ABSTRACT: The series of Joseph Fourier were an important mathematical
and physical invention, and a vital spur to the development
of analysis as we know it today. A deep property of
Fourier series is the Theorem of Carleson asserting
the pointwise convergence of square integrable Fourier series.
The question, evident already at the beginning of the subject,
had to wait a couple of centuries to find a resolution.
This result has recently the subject of a renewed interest.
I'll survey the Theorem, the sources of its enduring interest,
current results, and a challenge or two for the future.