# Oswald Veblen

**Oswald Veblen** (June 24, 1880 – August 10, 1960) was an American mathematician, geometer and topologist, whose work found application in atomic physics and the theory of relativity. He proved the Jordan curve theorem in 1905;[1] while this was long considered the first rigorous proof, many now also consider Camille Jordan's original proof rigorous.

Oswald Veblen | |
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Oswald Veblen (photograph c.1915) | |

Born | Decorah, Iowa, United States | June 24, 1880

Died | August 10, 1960 80) Brooklin, Maine, United States | (aged

Citizenship | USA |

Alma mater | University of Iowa Harvard University University of Chicago |

Scientific career | |

Institutions | Princeton University Institute for Advanced Study |

Thesis | A System of Axioms for Geometry (1903) |

Doctoral advisor | E. H. Moore |

Doctoral students | J. W. Alexander H. Roy Brahana Alonzo Church Philip Franklin Harold Hotelling Howard H. Mitchell Robert Lee Moore Tracy Thomas J. H. C. Whitehead |

## Early life

Veblen was born in Decorah, Iowa. His parents were Andrew Anderson Veblen (1848–1932), Professor of Physics at the University of Iowa, and Kirsti (Hougen) Veblen (1851–1908). Veblen's uncle was Thorstein Veblen, noted economist and sociologist.

Oswald went to school in Iowa City. He did his undergraduate studies at the University of Iowa, where he received an A.B. in 1898, and Harvard University, where he was awarded a second B.A. in 1900. For his graduate studies, he went to study mathematics at the University of Chicago, where he obtained a Ph.D. in 1903. His dissertation, *A System of Axioms for Geometry* was written under the supervision of E. H. Moore. During World War I, Veblen served first as a captain, later as a major in the United States Army.[2]

## Career

Veblen taught mathematics at Princeton University from 1905 to 1932. In 1926, he was named Henry B. Fine Professor of Mathematics. In 1932, he helped organize the Institute for Advanced Study in Princeton, resigning his professorship to become the first professor at the Institute that same year. He kept his professorship at the Institute until he was made emeritus in 1950. [3]

During his years in Princeton, Veblen and his wife, Elizabeth M D Richardson, accumulated land along the Princeton Ridge. In 1957 they donated 82 acres (33 ha) to establish the Herrontown Woods Arboretum, one of the largest nature preserves in Princeton, New Jersey.[4]

Veblen was a Plenary Speaker of the ICM in 1928 in Bologna and in 1936 in Oslo.[5]

Veblen died in Brooklin, Maine, in 1960 at age 80. After his death the American Mathematical Society created an award in his name, called the Oswald Veblen Prize in Geometry. It is awarded every three years, and is the most prestigious award in recognition of outstanding research in geometry.

## Accomplishments

During his career, Veblen made important contributions in topology and in projective and differential geometries, including results important in modern physics. He introduced the Veblen axioms for projective geometry and proved the Veblen–Young theorem. He introduced the Veblen functions of ordinals and used an extension of them to define the small and large Veblen ordinals. In World War II he was involved in overseeing ballistics work at the Aberdeen Proving Ground that involved early modern computing machines, in particular supporting the proposal for creation of the pioneering ENIAC electronic digital computer.[6][7][8] He also published a paper in 1912 on the four-color conjecture.

## Personal life

In 1908, he married Elizabeth Richardson, the sister of British physicist Owen Willans Richardson and sister-in-law of American physicist Clinton Joseph Davisson.[9][10]

## Books by O. Veblen

- Introduction to infinitesimal analysis; functions of one real variable with N. J. Lennes (John Wiley & Sons, 1907)[11]
- Projective geometry with John Wesley Young (Ginn and Co., Vol. 1, 1910;[12] Vol. 2, 1918[13])
- Analysis Situs (American Mathematical Society, 1922;[14] 2nd edn. 1931)
- Invariants of Quadratic Differential Forms (Cambridge University Press, 1927)[15]
- The Foundations of Differential Geometry with J. H. C. Whitehead (Cambridge University Press, 1932)[16]
- Projektive Relativitätstheorie (Springer Verlag, 1933)[17]

## References

- Mac Lane, Saunders (1964). "Oswald Veblen
*June 24, 1880—August 10, 1960*" (PDF).*Biographical Memoirs of the National Academy of Sciences*. Washington, D.C. - O'Connor, J. J. and E F Robertson. "Oswald Veblen". School of Mathematics and Statistics, University of St Andrews, Scotland. Retrieved April 20, 2016.CS1 maint: uses authors parameter (link)
- Batterson, Steve (May 2007). "The Vision, Insight, and Influence ofOswald Veblen" (PDF).
**54**(5). Notices of the American Mathematical Society. Retrieved April 20, 2016. Cite journal requires`|journal=`

(help) - "Large Tract Donated".
*The Town Topics*. 28 July 1957. Retrieved 19 April 2014. - Veblen, Oswald (1937). "Spinors and projective geometry". In:
*Comptes rendus du Congrès international des mathématiciens: Oslo, 1936*. vol. 1. pp. 111–127. - Mac Lane (1964), pg 333.
- "ARL Computing History". The Computer, from Pascal to von Neumann.
*Arl.Army.mil*. 2010. Retrieved 2019-09-09. - "The History of Computing at BRL" Archived 2005-04-19 at the Wayback Machine, [Mike Muuss]
- Nobel Foundation (1928). "Owen Willans Richardson: The Nobel Prize in Physics 1928".
*Les Prix Nobel*. Retrieved April 25, 2016. - Nobel Foundation (1937). "Clinton Joseph Davisson: The Nobel Prize in Physics 1937".
*Les Prix Nobel*. Retrieved April 25, 2016. - Pierpont, James (1908). "Review:
*Introduction to infinitesmal analysis, functions of one real variable*".*Bull. Amer. Math. Soc*.**15**(3): 133–134. doi:10.1090/s0002-9904-1908-01710-5. - Coolidge, Julian Lowell (1911). "Review:
*Projective Geometry*, Vol. 1".*Bull. Amer. Math. Soc*.**18**(2): 70–81. doi:10.1090/s0002-9904-1911-02156-5. - Moore, R. L. (1920). "Review:
*Projective Geometry*, Vol. 2".*Bull. Amer. Math. Soc*.**26**(9): 412–425. doi:10.1090/s0002-9904-1920-03332-x. - Lefschetz, S. (1924). "Review:
*Analysis Situs*, by O. Veblen".*Bull. Amer. Math. Soc*.**30**(7): 357–358. doi:10.1090/s0002-9904-1924-03901-9. - Taylor, J. H. (1929). "Review:
*Invariants of Quadratic Differential Forms*, by O. Veblen".*Bull. Amer. Math. Soc*.**35**(3): 416. doi:10.1090/s0002-9904-1929-04779-7. - MacDuffee, C. C. (1933). "Review:
*The Foundations of Differential Geometry*, by O. Veblen and J. H. C. Whitehead".*Bull. Amer. Math. Soc*.**39**(5): 322–324. doi:10.1090/s0002-9904-1933-05600-8. - Struik, D. J. (1934). "Review:
*Projektive Relativitätstheorie*, by O. Veblen".*Bull. Amer. Math. Soc*.**40**(3): 191–193. doi:10.1090/s0002-9904-1934-05803-8.

## External links

Wikiquote has quotations related to: Oswald Veblen |

Wikimedia Commons has media related to .Oswald Veblen |

- O'Connor, John J.; Robertson, Edmund F., "Oswald Veblen",
*MacTutor History of Mathematics archive*, University of St Andrews. - Obituary and Bibliography of Oswald Veblen (also available here.)
- Works by Oswald Veblen at Project Gutenberg
- Works by or about Oswald Veblen at Internet Archive
- "Projective relativity theory," transl. by D. H. Delphenich
- Oswald Veblen at the Mathematics Genealogy Project