that is offered at the freshman level elsewhere," says Hanlon. He notes that the NSF support enabled him to bring in two "exceptional senior mathematicians" – Curtis Greene from Haverford College and Joan Hutchinson from Macalester College – for a semester to simultaneously teach and help develop the course. "Clearly, this is something that I could not have done without the NSF support," says Hanlon.

Hanlon has created his own form of encouragement for young mathematicians. In 1996, he founded and is the executive director of the Michigan Math Scholars, a program for talented high school students to explore the challenges of higher mathematics. With seed money coming from the UM Provost’s Office, the program is now essentially self-funded through gifts and participant tuition. Math Scholars attend summer mini-courses at UM on mathematical research topics and are supported during the following academic year by self-paced courses run over the Internet and by mentoring from Michigan math faculty and graduate students. "It's a great way to expose talented students to some of the most exciting work being done in mathematics while they are still in high school," Hanlon says.