David Harbater
Encyclopedia
David Harbater is an American
mathematician
, well known for his work in Galois theory
, algebraic geometry
and arithmetic geometry.
and attended Stuyvesant High School
, where he was on the Math Team. After graduating in 1970, he entered Harvard University
, where one of his classmates and a fellow alumnus of the Columbia Science Honors Program was the future guru of open source
software, Richard Stallman
. Sam Williams' biography of Stallman, Free as in Freedom, paraphrases Harbater's remarks about Math 55
at Harvard, a "boot camp" advanced freshman course in mathematics:
After graduating summa cum laude in 1974, Harbater earned a master's degree from Brandeis University
and then a Ph.D. in 1978 from MIT, where he wrote a dissertation under the direction of Michael Artin
.
In 1995, Harbater was awarded the Cole Prize
for his solution, with Michel Raynaud
, of the long outstanding Abhyankar conjecture.
Harbater is now a professor at the University of Pennsylvania teaching various levels of mathematics.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, well known for his work in Galois theory
Galois theory
In mathematics, more specifically in abstract algebra, Galois theory, named after Évariste Galois, provides a connection between field theory and group theory...
, algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
and arithmetic geometry.
Life and work
Harbater was born in New York CityNew York City
New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and...
and attended Stuyvesant High School
Stuyvesant High School
Stuyvesant High School , commonly referred to as Stuy , is a New York City public high school that specializes in mathematics and science. The school opened in 1904 on Manhattan's East Side and moved to a new building in Battery Park City in 1992. Stuyvesant is noted for its strong academic...
, where he was on the Math Team. After graduating in 1970, he entered Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
, where one of his classmates and a fellow alumnus of the Columbia Science Honors Program was the future guru of open source
Open source
The term open source describes practices in production and development that promote access to the end product's source materials. Some consider open source a philosophy, others consider it a pragmatic methodology...
software, Richard Stallman
Richard Stallman
Richard Matthew Stallman , often shortened to rms,"'Richard Stallman' is just my mundane name; you can call me 'rms'"|last= Stallman|first= Richard|date= N.D.|work=Richard Stallman's homepage...
. Sam Williams' biography of Stallman, Free as in Freedom, paraphrases Harbater's remarks about Math 55
Math 55
Math 55 is a two-semester long first-year undergraduate mathematics course at Harvard University. The official titles of the course is Honors Abstract Algebra and Honors Real and Complex Analysis...
at Harvard, a "boot camp" advanced freshman course in mathematics:
- It was an amazing class. It's probably safe to say there has never been a class for beginning college students that was that intense and that advanced. The phrase I say to people just to get it across is that, among other things, by the second semester we were discussing the differential geometry of BanachBanach spaceIn mathematics, Banach spaces is the name for complete normed vector spaces, one of the central objects of study in functional analysis. A complete normed vector space is a vector space V with a norm ||·|| such that every Cauchy sequence in V has a limit in V In mathematics, Banach spaces is the...
manifolds. That's usually when their eyes bug out, because most people don't start talking about Banach manifolds until their second year of graduate school.
After graduating summa cum laude in 1974, Harbater earned a master's degree from Brandeis University
Brandeis University
Brandeis University is an American private research university with a liberal arts focus. It is located in the southwestern corner of Waltham, Massachusetts, nine miles west of Boston. The University has an enrollment of approximately 3,200 undergraduate and 2,100 graduate students. In 2011, it...
and then a Ph.D. in 1978 from MIT, where he wrote a dissertation under the direction of Michael Artin
Michael Artin
Michael Artin is an American mathematician and a professor emeritus in the Massachusetts Institute of Technology mathematics department, known for his contributions to algebraic geometry. and also generally recognized as one of the outstanding professors in his field.Artin was born in Hamburg,...
.
In 1995, Harbater was awarded the Cole Prize
Cole Prize
The Frank Nelson Cole Prize, or Cole Prize for short, is one of 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 theory. The prize is named after Frank Nelson Cole, who...
for his solution, with Michel Raynaud
Michel Raynaud
Michel Raynaud is a French mathematician working in algebraic geometry. Since 1967 he has been a professor at Paris-Sud 11 University.In 1983 he published a proof of the Manin-Mumford conjecture....
, of the long outstanding Abhyankar conjecture.
Harbater is now a professor at the University of Pennsylvania teaching various levels of mathematics.