John H. Hubbard

Last updated
John H. Hubbard
Hubbard at Oberwolfach (27 September 2011)
Born (1945-10-06) October 6, 1945 (age 75)
Alma mater Université de Paris-Sud (Dr.E.)
Harvard University (B.S.)
Scientific career
Institutions Cornell University (current), Harvard University
Thesis Sur Les Sections Analytiques de La Courbe Universelle de Teichmüller (1973)
Doctoral advisor Adrien Douady

John Hamal Hubbard (born October 6 or 7, 1945; the actual date is unknown) is an American mathematician and 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'État 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, [1] [2] [3] and he has written several books.


Hubbard is a former student of Harvard University's infamous Math 55, where he famously struggled initially because he "just didn't know proofs." He later returned to Harvard to teach that same class. However, Hubbard developed a profound distaste for Math 55's method of teaching proofs largely centered on algebraic induction. In response, he and his wife Barbara wrote the book Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach.

He has also published the first two volumes of a book on Teichmüller theory and its applications to four revolutionary theorems of William Thurston.

Personal life

He is married to Barbara Burke Hubbard, the science writer. Together they have a son, Alexander, and three younger daughters, Eleanor, Judith and Diana. The children sometimes help them with their books, in illustration, writing answer keys and pointing out the minor errors. [4]

Hubbard and his family live in Ithaca, New York.

Related Research Articles

Mandelbrot set Fractal named after mathematician Benoit Mandelbrot

The Mandelbrot set is the set of complex numbers for which the function does not diverge when iterated from , i.e., for which the sequence , , etc., remains bounded in absolute value. Its definition is credited to Adrien Douady who named it in tribute to the mathematician Benoit Mandelbrot, a pioneer of fractal geometry.

In mathematics, the Schwarzian derivative, named after the German mathematician Hermann Schwarz, is a certain operator that is invariant under all Möbius transformations. Thus, it occurs in the theory of the complex projective line, and in particular, in the theory of modular forms and hypergeometric functions. It plays an important role in the theory of univalent functions, conformal mapping and Teichmüller spaces.

In mathematics, differential refers to infinitesimal differences or to the derivatives of functions. The term is used in various branches of mathematics such as calculus, differential geometry, algebraic geometry and algebraic topology.

Donald Clayton Spencer was an American mathematician, known for work on deformation theory of structures arising in differential geometry, and on several complex variables from the point of view of partial differential equations. He was born in Boulder, Colorado, and educated at the University of Colorado and MIT.

Mathematics encompasses a growing variety and depth of subjects over history, and comprehension of it requires a system to categorize and organize these various subjects into a more general areas of mathematics. A number of different classification schemes have arisen, and though they share some similarities, there are differences due in part to the different purposes they serve.

Adrien Douady French mathematician

Adrien Douady was a French mathematician.

In mathematics, the derivative is a fundamental construction of differential calculus and admits many possible generalizations within the fields of mathematical analysis, combinatorics, algebra, and geometry.

<i>Calculus on Manifolds</i> (book) book by Michael Spivak

Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus (1965) by Michael Spivak is a brief, rigorous, and modern textbook of multivariable calculus, differential forms, and integration on manifolds for advanced undergraduates.

An external ray is a curve that runs from infinity toward a Julia or Mandelbrot set. Although this curve is only rarely a half-line (ray) it is called a ray because it is an image of a ray.

Tricorn (mathematics)

In mathematics, the tricorn, sometimes called the Mandelbar set, is a fractal defined in a similar way to the Mandelbrot set, but using the mapping instead of used for the Mandelbrot set. It was introduced by W. D. Crowe, R. Hasson, P. J. Rippon, and P. E. D. Strain-Clark. John Milnor found tricorn-like sets as a prototypical configuration in the parameter space of real cubic polynomials, and in various other families of rational maps.

<i>The Beauty of Fractals</i> Book by Heinz-Otto Peitgen

The Beauty of Fractals is a 1986 book by Heinz-Otto Peitgen and Peter Richter which publicises the fields of complex dynamics, chaos theory and the concept of fractals. It is lavishly illustrated and as a mathematics book became an unusual success.

Alexander Varchenko

Alexander Nikolaevich Varchenko is a Soviet and Russian mathematician working in geometry, topology, combinatorics and mathematical physics.

Clifford John Earle, Jr. was an American mathematician who specialized in complex variables and Teichmüller spaces.

Nessim Sibony

Nessim Sibony is a French mathematician, specializing in the theory of several complex variables and complex dynamics in higher dimension. Since 1981, he has been a professor at the University of Paris-Sud in Orsay.

Tan Lei Mathematician (1963-2016)

Tan Lei was a mathematician specialising in complex dynamics and functions of complex numbers. She is most well-known for her contributions to the study of the Mandelbrot set and Julia set.

Dinh Tien-Cuong Vietnamese-French mathematician

Dinh Tien-Cuong is a Vietnamese mathematician educated by the French school of mathematics, and Provost’s chair professor at National University of Singapore (NUS). He held professorship at Pierre and Marie Curie University (2005-2014), part-time professorship at Ecole Polytechnique de Paris (2005-2014) and at Ecole Normale Supérieure de Paris (2012-2014). He is known for his work on Several Complex Variables and Complex Dynamical Systems in Higher Dimension.


  1. Douady, Adrien; Hubbard, John Hamal (1985). "On the dynamics of polynomial-like mappings". Annales Scientifiques de l'École Normale Supérieure. 18 (2): 287–343. doi: 10.24033/asens.1491 . Archived from the original on 2007-05-24. Retrieved 2007-03-11.
  2. Hubbard, John H; Oberste-Vorth, Ralph W. (1994). "Hénon mappings in the complex domain I : the global topology of dynamical space". Publications Mathématiques de l'IHÉS. 79: 5–46. doi:10.1007/bf02698886. S2CID   122685150 . Retrieved 2007-03-11.
  3. John H. Hubbard and Ralph W. Oberste-Vorth (1994) Henon mappings in the complex domain II: projective and inductive limits of polynomials
  4. Hubbard, John; Hubbard, Barbara. Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach