This is an announcement for the paper "Numerical index and duality" by Konstantin Boyko, Vladimir Kadets, Miguel Martin, and Dirk Werner. Abstract: We present an example of a Banach space whose numerical index is strictly greater than the numerical index of its dual, giving a negative answer to a question which has been latent since the beginning of the seventies. We also show a particular case in which the numerical index of the space and the one of its dual coincide. Archive classification: Functional Analysis Mathematics Subject Classification: 46B20; 47A12; 46B22; 46E15 The source file(s), miguelvovakostya.tex: 34653 bytes, is(are) stored in gzipped form as 0509374.gz with size 12kb. The corresponding postcript file has gzipped size 63kb. Submitted from: werner@math.fu-berlin.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0509374 or http://arXiv.org/abs/math.FA/0509374 or by email in unzipped form by transmitting an empty message with subject line uget 0509374 or in gzipped form by using subject line get 0509374 to: math@arXiv.org.