John H. Hubbard
Encyclopedia
John Hamal Hubbard was born on October 6 or 7, 1945 (the actual date is unknown). He is an American
mathematician
who is currently a professor at Cornell University
and the Université de Provence. He is well known for the mathematical contributions he made with Adrien Douady
in the field of complex dynamics
, including a study of the Mandelbrot set
. One of their most important results is that the Mandelbrot set
is connected
.
Hubbard graduated with a Doctorat d'Etat from Université de Paris-Sud in 1973 under the direction of Adrien Douady
; his thesis was entitled Sur Les Sections Analytiques de La Courbe Universelle de Teichmüller and was published by the American Mathematical Society
. Hubbard has a variety of mathematical interests ranging from complex analysis
to differential geometry. He has written many influential papers on complex dynamics
, and he has written several books. In 2006, he has completed another: the first volume of a series devoted to Teichmüller theory
and applications to four revolutionary theorems of William Thurston
. Hubbard is a former student of Harvard University
's infamous Math 55
, where he famously struggled initially because he "just didn't know proofs," a somewhat shocking fact considering his eventual mathematical successes. He later returned to Harvard to teach that same class. However, Hubbard garnered a rather profound distaste for Math 55
's method of teaching proofs largely centered around algebraic
induction
. In response, he wrote a book entitled Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach, on which his wife Barbara is listed as a co-author. At Cornell University
, he routinely teaches Math 2230 & 2240, classes specifically structured around this same text. When asked how well these classes correspond to Math 55
, he responded: "This class may indeed be somewhat easier than Math 55
, albeit perhaps covering slightly more material." Hubbard is known throughout the Cornell community for his very relaxed style of teaching. He often starts class late, after a period of conversing with students on a variety of more personal, informal topics, such as his hobby of collecting and purveying various local varieties of mushrooms found across campus, easily citing the given binomial nomenclature
for each species
.
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....
who is currently a professor at Cornell University
Cornell University
Cornell University is an Ivy League university located in Ithaca, New York, United States. It is a private land-grant university, receiving annual funding from the State of New York for certain educational missions...
and the Université de Provence. He is well known for the mathematical contributions he made with Adrien Douady
Adrien Douady
Adrien Douady was a French mathematician.He was a student of Henri Cartan at the Ecole Normale Supérieure, and initially worked in homological algebra. His thesis concerned deformations of complex analytic spaces...
in the field of complex dynamics
Complex dynamics
Complex dynamics is the study of dynamical systems defined by iteration of functions on complex number spaces. Complex analytic dynamics is the study of the dynamics of specifically analytic functions.-Techniques:*General** Montel's theorem...
, including a study of the Mandelbrot set
Mandelbrot set
The Mandelbrot set is a particular mathematical set of points, whose boundary generates a distinctive and easily recognisable two-dimensional fractal shape...
. One of their most important results is that the Mandelbrot set
Mandelbrot set
The Mandelbrot set is a particular mathematical set of points, whose boundary generates a distinctive and easily recognisable two-dimensional fractal shape...
is connected
Connected space
In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint nonempty open subsets. Connectedness is one of the principal topological properties that is used to distinguish topological spaces...
.
Hubbard graduated with a Doctorat d'Etat from Université de Paris-Sud in 1973 under the direction of Adrien Douady
Adrien Douady
Adrien Douady was a French mathematician.He was a student of Henri Cartan at the Ecole Normale Supérieure, and initially worked in homological algebra. His thesis concerned deformations of complex analytic spaces...
; his thesis was entitled Sur Les Sections Analytiques de La Courbe Universelle de Teichmüller and was published by the American Mathematical Society
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
. Hubbard has a variety of mathematical interests ranging from complex analysis
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...
to differential geometry. He has written many influential papers on complex dynamics
Complex dynamics
Complex dynamics is the study of dynamical systems defined by iteration of functions on complex number spaces. Complex analytic dynamics is the study of the dynamics of specifically analytic functions.-Techniques:*General** Montel's theorem...
, and he has written several books. In 2006, he has completed another: the first volume of a series devoted to Teichmüller theory
Teichmüller space
In mathematics, the Teichmüller space TX of a topological surface X, is a space that parameterizes complex structures on X up to the action of homeomorphisms that are isotopic to the identity homeomorphism...
and applications to four revolutionary theorems of William Thurston
William Thurston
William Paul Thurston is an American mathematician. He is a pioneer in the field of low-dimensional topology. In 1982, he was awarded the Fields Medal for his contributions to the study of 3-manifolds...
. Hubbard is a former student of 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...
's infamous 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...
, where he famously struggled initially because he "just didn't know proofs," a somewhat shocking fact considering his eventual mathematical successes. He later returned to Harvard to teach that same class. However, Hubbard garnered a rather profound distaste for 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...
's method of teaching proofs largely centered around algebraic
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
induction
Mathematical induction
Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true of all natural numbers...
. In response, he wrote a book entitled Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach, on which his wife Barbara is listed as a co-author. At Cornell University
Cornell University
Cornell University is an Ivy League university located in Ithaca, New York, United States. It is a private land-grant university, receiving annual funding from the State of New York for certain educational missions...
, he routinely teaches Math 2230 & 2240, classes specifically structured around this same text. When asked how well these classes correspond to 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...
, he responded: "This class may indeed be somewhat easier than 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...
, albeit perhaps covering slightly more material." Hubbard is known throughout the Cornell community for his very relaxed style of teaching. He often starts class late, after a period of conversing with students on a variety of more personal, informal topics, such as his hobby of collecting and purveying various local varieties of mushrooms found across campus, easily citing the given binomial nomenclature
Binomial nomenclature
Binomial nomenclature is a formal system of naming species of living things by giving each a name composed of two parts, both of which use Latin grammatical forms, although they can be based on words from other languages...
for each species
Species
In biology, a species is one of the basic units of biological classification and a taxonomic rank. A species is often defined as a group of organisms capable of interbreeding and producing fertile offspring. While in many cases this definition is adequate, more precise or differing measures are...
.