I'm pretty sure if you solve any of these problems you might be in a good place. I was just reading about the Unabomber, who didn't win a Nobel for his work or anything, but was quite a talented mathematician before he went Luddite and hid in the woods and, well, you know, bombed people. In general though I'm under the impression there are several unsolved problems out there that people still work on trying to solve, for kicks, and to prove stuff. I think Erdos left behind several unsolved problems that people have been working on; IIRC one got solved relatively recently and it was a big to-do. But it's been a while since I took any math classes, even about Erdos. Pretty great idea of the Bible, tbh, if you ask me.He had his own idiosyncratic vocabulary: Although an agnostic atheist,[18][19] he spoke of "The Book", a visualization of a book in which God had written down the best and most elegant proofs for mathematical theorems.
I like the idea of "The Book". There's a lot of very elegant proofs in mathematics. One of my favorite is the proof that there is no greatest prime number. Assume there were a biggest prime, P. Now make the number 1 x 2 x 3 x 4 x 5 x .... x P plus 1. This number cannot be evenly divided by 2 or 3 or 4 or any number up to P because there will always be a remainder of 1 (that's the plus 1 on the end of the expression). That means the number must itself be prime or it must have a prime factor that is greater than P. Either way, we've shown that there must exist a prime greater than P, and we started by saying that P is the greatest prime. Therefore there is no greatest prime number. For example, if you suppose the greatest prime number is 5, make a new number 1 x 2 x 3 x 4 x 5 + 1 = 121. Try dividing 121 by 2, 3, 4, and 5. There will always be a remainder of 1. That means 121's prime factors must be greater that 5 (they are: 11 and 11). So 5 is not the greatest prime.
Have you heard about Britain's infinite coastline? I'm sure you have, if you're telling me about this. But that's one I like. Although your proof got messed up by the markup, I understand that there should be a plus at the beginning, and end, of your bolded section.