Comment by creatonez
11 hours ago
Reshetnikov didn't confess to them being reverse engineered, though. He confessed to them being conjecture arrived at after working on the problem for a bit by tweaking similar integrals in symbolic math software / numerical approximations. Every post was a gamble because it could have been wrong.
Of course, that could be a lie, but he came clean about other things that make sense retrospectively.
> Every post was a gamble because it could have been wrong
Symbolic differentiation is a deterministic algorithm. There is no reason for his posts to be a gamble. I'm sure there was a lots of interesting trial and error in developing good question and answer pairs, but once he posted the question he knew what the answer was already.
As I understand, he was specifically targeting problems that symbolic math software had given up on. He was only using symbolic software to solve the similarly shaped problems first, which allowed him to be fairly confident in his conjecture, as he became quite keen on how to slip his way from the output of symbolic math software from one solvable formula to a closely related formula that broke the software.
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.
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That is frankly, obvious horseshit. It couldn’t possibly be a gamble because you can just trivially differentiate the answer and see if it came out to be the expression in the question.