Buhler received his undergraduate degree from Reed College in 1972, and his Ph.D. from Harvard University in 1977 with thesis Icosahedral Galois Representations and thesis advisor John Tate.
[1][2] Buhler was a professor at Reed College in Portland, Oregon from 1980 until his retirement in 2005.
[3] From 2004 to 2017, he was director of the IDA Center for Communications Research in La Jolla, California.
[5] Buhler is involved in a project to numerically verify the Kummer–Vandiver conjecture of Harry Vandiver and Ernst Eduard Kummer concerning the class number of cyclotomic fields.
Vandiver proved it with a desk calculator up to class number 600, Derrick Lehmer (in the late 1940s) to about 5000, and Buhler with colleagues (in 2001) to 12 million.