Benjamin Alvord

Benjamin Alvord (August 18, 1813 – October 16, 1884) was an American soldier, mathematician, and botanist.

Early life and career Alvord was born in Rutland, Vermont, where he developed an interest in nature. He attended the United States Military Academy and displayed a talent in mathematics. He graduated in 1833.

He was assigned to the 4th U.S. Infantry and participated in the Seminole Wars. He was ordered to the East Coast, where he resigned his volunteer commission and became paymaster in New York City.

Circles and spheres

Alvord was interested in the classical problem of Apollonius, to find a circle tangent to three given circles, and the special cases of Apollonius' problem, as well as the generalization to spheres. In 1855, he published in Smithsonian Contributions to Knowledge.

Posted to the remote Fort Vancouver, he continued his investigations and submitted his findings in 1860, but was frustrated by a fire. In 1882, when he found that there are 96 circles which cut four given circles at a fixed angle and there are 640 spheres which cut five given spheres at a fixed angle, he assembled all his results for an article in American Journal of Mathematics, where he explained the delay: All of this memoir, except the last two problems, were completed and sent to the Smithsonian Institute in January 1860, from Fort Vancouver, Washington Territory, but the manuscript was burned in January 1865 when the upper story of the Smithsonian building was on fire. The article is graced with annotations by Arthur Cayley and the concession that Darboux had preceded Alvord in print.

Postbellum After the war, he subsequently became paymaster of the District of Omaha and paymaster of the Department of the Platte. He became Paymaster General of the Army in 1872 and served in that capacity until his retirement from active service in 1880, when he was succeeded by Nathan W. Brown. as well as writing about winter grazing in the Rocky Mountains. Alvord was a contributor to Harper's Magazine, and a member of the Literary Society of Washington.

Personal life and family

He married Emily Louise Mussey in 1846, and they had six children.