The symbolic math software couldn't perform the integration problems he posted. Integration lacks a deterministic algorithm and therefore permits constructing challenges for stack overflow and computer algebra systems. However, there
is a deterministic algorithm to go the other way.
In other words, he was posting challenges to go from X -> Y (hard). However, going from Y -> X is easy. Therefore, since he had both X and Y before posting, he could verify the solutions perfectly well. The reason why constructing (X, Y) together is easier than going from Y->X is because you can always tweak Y a bit and then work backwards to see what X falls out.
There was certainly creativity in finding (X, Y) pairs where the symbolic software couldn't go from X -> Y. However, again this is more about trial and error iteration than producing brilliant insights from scratch, which is what it appeared Cleo was doing on Stack Overflow. Again, this is just a consequence of X -> Y being hard but Y -> X being easy. It was a wonderful parlor trick that took a good deal of effort to set up.
In other words, he was posting challenges to go from X -> Y (hard). However, going from Y -> X is easy. Therefore, since he had both X and Y before posting, he could verify the solutions perfectly well. The reason why constructing (X, Y) together is easier than going from Y->X is because you can always tweak Y a bit and then work backwards to see what X falls out.
There was certainly creativity in finding (X, Y) pairs where the symbolic software couldn't go from X -> Y. However, again this is more about trial and error iteration than producing brilliant insights from scratch, which is what it appeared Cleo was doing on Stack Overflow. Again, this is just a consequence of X -> Y being hard but Y -> X being easy. It was a wonderful parlor trick that took a good deal of effort to set up.