Foreword
It is a pleasure to introduce this testament to Tom Wolff’s mathematics.
Humbly and unpretentiously, Tom made repeated fundamental contribu-
tions to analysis. The core of his work deals with geometrical and measure-
theoretic questions related to the Kakeya needle problem. The significance of
these problems can hardly be overstated. Tom attacked them with awesome
power and originality, using both geometric and combinatorial ideas, includ-
ing (as far as I know) the first serious application of theoretical computer
science in
analysis.1
Tom has also proven major results in other branches
of analysis, particularly regarding harmonic and analytic functions. I will
never forget Tom’s lecture at Princeton, in which he simultaneously solved
three outstanding open problems in this area, not previously known to be
mutually related. Tom published few papers, but several of them went as
deep as the human mind can go. “Pauca sed matura”.
Charles Fefferman
Princeton, March 2003
1It
should be mentioned that computer-assisted proofs play a significant and growing
role in mathematics. One of Tom’s best papers is, in his words, “calculator-assisted”.
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