Jacob Lurie is, imo, one of the most exciting mathematicians in the world today. He genuinely cares that people understand what he is saying. I have watched all of his videos many times, and I am excited for field that I wasn't particularly excited about before until after his presentations, in particular topological quantum field theories. This lecture if far more accessible.
Here is a video that is dear to my heart, as it is what I would probably be working on if I were doing research. Unfortunately, this video starts out with high school algebra, but it dives into deep mathematics at about 20 minutes in. http://www.cornell.edu/video/jacob-lurie-the-siegel-mass-formula
I wonder if Aliens on other planets use the same mathmatical symbols as we do? From a video I watched on Youtube, the Aliens that we have here on Earth (Area 51) had to create a new way of communicating with humans in order to talk to us. Whether that is true or not, who knows.
Unfortunately there is an annoying buzz in the video, but ignore it. Or, even better, do a fourier or wavelet transform of the video sound, remove the noise, and post it back to youtube.
A very nice simple video that can wet the appetite of a junior or high school kid to study real mathematics
What's surprising is that they would even understand us. I wonder it the laws of physics change with each solar system. I don't think it would be constant across the universe.