This week has seen some big news in mathematics. In a lecture given at Harvard, Yitang Zhang proved a weak from of the Twin Prime Conjecture. He proved that there is a constant C such that there are an infinite number prime pairs, p > q with p - q < C. His proof included a bound that C is less than seventy million! The Twin Prime Conjecture says that C = 2.
Patrick Honner has a good description of the result here. For a few more details, check out the n-Category Cafe's report.