If math can make you feel awe, you've got to watch the Numberphile series on very big numbers. They're constants used in proofs that are specific, well-defined

If math can make you feel awe, you've got to watch the Numberphile series on very big numbers. They're constants used in proofs that are specific, well-defined integers known to be finite, but so huge that the physical universe does not have enough particles (or even Plank-scale microstates) in it to represent the number of digits these numbers have! Absolutely mind-bending stuff. Listed in increasing order: "Graham's Number" https://www.youtube.com/watch?v=XTeJ64KD5cg https://www.youtube.com/watch?v=XTeJ64KD5cg "How Big is Graham's Number? (feat Ron Graham)" https://www.youtube.com/watch?v=GuigptwlVHo https://www.youtube.com/watch?v=GuigptwlVHo "The Enormous TREE(3)" https://www.youtube.com/watch?v=3P6DWAwwViU https://www.youtube.com/watch?v=3P6DWAwwViU "TREE(3) (extra footage)" https://www.youtube.com/watch?v=IihcNa9YAPk https://www.youtube.com/watch?v=IihcNa9YAPk "The Daddy of Big Numbers (Rayo's Number)" https://www.youtube.com/watch?v=X3l0fPHZja8 https://www.youtube.com/watch?v=X3l0fPHZja8