Certain fields of mathematics have clearly no physical manifestations, yet others do. While number theory has supposedly no manifestation, it turned out to have a very strong one in crypto.

Mathematical Illusions: Like an optical illusion tricking the visual system and then the cognitive faculties, mathemtical illusions are an honest mistake and tricking of our reasoninig and the cognitive senses. They seem true, and we have good reasons to Obfuscation One Way Functions Cryptography

Mathematical Delusions:

(Collective) Mathematical Hallucinations: Hypercomputation

Mathematical Frauds: