The Computer Science Dept blog passed on the report from the New Scientist that Harald Halfgott ’98 (Math/Co Sci), now working at the École Normale Supérieure in Paris, has proved the odd (weak) Goldbach conjecture, which states that every odd number above 5 is the sum of three primes. For the paper “Major Arcs for Goldbach’s Problem”, see http://arxiv.org/abs/1305.2897
see also: http://blogs.scientificamerican.com/roots-of-unity/2013/05/15/goldbach-variations/