The mathematical group called E8 is a complex object described by a numerical matrix of more than 400,000 rows and columns. It is a 57-dimensional solid. Think about that for a sec.
To find someone on the surface of Earth you need two coordinates; latitude and longitude, or at most four if you are locating, say, someone in an apartment building at a certain point in time, but with this object you would need 57 coordinates to define a location, and the group of symmetries has 248 dimensions!
It took 77 hours to compute on a supercomputer and created a file approximately 60GB in size. In comparison, the entire human genome is less than 1GB. The supercomputer obviously was very fast, but what made it able to finally do this massive calculation was that it had tens of gigabytes of RAM, something that has only recently become possible with any computer.
This advancement in mathematics can also be compared with mapping the human genome, as in and of itself it doesn't solve any problems, but it provides a great base. It will allow for breakthroughs in geometry, number theory and (most exciting for me) the physics of string theory.
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