Gilbert Allan Stengle, 77, of Princeton, N.J., passed away following a prolonged illness on Monday, Nov. 8, 2010, at Potomac Homes in Princeton, N.J., with his family at his side.

Born in Regina, Saskatchewan, he moved to Buffalo, N.Y., in his early childhood and went on to earn Bachelors' and Master of Science degrees in Engineering Physics at Cornell University, Cornell, N.Y.

After working as a senior project engineer at General Motors Corporation in Milwaukee, Wis., he went on to complete his Ph.D. in Mathematics from the University of Wisconsin-Madison, followed by a postdoctoral appointment at the Courant Institute at New York University.

Professor Emeritus from Lehigh University in Bethlehem, Pa., Stengle retired in 2002 after 42 years of mathematics teaching and research. He served as an advisor to twelve Ph.D. candidates and served as department chair for three years. Either as a solo author or with one of 10 collaborators, he published numerous papers in more than 25 technical journals in subject areas such as differential equations, numerical analysis, probability and statistics, and real algebraic geometry.

Stengle is credited for discovering the Positivstellensatz, an improved characterization of positive definiteness for polynomials over the one identified in Hilbert's 17th problem, as well as for discovering a positive semi-definite polynomial with the property that no odd power is a sum of squares. As a regular speaker at the Mathematisches Forschungsinstitut Oberwolfach, Stengle was instrumental in transforming the field of Real Algebraic Geometry into the discipline it is today.

He held research appointments at the Mathematical Sciences Research Institute in Berkeley, Calif., Stanford University, the University of Regensburg, Germany, and the University Complutense in Madrid, Spain. He taught graduate courses for one semester at Wuhan University in the People's Republic of China.

An avid music lover, Stengle sang in several choruses including the Lehigh University Chorus and the Westminster Community Chorus.

Stengle is survived by his wife, Sylvia Stengle, his son and daughter-in-law, David and Karin Borchert Stengle, and his daughter, Sarah Stengle, of Princeton; his daughter and son-in-law, Rebekah and Stephen Dupont, of Minneapolis, Minn.; his brother and sister-in-law, Bill and Rebecca Stengle, of Ann Arbor, Mich., and his sister and brother-in-law, Barbara and Corky Stengle, of Marathon, N.Y., along with six grandchildren.

A memorial service will be conducted on Saturday, Dec. 4, 2010, at 11:45 a.m., at the Princeton Senior Resource Center in Princeton, N.J.. Visitors will be welcomed beginning at 10:00 a.m.

In lieu of flowers, contributions may be made to the Gilbert Stengle Memorial Scholarship Fund, P.O. Box 642, Princeton, NJ 08540. His family has created this fund to show appreciation for the aides who gave loving care to him during his stay at Potomac Homes for the past 14 months.