A theoretical computer science analog to the physics crackpots might be semi-knowledgeable people who purport to prove P vs. NP one way or the other or solve some other open mathematical question or disprove a known existing result. Quantum computing probably attracts some as well but that's a bit of an overlap with physics.
Theoretical CS is of course niche enough that it probably doesn't attract mainstream people from outside of the field, so I suppose the field has its own crackpots. I suspect mathematics would be similar except somewhat more mainstream.
Of course some day someone will probably come along and actually prove something about those open questions but claims of proofs are much more common than actual proofs.
As for crackpot things within the academia itself, computer science also has areas such as AGI that are so hard to get actual scientific results from that it might be easy to deem it as just handwaving rather than actual research. Trying to build general AI with automated reasoning and knowledge bases back in the early days may not have been exactly a crackpot idea -- if anything, it was overly optimistic about hard logic -- but it certainly wasn't realistically going to succeed either, at least in hindsight.
Theoretical CS is of course niche enough that it probably doesn't attract mainstream people from outside of the field, so I suppose the field has its own crackpots. I suspect mathematics would be similar except somewhat more mainstream.
Of course some day someone will probably come along and actually prove something about those open questions but claims of proofs are much more common than actual proofs.
As for crackpot things within the academia itself, computer science also has areas such as AGI that are so hard to get actual scientific results from that it might be easy to deem it as just handwaving rather than actual research. Trying to build general AI with automated reasoning and knowledge bases back in the early days may not have been exactly a crackpot idea -- if anything, it was overly optimistic about hard logic -- but it certainly wasn't realistically going to succeed either, at least in hindsight.