> I am not a fan of these types of proofs. Baez didn't explain how one would go about searching for this proof, he just happened to know that repeatedly using t

> I am not a fan of these types of proofs. Baez didn't explain how one would go about searching for this proof, he just happened to know that repeatedly using the differential operator on a seemingly random differential equation would create a pattern that resembles the original equation after using substitution repeatedly. Indeed. But without knowing what really happend here, I suspect the following: Somebody (I guess Ramanujan), came up with the random differential equation, then found two equal solutions that looked structurally different. So he asked how you can prove that they are equal. So, I'm not sure here, but in general, this is how many mathematical puzzles are created: You come up with a random proof by starting somewhere in the middle that then transforming your equation in two totally different directions. If you now throw away the middle part, you have a hard to prove fact.