, birth_date = , birth_place =

Kobrin Kobryn ( be, Кобрын; russian: Кобрин; pl, Kobryń; lt, Kobrynas; uk, Кобринь, Kobryn'; yi, קאָברין) is a city in the Brest Region of Belarus and the center of the Kobryn District. The city is located in the southwest ...

Russian Empire The Russian Empire was an empire and the final period of the Russian monarchy from 1721 to 1917, ruling across large parts of Eurasia. It succeeded the Tsardom of Russia following the Treaty of Nystad, which ended the Great Northern War. ...

, death_date = , death_place =

Brookline, Massachusetts Brookline is a town in Norfolk County, Massachusetts, Norfolk County, Massachusetts, in the United States, and part of the Greater Boston, Boston metropolitan area. Brookline borders six of Boston's neighborhoods: Brighton, Boston, Brighton, A ...

, United States , nationality =

American American(s) may refer to: * American, something of, from, or related to the United States of America, commonly known as the "United States" or "America" ** Americans, citizens and nationals of the United States of America ** American ancestry, pe ...

, field =

Mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, work_institutions =

Johns Hopkins University Johns Hopkins University (Johns Hopkins, Hopkins, or JHU) is a private university, private research university in Baltimore, Maryland. Founded in 1876, Johns Hopkins is the oldest research university in the United States and in the western hem ...

University of Illinois The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the University ...

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 ...

, alma_mater =

University of Kyiv Kyiv University or Shevchenko University or officially the Taras Shevchenko National University of Kyiv ( uk, Київський національний університет імені Тараса Шевченка), colloquially known as KNU ...

University of Rome , doctoral_advisor =

Guido Castelnuovo Guido Castelnuovo (14 August 1865 – 27 April 1952) was an Italian mathematician. He is best known for his contributions to the field of algebraic geometry, though his contributions to the study of statistics and probability theory are also signi ...

, doctoral_students =

S. S. Abhyankar Shreeram Shankar Abhyankar (22 July 1930 – 2 November 2012) was an Indian American mathematician known for his contributions to algebraic geometry. He, at the time of his death, held the Marshall Distinguished Professor of Mathematics Chair ...

Michael Artin Michael Artin (; born 28 June 1934) is a German-American mathematician and a professor emeritus in the Massachusetts Institute of Technology mathematics department, known for his contributions to algebraic geometry.Iacopo Barsotti Iacopo Barsotti, or Jacopo Barsotti (Turin, 28 April 1921 – Padua, 27 October 1987) was an Italian mathematician who introduced Barsotti–Tate groups. In 1942 he graduated from the Scuola Normale Superiore in Pisa, and became assistant profess ...

Irvin Cohen Irvin Sol Cohen (1917 – February 14, 1955) was an American mathematician at the Massachusetts Institute of Technology who worked on local rings. He was a student of Oscar Zariski at Johns Hopkins University. In his thesis he proved the Cohen ...

Daniel Gorenstein Daniel E. Gorenstein (January 1, 1923 – August 26, 1992) was an American mathematician. He earned his undergraduate and graduate degrees at Harvard University, where he earned his Ph.D. in 1950 under Oscar Zariski, introducing in his dissertati ...

Robin Hartshorne __NOTOC__ Robin Cope Hartshorne ( ; born March 15, 1938) is an American mathematician who is known for his work in algebraic geometry. Career Hartshorne was a Putnam Fellow in Fall 1958 while he was an undergraduate at Harvard University (under ...

Heisuke Hironaka is a Japanese mathematician who was awarded the Fields Medal in 1970 for his contributions to algebraic geometry. Career Hironaka entered Kyoto University in 1949. After completing his undergraduate studies at Kyoto University, he received his ...

Steven Kleiman Steven Lawrence Kleiman (born March 31, 1942) is an American mathematician. Professional career Kleiman is a Professor of Mathematics at the Massachusetts Institute of Technology. Born in Boston, he did his undergraduate studies at MIT. He rece ...

Joseph Lipman Joseph Lipman (born June 15, 1938) is a Canadian-American mathematician, working in algebraic geometry. Lipman graduated from the University of Toronto with a Bachelor's degree in 1960 and then went to Harvard University, receiving his master's d ...

David Mumford David Bryant Mumford (born 11 June 1937) is an American mathematician known for his work in algebraic geometry and then for research into vision and pattern theory. He won the Fields Medal and was a MacArthur Fellow. In 2010 he was awarded t ...

Maxwell Rosenlicht Maxwell Alexander Rosenlicht (April 15, 1924 – January 22, 1999) was an American mathematician known for works in algebraic geometry, algebraic groups, and differential algebra. Rosenlicht went to school in Brooklyn ( Erasmus High School) and ...

Pierre Samuel Pierre Samuel (12 September 1921 – 23 August 2009) was a French mathematician, known for his work in commutative algebra and its applications to algebraic geometry. The two-volume work ''Commutative Algebra'' that he wrote with Oscar Zariski ...

Abraham Seidenberg Abraham Seidenberg (June 2, 1916 – May 3, 1988) was an American mathematician. Early life Seidenberg was born on June 2, 1916 to Harry and Fannie Seidenberg in Washington D.C. He graduated with a B.A. from the University of Maryland in 1937. ...

, known_for = Contributions to

algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

, prizes =

Cole Prize The Frank Nelson Cole Prize, or Cole Prize for short, is one of twenty-two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to number ...

in Algebra (1944)

National Medal of Science The National Medal of Science is an honor bestowed by the President of the United States to individuals in science and engineering who have made important contributions to the advancement of knowledge in the fields of behavioral and social scienc ...

(1965)

Wolf Prize The Wolf Prize is an international award granted in Israel, that has been presented most years since 1978 to living scientists and artists for ''"achievements in the interest of mankind and friendly relations among people ... irrespective of natio ...

(1981)

Steele Prize The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. Since 1993, there has been a formal division into three categories. The prizes have ...

(1981) , footnotes = Oscar Zariski (April 24, 1899 – July 4, 1986) was a

Russia Russia (, , ), or the Russian Federation, is a List of transcontinental countries, transcontinental country spanning Eastern Europe and North Asia, Northern Asia. It is the List of countries and dependencies by area, largest country in the ...

n-born

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 ...

and one of the most influential

algebraic geometers Algebraic may refer to any subject related to algebra in mathematics and related branches like algebraic number theory and algebraic topology. The word algebra itself has several meanings. Algebraic may also refer to: * Algebraic data type, a data ...

of the 20th century.

Education

Zariski was born Oscher (also transliterated as Ascher or Osher) Zaritsky to a Jewish family (his parents were Bezalel Zaritsky and Hanna Tennenbaum) and in 1918 studied at the

. He left Kyiv in 1920 to study at the University of Rome where he became a disciple of the

Italian school of algebraic geometry In relation to the history of mathematics, the Italian school of algebraic geometry refers to mathematicians and their work in birational geometry, particularly on algebraic surfaces, centered around Rome roughly from 1885 to 1935. There were 30 ...

, studying with

Federigo Enriques Abramo Giulio Umberto Federigo Enriques (5 January 1871 – 14 June 1946) was an Italian mathematician, now known principally as the first to give a classification of algebraic surfaces in birational geometry, and other contributions in algebraic ...

and

Francesco Severi Francesco Severi (13 April 1879 – 8 December 1961) was an Italian mathematician. He was the chair of the committee on Fields Medal on 1936, at the first delivery. Severi was born in Arezzo, Italy. He is famous for his contributions to algeb ...

. Zariski wrote a doctoral dissertation in 1924 on a topic in

Galois theory In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems in field theory to ...

, which was proposed to him by Castelnuovo. At the time of his dissertation publication, he changed his name to Oscar Zariski.

Johns Hopkins University years

Zariski emigrated to the

United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territorie ...

in 1927 supported by

Solomon Lefschetz Solomon Lefschetz (russian: Соломо́н Ле́фшец; 3 September 1884 – 5 October 1972) was an American mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear o ...

. He had a position at

where he became professor in 1937. During this period, he wrote ''Algebraic Surfaces'' as a summation of the work of the Italian school. The book was published in 1935 and reissued 36 years later, with detailed notes by Zariski's students that illustrated how the field of algebraic geometry had changed. It is still an important reference. It seems to have been this work that set the seal of Zariski's discontent with the approach of the Italians to

birational geometry In mathematics, birational geometry is a field of algebraic geometry in which the goal is to determine when two algebraic varieties are isomorphic outside lower-dimensional subsets. This amounts to studying mappings that are given by rational fu ...

. He addressed the question of rigour by recourse to

commutative algebra Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent ...

. The

Zariski topology In algebraic geometry and commutative algebra, the Zariski topology is a topology which is primarily defined by its closed sets. It is very different from topologies which are commonly used in the real or complex analysis; in particular, it is n ...

, as it was later known, is adequate for ''biregular geometry'', where varieties are mapped by polynomial functions. That theory is too limited for algebraic surfaces, and even for curves with singular points. A rational map is to a regular map as a

rational function In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rat ...

is to a polynomial: it may be indeterminate at some points. In geometric terms, one has to work with functions defined on some open,

dense Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematically ...

set of a given variety. The description of the behaviour on the complement may require infinitely near points to be introduced to account for limiting behaviour ''along different directions''. This introduces a need, in the surface case, to use also

valuation theory In algebra (in particular in algebraic geometry or algebraic number theory), a valuation is a function on a field that provides a measure of size or multiplicity of elements of the field. It generalizes to commutative algebra the notion of size inhe ...

to describe the phenomena such as

blowing up In mathematics, blowing up or blowup is a type of geometric transformation which replaces a subspace of a given space with all the directions pointing out of that subspace. For example, the blowup of a point in a plane replaces the point with th ...

(balloon-style, rather than explosively).

Harvard University years

After spending a year 1946–1947 at the

University of Illinois at Urbana–Champaign The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the Universit ...

, Zariski became professor at

in 1947 where he remained until his retirement in 1969. In 1945, he fruitfully discussed foundational matters for algebraic geometry with

André Weil André Weil (; ; 6 May 1906 – 6 August 1998) was a French mathematician, known for his foundational work in number theory and algebraic geometry. He was a founding member and the ''de facto'' early leader of the mathematical Bourbaki group. Th ...

. Weil's interest was in putting an abstract variety theory in place, to support the use of the

Jacobian variety In mathematics, the Jacobian variety ''J''(''C'') of a non-singular algebraic curve ''C'' of genus ''g'' is the moduli space of degree 0 line bundles. It is the connected component of the identity in the Picard group of ''C'', hence an abelian vari ...

in his proof of the

Riemann hypothesis for curves over finite fields In number theory, the local zeta function (sometimes called the congruent zeta function or the Hasse–Weil zeta function) is defined as :Z(V, s) = \exp\left(\sum_^\infty \frac (q^)^m\right) where is a non-singular -dimensional projective algeb ...

, a direction rather oblique to Zariski's interests. The two sets of foundations weren't reconciled at that point. At Harvard, Zariski's students included Shreeram Abhyankar,

Michael Artin Michael Artin (; born 28 June 1934) is a German-American mathematician and a professor emeritus in the Massachusetts Institute of Technology mathematics department, known for his contributions to algebraic geometry.Steven Kleiman Steven Lawrence Kleiman (born March 31, 1942) is an American mathematician. Professional career Kleiman is a Professor of Mathematics at the Massachusetts Institute of Technology. Born in Boston, he did his undergraduate studies at MIT. He rece ...

—thus spanning the main areas of advance in

singularity theory In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up, dropping it ...

moduli theory In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects. Such space ...

and

cohomology In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewe ...

in the next generation. Zariski himself worked on equisingularity theory. Some of his major results,

Zariski's main theorem In algebraic geometry, Zariski's main theorem, proved by , is a statement about the structure of birational morphisms stating roughly that there is only one branch at any normal point of a variety. It is the special case of Zariski's connectedness ...

and the Zariski theorem on holomorphic functions, were amongst the results generalized and included in the programme of Alexander Grothendieck that ultimately unified algebraic geometry. Zariski proposed the first example of a

Zariski surface In algebraic geometry, a branch of mathematics, a Zariski surface is a surface over a field of characteristic ''p'' > 0 such that there is a dominant inseparable map of degree ''p'' from the projective plane to the surface. In particu ...

in 1958.

Views

Zariski was a

Jewish atheist Jewish atheism refers to the atheism of people who are ethnically and (at least to some extent) culturally Jewish. Contrary to popular belief, the term "Jewish atheism" is not a contradiction because Jewish identity encompasses not only religiou ...

Awards and recognition

Zariski was awarded the

in 1981, and in the same year the

Wolf Prize in Mathematics The Wolf Prize in Mathematics is awarded almost annually by the Wolf Foundation in Israel. It is one of the six Wolf Prizes established by the Foundation and awarded since 1978; the others are in Agriculture, Chemistry, Medicine, Physics and Arts. ...

with

Lars Ahlfors Lars Valerian Ahlfors (18 April 1907 – 11 October 1996) was a Finnish mathematician, remembered for his work in the field of Riemann surfaces and his text on complex analysis. Background Ahlfors was born in Helsinki, Finland. His mother, S ...

. He wrote also ''Commutative Algebra'' in two volumes, with

. His papers have been published by

MIT Press The MIT Press is a university press affiliated with the Massachusetts Institute of Technology (MIT) in Cambridge, Massachusetts (United States). It was established in 1962. History The MIT Press traces its origins back to 1926 when MIT publish ...

, in four volumes. In 1997 a conference was held in his honor in

Obergurgl Obergurgl is a village in the Ötztal Alps in Tyrol, Austria. Located in the municipality of Sölden, the village has approximately 400 year-round inhabitants, and is mainly a tourist resort. At an elevation of , Obergurgl is the highest parish i ...

, Austria.

Publications

* * * * * * * * * *

Notes

References

* * * *

External links

* *
Biography
from

United States Naval Academy The United States Naval Academy (US Naval Academy, USNA, or Navy) is a federal service academy in Annapolis, Maryland. It was established on 10 October 1845 during the tenure of George Bancroft as Secretary of the Navy. The Naval Academy ...

. {{DEFAULTSORT:Zariski, Oscar 1899 births 1986 deaths People from Kobryn People from Brookline, Massachusetts Belarusian atheists Belarusian Jews Jewish American atheists American people of Belarusian-Jewish descent 20th-century American mathematicians American mathematicians Institute for Advanced Study visiting scholars Belarusian scientists National Medal of Science laureates Algebraic geometers Johns Hopkins University faculty Harvard University faculty Wolf Prize in Mathematics laureates Presidents of the American Mathematical Society University of Illinois Urbana-Champaign faculty Members of the United States National Academy of Sciences Ukrainian mathematicians Italian mathematicians Emigrants from the Russian Empire to the United States