The Times has this article up on the life and work of Terence Tao. Unfortunately, they mis-state the Green-Tao Theorem:
Dr. Tao and Dr. Green proved that it is always possible to find, somewhere in the infinity of integers, a progression of prime numbers of any spacing and any length.
If this were the theorem, it would imply the twin prime conjecture. The correct statement (as well as a link to the paper of Green and Tao) can be found here. The difference between that and what the Times article is that, for a given k, you cannot specify the spacing you want your arithmetic progression of primes of length k to have. The theorem says that a suitable spacing can be found for each k, and this spacing may never be 2, as far as the theorem itself says.
Nevertheless, Green and Tao’s work is huge progress towards the twin prime conjecture, even if it doesn’t solve it outright (yet).del.icio.us |Digg it |ma.gnolia |StumbleUpon |