While not a logical proof, this appears to be a practical disproof of AI.
If it were possible to replace programmers, with all the brainpower and sheer quantities of money directed at computer science we'd have discovered an algorithm to replace programmers by this point. But we haven't. Instead, the number of programmers is increasing rapidly.
Therefore, programmers can solve a class of problems that algorithms cannot. Since AI is a kind of algorithm, true AI that replicates human intelligence is impossible.
Is there any evidence to the contrary?
NOTE: Giving credit where credit is due, this argument I took from the following paper where it is argued much better: http://www.blythinstitute.org/images/data/attachments/0000/0041/bartlett1.pdf