Annie Smith Peck (1850 - 1935)

Annie was born in Rhode Island and graduated from Rhode Island College (what was then Rhode Island Normal School). She moved to Michigan to teach school and soon enrolled at the University of Michigan. The University had just begun to allow women to enroll. She finished a degree in Greek and classical languages. She then taught at Purdue University ( the first woman to do so) and after a two sojourn in Europe she moved to Smith College. At the age of 42 she took up mountain climbing. She became first woman to climb the Matterhorn. In 1908 at the age of 58 she climbed Mt. Huascaran in Peru. At that time she thought it to be the tallest mountain in South America. She was not only the first woman to climb the mountain, but also the first person to do so. Her climbing gear was self-designed as there were no sources of gear for woman at this time. In 1909 she climbed another South American peak, Mt. Coropuna (21,083 ft). She continued to climb throughout the remainder of her life and in fact, climbed Mt. Madison at the age of 82.  

Some sources of information:

Webpage dealing with Annie Smith Peck
Living on Earth broadcast dealing with Annie Smith Peck--This webpage has some photos of her climbing experiences in South America.