What does "hard sums" mean?

"Hard sums" is used to mean "difficult mathematics" in a self-deprecating way, depending on the speaker.

If someone says

I can do hard sums.

and they are:

  • A four year-old: It means they've started doing addition.
  • An eight year-old: It means they've mastered multiplication.
  • A high-school student: It means they can do some simple calculus.
  • An undergraduate: It means they can do more complex calculus / analysis / algebra.
  • A post-graduate: It means they're Einstein. :-)

And each group is more self-deprecating than the last.