Random Shower thought - Aerogel Vacuum Balloons

Instead of filling a balloon with a light gas to make it fly... what if it was possible to just have NO gas at all in a volume to achieve lift. In other words a complete vacuum. Would that make a significant difference to buoyancy?  The problem of course is the crushing pressure of the atmosphere so the shell would need to be strong to withstand it, adding weight. But what if you had a hollow sphere made from aerogel and coated it with a thin layer of an air tight material... Would that be strong enough to maintain a vacuum inside it without being crushed? ... and would a construction like that be light enough to float up into the atmosphere? 

Wish I had more time learning science stuff so I could answer these questions.