Mathematics of Eternity Prove The Universe Must Have Had A Beginning - Technology Review: Today, Audrey Mithani and Alexander Vilenkin at Tufts University in Massachusetts say that these models are mathematically incompatible with an eternal past. Indeed, their analysis suggests that these three models of the universe must have had a beginning too.
Their argument focuses on the mathematical properties of eternity--a universe with no beginning and no end. Such a universe must contain trajectories that stretch infinitely into the past.
However, Mithani and Vilenkin point to a proof dating from 2003 that these kind of past trajectories cannot be infinite if they are part of a universe that expands in a specific way.