Oscar Zariski

Oscar Zariski (April 24, 1899 – July 4, 1986) was an American mathematician. He was born in Russia and became one of the most important algebraic geometers of the 20th century. Algebraic geometry is a part of math that combines algebra with geometry to study shapes and their properties.

Zariski made many big discoveries that helped change how mathematicians understand these shapes. His work gave new tools and ideas that people still use today. Because of his important contributions, he is remembered as a great thinker in the world of mathematics.

Education

Oscar Zariski was born into a Jewish family in Kobrin, Russian Empire. He began his studies at the University of Kiev in 1918 but later moved to the University of Rome in 1920. There, he studied under famous mathematicians and became part of the Italian school of algebraic geometry.

In 1924, Zariski completed his doctoral dissertation on a topic in Galois theory, suggested by his teacher Guido Castelnuovo. Around this time, he also changed his name to Oscar Zariski.

Johns Hopkins University years

Zariski moved to the United States in 1927, supported by Solomon Lefschetz. He worked at Johns Hopkins University and became a professor there in 1937. During this time, he wrote a book called Algebraic Surfaces, sharing ideas from Italian mathematicians. The book came out in 1935 and was printed again 36 years later with notes from his students showing how the study of shapes changed over time. It remains a useful guide today.

Zariski was not happy with how Italian mathematicians studied certain shapes. He used ideas from commutative algebra to make things clearer. He developed what is now called the Zariski topology, which helps describe smooth shapes. However, this method was not enough for more complex shapes, like those with unusual points. To understand these, he needed to look at points very close together and use special tools to describe what happens when shapes get "blown up" — like stretching a balloon.

Harvard University years

After a year at the University of Illinois at Urbana–Champaign, Zariski became a professor at Harvard University in 1947 and stayed there until he retired in 1969. During this time, he talked about important ideas in math with another mathematician named André Weil.

Zariski taught many students who later became famous mathematicians, such as Shreeram Abhyankar, Heisuke Hironaka, David Mumford, Michael Artin, and Steven Kleiman. He also worked on special topics in math and wrote a book called Commutative Algebra with Pierre Samuel.

Views

Zariski was a Jewish atheist. This means he did not believe in any gods.

Awards and recognition

Oscar Zariski was honored with many important awards for his work. He became a member of the United States National Academy of Sciences in 1944, the American Academy of Arts and Sciences in 1948, and the American Philosophical Society in 1951. He received a Guggenheim Fellowship in 1939 and the U.S. National Medal of Science in 1965.

Zariski also won the Cole Prize in 1944, the Steele Prize in 1981, and the Wolf Prize in Mathematics together with Lars Ahlfors in 1981. From 1969 to 1970, he served as President of the American Mathematical Society. His writings were published by MIT Press in four books, and a special event was held for him in Obergurgl, Austria, in 1997.

Publications

Here are some important books written by Oscar Zariski, a famous mathematician known for his work in algebraic geometry:

• Zariski, Oscar (2004) [1935], Abhyankar, Shreeram S.; Lipman, Joseph; Mumford, David (eds.), Algebraic surfaces, Classics in mathematics (second supplemented ed.), Berlin, New York: Springer-Verlag, ISBN 978-3-540-58658-6, MR (https://mathscinet.ams.org/mathscinet-getitem?mr=0469915)
• Zariski, Oscar (1958), Introduction to the problem of minimal models in the theory of algebraic surfaces, Publications of the Mathematical Society of Japan, vol. 4, The Mathematical Society of Japan, Tokyo, MR (https://mathscinet.ams.org/mathscinet-getitem?mr=0097403)
• Zariski, Oscar (1969) [1958], Cohn, James (ed.), An Introduction to the Theory of Algebraic Surfaces, Lecture notes in mathematics, vol. 83, Berlin, New York: Springer-Verlag, doi:10.1007/BFb0082246, ISBN 978-3-540-04602-8, MR (https://mathscinet.ams.org/mathscinet-getitem?mr=0263819)
• Zariski, Oscar; Samuel, Pierre (1975) [1958], Commutative algebra I, Graduate Texts in Mathematics, vol. 28, Berlin, New York: Springer-Verlag, ISBN 978-0-387-90089-6, MR (https://mathscinet.ams.org/mathscinet-getitem?mr=0090581)
• Zariski, Oscar; Samuel, Pierre (1975) [1960], Commutative algebra. Vol. II, Berlin, New York: Springer-Verlag, ISBN 978-0-387-90171-8, MR (https://mathscinet.ams.org/mathscinet-getitem?mr=0389876)
• Zariski, Oscar (2006) [1973], Kmety, François; Merle, Michel; Lichtin, Ben (eds.), The moduli problem for plane branches, University Lecture Series, vol. 39, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-2983-7, MR (https://mathscinet.ams.org/mathscinet-getitem?mr=0414561)(original title): Le problème des modules pour les branches planes`{{}}: CS1 maint: postscript (link)
• Zariski, Oscar (1972), Collected papers. Vol. I: Foundations of algebraic geometry and resolution of singularities, Cambridge, Massachusetts-London: MIT Press, ISBN 978-0-262-08049-1, MR (https://mathscinet.ams.org/mathscinet-getitem?mr=0505100)
• Zariski, Oscar (1973), Collected papers. Vol. II: Holomorphic functions and linear systems, Mathematicians of Our Time, Cambridge, Massachusetts-London: MIT Press, ISBN 978-0-262-01038-2, MR (https://mathscinet.ams.org/mathscinet-getitem?mr=0505100)
• Zariski, Oscar (1978), Artin, Michael; Mazur, Barry (eds.), Collected papers. Volume III. Topology of curves and surfaces, and special topics in the theory of algebraic varieties, Mathematicians of Our Time, Cambridge, Massachusetts-London: MIT Press, ISBN 978-0-262-24021-5, MR (https://mathscinet.ams.org/mathscinet-getitem?mr=0505104)
• Zariski, Oscar (1979), Lipman, Joseph; Teissier, Bernard (eds.), Collected papers. Vol. IV. Equisingularity on algebraic varieties, Mathematicians of Our Time, vol. 16, MIT Press, ISBN 978-0-262-08049-1, MR (https://mathscinet.ams.org/mathscinet-getitem?mr=0545653)