The natural expression of speed in relativity (and thus the true meaning of speed) is through the concept of rapidity, which comes from incorporating the gamma factor. It turns out that the rapidity of light is infinite. So the question of whether there can be speeds greater than light becomes the question of whether there can be rapidities greater than infinity. Here comes Cantor, who as you may know, proved one of the most surprising results in all of mathematics. He proved that there are different sizes of infinities and, on top of that, that there is no "largest" infinity. The last part also clears the waters as to what kind of rapidity is the rapidity of light. Is it the infinity of integers or of real numbers (which is a larger infinity)? It doesn't matter, because there is no largest infinity. So, Cantor's result gives a little hope that, at least mathematically, the infinite rapidity of light is not a limit. What are your thoughts on this?