Very interesting to watch this video. I really didn't know that these views on math existed, but I suspected their existence. I (tried) to read a very interesting book: Godel, Escher, Bach: An Eternal Golden Braid. Basically, from what I understood (this is a very complex book), this book goes into how we give meaning to meaningless things, like numbers. But the book also questions whether math is a product of the universe, a product of our observations, or if it has always existed. I've always wondered if there is other kinds of math out there in the universe...
GEB is a great book. I'd suggest taking another crack at it after you give it some distance. It wasn't until I picked it up a second time that I was able to read it cover to cover. I'd suggest Hofstadter's Metamagical Themas as a good primer for GEB. It's a collection of columns that wrote for the Scientific American when he took over for Martin Gardner after Gardner stopped writing Mathematical Games. He presents many of the same ideas, but pared down for the periodical format.