Oswald Veblen (June 24, 1880 – August 10, 1960) was an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

geometer A geometer is a mathematician whose area of study is geometry. Some notable geometers and their main fields of work, chronologically listed, are: 1000 BCE to 1 BCE * Baudhayana (fl. c. 800 BC) – Euclidean geometry, geometric algebra * ...

and

topologist In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ho ...

, whose work found application in

atomic physics Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. Atomic physics typically refers to the study of atomic structure and the interaction between atoms. It is primarily concerned wit ...

and the

theory of relativity The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in ...

. He proved the

Jordan curve theorem In topology, the Jordan curve theorem asserts that every ''Jordan curve'' (a plane simple closed curve) divides the plane into an " interior" region bounded by the curve and an "exterior" region containing all of the nearby and far away exterior ...

in 1905; while this was long considered the first rigorous proof of the theorem, many now also consider

Camille Jordan Marie Ennemond Camille Jordan (; 5 January 1838 – 22 January 1922) was a French mathematician, known both for his foundational work in group theory and for his influential ''Cours d'analyse''. Biography Jordan was born in Lyon and educated at ...

's original proof rigorous.

Early life

Veblen was born in

Decorah, Iowa Decorah is a city in and the county seat of Winneshiek County, Iowa, United States. The population was 7,587 at the time of the 2020 census. Decorah is located at the intersection of State Highway 9 and U.S. Route 52, and is the largest commun ...

. His parents were Andrew Anderson Veblen (1848–1932), Professor of Physics at the

University of Iowa The University of Iowa (UI, U of I, UIowa, or simply Iowa) is a public university, public research university in Iowa City, Iowa, United States. Founded in 1847, it is the oldest and largest university in the state. The University of Iowa is org ...

, and Kirsti (Hougen) Veblen (1851–1908). Veblen's uncle was

Thorstein Veblen Thorstein Bunde Veblen (July 30, 1857 – August 3, 1929) was a Norwegian-American economist and sociologist who, during his lifetime, emerged as a well-known critic of capitalism. In his best-known book, ''The Theory of the Leisure Class'' ...

, noted economist and sociologist. Oswald went to school in

Iowa City Iowa City, offically the City of Iowa City is a city in Johnson County, Iowa, United States. It is the home of the University of Iowa and county seat of Johnson County, at the center of the Iowa City Metropolitan Statistical Area. At the time ...

. He did his undergraduate studies at the University of Iowa, where he received an AB in 1898, and

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

, where he was awarded a second BA in 1900. For his graduate studies, he went to study mathematics at the

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the b ...

, where he obtained a

PhD PHD or PhD may refer to: * Doctor of Philosophy (PhD), an academic qualification Entertainment * '' PhD: Phantasy Degree'', a Korean comic series * ''Piled Higher and Deeper'', a web comic * Ph.D. (band), a 1980s British group ** Ph.D. (Ph.D. albu ...

in 1903. His dissertation, ''A System of Axioms for Geometry'' was written under the supervision of

E. H. Moore Eliakim Hastings Moore (; January 26, 1862 – December 30, 1932), usually cited as E. H. Moore or E. Hastings Moore, was an American mathematician. Life Moore, the son of a Methodist minister and grandson of US Congressman Eliakim H. Moore, di ...

. During

World War I World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fightin ...

, Veblen served first as a captain, later as a major in the

United States Army The United States Army (USA) is the land service branch of the United States Armed Forces. It is one of the eight U.S. uniformed services, and is designated as the Army of the United States in the U.S. Constitution.Article II, section 2, cla ...

Career

Veblen taught mathematics at

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

from 1905 to 1932. In 1926, he was named

Henry B. Fine Henry Burchard Fine (September 14, 1858 – December 22, 1928) was an American university dean and mathematician. Life and career Henry Burchard Fine (1858 – 1928) played a critical role in modernizing the American university and raising ...

Professor of Mathematics. In 1932, he helped organize the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

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. During his years in Princeton, Veblen and his wife, Elizabeth M D Richardson, accumulated land along the Princeton Ridge. In 1957 they donated to establish the

Herrontown Woods Arboretum Herrontown Woods Arboretum (142 acres) is an arboretum located on Snowden Lane near the junction with Herrontown Road, in Princeton, New Jersey. It is open to the public every day at no cost. There are walking trails, but trail bicycles are proh ...

, the first and one of the largest nature preserves in

Princeton, New Jersey Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of whi ...

. Veblen was a Plenary Speaker of the ICM in 1928 in Bologna and in 1936 in Oslo. Veblen died in

Brooklin, Maine Brooklin is a town in Hancock County, Maine, United States. The population was 827 at the 2020 census. History Brooklin was originally part the larger town of Sedgwick. Brooklin broke off and formed its own town in 1849. A few weeks later, t ...

, in 1960 at age 80. After his death the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

created an award in his name, called the

Oswald Veblen Prize in Geometry __NOTOC__ The Oswald Veblen Prize in Geometry is an award granted by the American Mathematical Society for notable research in geometry or topology. It was founded in 1961 in memory of Oswald Veblen. The Veblen Prize is now worth US$5000, and is ...

. 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 Modern physics is a branch of physics that developed in the early 20th century and onward or branches greatly influenced by early 20th century physics. Notable branches of modern physics include quantum mechanics, special relativity and general ...

. He introduced the Veblen axioms for projective geometry and proved the

Veblen–Young theorem In mathematics, the Veblen–Young theorem, proved by , states that a projective space of dimension at least 3 can be constructed as the projective space associated to a vector space over a division ring. Non-Desarguesian planes give examples of 2 ...

. He introduced the

Veblen function In mathematics, the Veblen functions are a hierarchy of normal functions ( continuous strictly increasing functions from ordinals to ordinals), introduced by Oswald Veblen in . If φ0 is any normal function, then for any non-zero ordinal α, φ ...

s of ordinals and used an extension of them to define the small and large Veblen ordinals. In

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...

he was involved in overseeing ballistics work at the

Aberdeen Proving Ground Aberdeen Proving Ground (APG) (sometimes erroneously called Aberdeen Proving ''Grounds'') is a U.S. Army facility located adjacent to Aberdeen, Harford County, Maryland, United States. More than 7,500 civilians and 5,000 military personnel work at ...

that involved early modern

computing machine A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These programs ...

s, in particular supporting the proposal for creation of the pioneering

ENIAC ENIAC (; Electronic Numerical Integrator and Computer) was the first programmable, electronic, general-purpose digital computer, completed in 1945. There were other computers that had these features, but the ENIAC had all of them in one packa ...

electronic

digital computer A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations ( computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These pro ...

. He also published a paper in 1912 on the

four-color conjecture In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color. ''Adjacent'' means that two regions sh ...

Personal life

In 1908, he married Elizabeth Richardson, the sister of British physicist

Owen Willans Richardson Sir Owen Willans Richardson, FRS (26 April 1879 – 15 February 1959) was a British physicist who won the Nobel Prize in Physics in 1928 for his work on thermionic emission, which led to Richardson's law. Biography Richardson was born in Dews ...

and sister-in-law of American physicist

Clinton Joseph Davisson Clinton Joseph Davisson (October 22, 1881 – February 1, 1958) was an American physicist who won the 1937 Nobel Prize in Physics for his discovery of electron diffraction in the famous Davisson–Germer experiment. Davisson shared the Nobel Priz ...

Veblen Research Instructorship

The Veblen Research Instructorship is a three-year position offered by the Department of Mathematics at

and the

. This position was established in 1998 and offered each year to outstanding candidates in pure and applied mathematics who have received their PhD within the last three years. The Veblen instructors are Members of the Institute for Advanced Study and regular faculty members at Princeton University. The first and third year of the instructorship are spent at Princeton University and carry regular teaching responsibilities. The second year is spent at the Institute and dedicated to independent research of the instructor's choice.

Books by O. Veblen

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

References

External links

*
Obituary and Bibliography of Oswald Veblen
(also available
here
) * *
"Projective relativity theory," transl. by D. H. Delphenich
* {{DEFAULTSORT:Veblen, Oswald 20th-century American mathematicians Topologists Geometers Ballistics experts 1880 births 1960 deaths Institute for Advanced Study faculty People from Decorah, Iowa University of Iowa alumni Harvard University alumni University of Chicago alumni Princeton University faculty American people of Norwegian descent Presidents of the American Mathematical Society Mathematicians from Iowa