Reply to comment  Count-abel even if not solve-abel   Sometimes
great leaps forward in understanding come not from answering the
question that is puzzling you, but from asking a different
question. So it was with the ground-breaking achievement of Sir
Michael Atiyah and Isadore Singer with their index theorem,
which, rather than giving a way to solve a particular set of
equations, gives an ingenious way to calculate the number of
solutions. This may not seem immediately useful, but in fact it
has provided a way to link the areas of analysis and topology,
and has led to a cross-fertilization of ideas between physics
and mathematics. In recognition of their achievement, Atiyah and
Singer have been awarded the 2004 Abel Prize, the equivalent of
the Nobel Prize in mathematics.  Mathematics is used to model
many aspects of our lives, from the weather, to economics, to
the electrical impulses from the heart. However, due to the
complex nature of our world, finding solutions to the systems of
differential equations