When your math is so mind-blowing that even the pros just surrender and believe it. Ramanujan sends Hardy these continued fraction formulas that look like they were scribbled by a mathematical deity, and Hardy's response is basically "well, this is too weird to be made up, so I guess it's true." It's the mathematical equivalent of "pics or it didn't happen" except it's "this is too bizarre to be fiction." Hardy essentially invented the "no one would make this up" proof technique, which isn't in any textbook but is secretly used by every mathematician who's ever been stumped.