If math vs. engineering is a mystery that can't be 
  explained by streotypes,

Scott gives an explanation in the article. Interestingly, it's exactly the suggestion commenter peacetreefrog puts forward: relatively many math graduates become teachers. And teaching is a 'person' thing.

As for engineering: the variation within engineering disciplines is much smaller than the variation between engineering and other disciplines and since we already have a hard time explaining the large difference, let's not worry about the small differences. Perhaps chemical engineering is perceived to be about 'people' more often.