Benjamin Alvord (mathematician)

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Benjamin Alvord
Benjamin Alvord mathematician - Brady-Handy.jpg
Brigadier General Benjamin Alvord
Born (1813-08-18)August 18, 1813
Rutland, Vermont
Died October 16, 1884(1884-10-16) (aged 71)
Washington, D.C.
Place of burial Arlington Cemetery Section 4, Grave 2215-WS
Allegiance United States of America
Service/branch United States Army
Union Army
Years of service 1833–1880
Rank Union Army brigadier general rank insignia.svg Brigadier General
Unit 4th U.S. Infantry
Commands held District of Oregon
Paymaster-General of the United States Army

Indian Wars

Mexican–American War

American Civil War

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

Early life and career[edit]

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.[1]

He was assigned to the 4th U.S. Infantry and participated in the Seminole Wars.[1] He returned to West Point as an assistant professor of mathematics until 1839, when he was again assigned to the 4th Infantry. He spent 21 years of his military career with that regiment.

He was on frontier, garrison, and engineer duty until 1846, when he participated in the military occupation of the new state of Texas. Subsequently, he served during the Mexican–American War, being brevetted successively to captain and major for gallantry in a number of important battles including the Battle of Palo Alto and the Battle of Resaca de la Palma. He served as chief of staff to Major Folliott T. Lally's column on the march from Vera Cruz to Mexico City in 1847.

After the Mexican–American War, he went from line to staff when he was named paymaster and promoted to major. He was assigned to various posts and was sent with the 4th Infantry to the West Coast. He was the engineer in charge of building the military road in southern Oregon. He was then chief paymaster in Oregon from 1854 until 1862.[1]

Civil War service[edit]

From 1862 to 1865, during the American Civil War, Alvord was at Fort Vancouver as the commander of the District of Oregon with the rank of brigadier general of volunteers. He was named to that post by George Wright, the commanding officer of the Department of the Pacific. Wright wanted an experienced Regular Army officer in that post, rather than a volunteer, since the District was large (encompassing the present-day states of Oregon, Washington, and Idaho), underdeveloped, and had a history of friction between the native peoples and settlers. As commander of the District, Alvord built up the defenses around the mouth of the Columbia River, but was unable to do the same for Puget Sound. Because of low enlistments from Oregon and Washington, he supported the military draft, and failing that, supported the payment of bounties. He was removed from command in March 1865.[2][3] He was ordered to the East Coast, where he resigned his volunteer commission and became paymaster in New York City.

Circles and spheres[edit]

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.[4]

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.[5] where he explained the delay:

All of this memoir, except the last two problems, were completed and sent to the Smithsonian Institute [sic] 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.[6]

The article is graced with annotations by Arthur Cayley and the concession that Darboux had preceded Alvord in print.[7]


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. He was promoted to brigadier general in 1876.

He also wrote on natural history, writing the first scientific description of the ability of the compass plant (Silphium laciniatum) to orient itself in a north-south direction,[8] as well as writing about winter grazing in the Rocky Mountains.[9] Alvord was a contributor to Harper's Magazine,[10] and a member of the Literary Society of Washington.[11]

Personal life and family[edit]

He married Emily Louise Mussey in 1846 and they had six children.[1] His son, Benjamin Alvord, Jr., became a soldier and was a general in World War I. His daughter Louise married Thomas Craig, one of the main professors of mathematics at Johns Hopkins University during its first two decades.

Death and legacy[edit]

He died on October 16, 1884[1] in Washington, D.C. and is buried at Arlington National Cemetery Section 4, Grave 2215-WS.

Alvord Valley and the Alvord Desert in Oregon were named in his honor.[12]

See also[edit]


  1. ^ a b c d e Marquis Who's Who, Inc. Who Was Who in American History, the Military. Chicago: Marquis Who's Who, 1975. P. 9 ISBN 0837932017 OCLC 657162692
  2. ^ Hubbell and Geary (p. 6) state he was removed because: Army commanding general, Ulysses S. Grant, thought Alvord ill-suited for command; Oregon's Representative, John R. McBride, accused him of being a "tool of anti-Union men"; and because of Alvord's support of the draft and bounties.
  3. ^ Alvord apparently had heard rumors about his service and asked Department commander Irvin McDowell about them. In a letter dated April 12, 1865, McDowell wrote to Secretary of War, Edwin Stanton, addressing Alvord's concerns. McDowell praised Alvord and said that he was unaware of any negative remarks (War of the Rebellion, Series I, Vol. L, Part II, pp. 1193–1194)
  4. ^ B. Alvord (1855) Tangencies of Circles and of Spheres, Smithsonian Contributions, volume 8, from Google Books
  5. ^ B. Alvord (1882) The Intersection of Circles and the Intersection of Spheres, American Journal of Mathematics 5(1): 25–44
  6. ^ B. Alvord (1882) The Intersection of Circles and the Intersection of Spheres, American Journal of Mathematics 5(1): 25–44
  7. ^ Jean Gaston Darboux (1872) "The relations between groups of points of circles and spheres in a plane and in space", Annales de l’Ecole Normale Superieure, Series 2, volume 1, page 323
  8. ^ Alvord, Benjamin. "On the Compass Plant". The American Naturalist. 16 (8): 625–635. doi:10.1086/273143. JSTOR 2449634. 
  9. ^ Alvord, Benjamin. "Winter Grazing in the Rocky Mountains". Journal of the American Geographical Society of New York. 15: 257–288. JSTOR 196543. 
  10. ^ Essays by Benjamin Alvord in Harper's Magazine are listed at
  11. ^ Alvord is listed in the directory of members of the Society in Helen Nicolay's Sixty Years of the Literary Society, Washington, D.C., 1934. Library of Congress call number PN22.L53 N5. Google Books [1].
  12. ^ Corning, Howard M. Dictionary of Oregon History. Binfords & Mort Publishing, 1956.


  • Hubbell, John T., and James W. Geary (editors). Biographical Dictionary of the Union: Northern Leaders of the Civil War. Westport, CT: Greenwood Press, 1995. ISBN 0-313-20920-0.
  • Johnson, Allen (editor). Dictionary of American Biography. New York: Charles Scribner's Sons, 1946. OCLC 796804
  • Johnson, Rossiter (editor). The Twentieth Century Biographical Dictionary of Notable Americans. Boston: The Biographical Society, 1904. OCLC 6182270
  • Warner, Ezra J., Generals in Blue: Lives of the Union Commanders. Louisiana State University Press, 1964. OCLC 445056 Reissued in 2006 by Easton Press. OCLC 652052238


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