The 10 black students in his incoming class were the largest group Caltech had ever enrolled, he learned when he wrote a paper on the little-known history of being black at Caltech for a summer research project. Only three of the others graduated with him four years later.

Most of his classmates, Dr. Goins quickly realized, had arrived with math training that went far beyond his own. In his freshman year, he sometimes called his high school calculus teacher for help with the homework. In his sophomore year, he watched from his dormitory television as the 1992 Los Angeles riots erupted a few blocks from his mother’s home. But he also came to excel in applied math, which traffics in real-world problems, and, later, to immerse himself in “pure math,” which seeks to elucidate the questions intrinsic to mathematics itself.

Dr. Goins won two math prizes at Caltech, and in 1999 he received a Ph.D. from Stanford’s math department — one of three African-Americans that have ever done so, according to an informal count by William Massey, a Princeton professor who received the second. In 2004, after holding a visiting scholar position at the Institute for Advanced Study in Princeton and another at Harvard, Dr. Goins joined the faculty of Purdue in West Lafayette, Ind.

“You are such an inspiration to us all,” Talitha Washington, a black mathematician who is now a tenured professor at Howard University, wrote on his Facebook page when he received tenure in the spring of 2010.

Yet having emerged at the far end of the pipeline, Dr. Goins found himself unwilling to stay. Last fall, in a move almost unheard-of in the academic ecosystem, he traded his full professor post at Purdue, where federal resources are directed at tackling science’s unsolved problems and training a new generation of Ph.D.’s, for a full professorship at Pomona, a liberal arts college outside Los Angeles that prioritizes undergraduate teaching.