The Correspondence between Sophie Germain and Carl Friedrich Gauss

Published and discussed here is the correspondence between Sophie Germain and Carl Friedrich Gauss. The mathematical notes enclosed in her letters are published for the first time. These notes in which she submitted some of her results, proofs and conjectures to Gauss for his evaluation, were inspired to her by the study of the Disquisitiones Arithmeticae. The interpretation of these mathematical notes, not only shows how she went deeply into Gauss's treatise and mastered it long before any other mathematician, but also, more importantly, that she got interesting results in the theory of power residues that had never previously been attributed to her

Measurement of the tau lepton lifetime

The mean lifetime of the τ lepton is measured from a sample of Z→τ+τ− decays observed with the ALEPH detector at LEP in 1989 and 1990. A new technique is applied to the events containing two one-prong decays: the lifetime is measured from the observed correlation between the impact parameters and azimuthal angles of the two charged tracks. The lifetime is also determined from measured vertex displacements for three-prong decays and track impact parameters for one-prong decays. The combined results is ττ=291 ± 13 (stat) ±6 (syst.) fs