Phillip Griffiths

American mathematician

Phillip Augustus Griffiths IV (born October 18, 1938) is an American mathematician, known for his research on complex manifolds, algebraic geometry, and partial differential equation. He was elected in 1979 a Member the National Academy of Sciences. In 2008 he was awarded (jointly with Pierre Deligne and David Mumford) the Wolf Prize. At the 2014 International Congress of Mathematicians, Griffiths received the Chern Medal.

Phillip Griffiths in 2010


  • The theory of exterior differential systems in approximately one century old, although its origin may be traced back much further. As originally formulated by Cartan and subsequently used throughout his work, the theory was intended as a tool to be used in the study of geometric problems. After two periods of theoretical development, one in the 1930s and the other in the 1960s, there has recently been a renewed interest in exterior differential systems as providing a systematic framework for the study of geometric problems. It is my opinion that this development is just beginning, and that exterior differential systems should become a standard tool for geometers, especially for questions where the differential equations expressing the problem are overdetermined systems, and for global questions. When used properly, the theory has a marvelous ability to reveal the underlying geometry in a complicated problem.
    • "Some aspects of exterior differential systems". Complex geometry and Lie theory (Sundance, UT, 1989). Proceedings of Symposia in Pure Mathematics, volume 53. Providence, Rhode Island: American Mathematical Society. 1991. pp. 151-173.  (quote from p. 151)
  • One of the points I have tried to make is that mathematics is extremely useful to our society. If this is true, one would think that we as a society would vigorouly support the research that leads to new uses and that students would be at an all time high. Today that is not the case. The mathematics community has yet to effectvely demonstrate to the public and their elected representatives that our subject is dfferent from the sciences. We do not design widgets or cure diseases, yet our impact on engineering and medicine is enabling and significant. But the community has dwelled so long in splendid isolation that the public poorly understands what we do.
  • Hodge theory for a smooth algebraic curve includes both the Hodge structure (period matrix) on cohomology and the use of that Hodge structure to study the geometry of the curve, via the Jacobian variety. Hodge extended the theory of the period matrix to smooth algebraic varieties of any dimension, defining in general a Hodge structure on the cohomology of the variety. He gave a few applications to the geometry of the variety, but these did not attain the richness of the Jacobian variety. In recent years, Hodge theory has been successfully extended to arbitrary varieties, and to families of varieties.

  Encyclopedic article on Phillip Griffiths on Wikipedia