I was at Buzzard's talk at Microsoft last week. Kevin spent a lot of time in the live talk explaining what he thinks Szegedy actually meant (there should eventually be video on youtube of this). Kevin clarified that in his opinion what Szegedy means by "math" isn't at all what Kevin means by "math", since it takes so long to get to the frontiers of research math. In particular, Kevin speculated that for Szegedy "math" is some specific research questions in combinatorics, which isn't at all what Kevin's view of "math" is. So Kevin's conclusion was that Szegedy really means that computers will beat humans at "something specific involving combinatorics" in the next ten years. Kevin wasn't optimistic about the same claim was about number theory, unless 10 years is replaced by "some day".
Kevin also explained live in his talk that his main motivation for his recent interest in interactive theorem provers is a very bad experience he had a few years ago refereeing an important research paper by some famous mathematicians. That experience very much shook his faith in the ability of humans to do correct deep mathematics... I suppose from that perspective "computers will be beating humans" might just mean that humans are convinced of a (false!) result, but computers can't be convinced of that same false result (in the sense that nobody can formalize it).
(Incidentally, some of the people at Kevin's talk were at Richard Stallman's talk in the same place the day before. Evidently RMS didn't allow any pictures or video, so not much will appear from that.)
Kevin also explained live in his talk that his main motivation for his recent interest in interactive theorem provers is a very bad experience he had a few years ago refereeing an important research paper by some famous mathematicians. That experience very much shook his faith in the ability of humans to do correct deep mathematics... I suppose from that perspective "computers will be beating humans" might just mean that humans are convinced of a (false!) result, but computers can't be convinced of that same false result (in the sense that nobody can formalize it).
(Incidentally, some of the people at Kevin's talk were at Richard Stallman's talk in the same place the day before. Evidently RMS didn't allow any pictures or video, so not much will appear from that.)