Benjamin Peirce was a graduate of Harvard and became a tutor there in 1831, two years after graduating. He worked on a wide range of mathematical topics from celestial mechanics and geodesy on the applied side to linear associative algebra and number theory on the pure side.
In an early number theory paper he proved that there is no odd
perfect number with fewer
than four distinct prime factors. He also
revised and wrote a commentary on Bowditch's translation of the first four
volumes of Laplace's Traité de mécanique céleste.
Appointed
professor at Harvard in 1833 he was to establish the Harvard Observatory. Peirce
helped determine the orbit of Neptune (discovered in 1846) and calculated the
perturbations produced by Neptune on the orbit of Uranus and on the other
planets.
In 1870 Peirce published, at his own expense, Linear Associative Algebra a classification of all complex associative algebras of dimension less than seven. He used the, now familiar, tools of idempotent and nilpotent elements.
Earlier, in 1852, Peirce had introduced methods into the theory of errors applied to observations which would allow faulty observations to be discarded.