A trivial exercise in mathematics

Let P(f)=0 be an elliptic system of partial differential equations defined over a closed, smooth, oriented n-dimensional manifold X. then:

Topological index of P = Analytical index of P = (-1)^n <ch(s(P)) . td(T_C X), [X]>

where
n is the dimension of the space
s(P) is the symbol of the system
ch is the Chern character
T_C X is the complexified tangent bundle on X
td is the Todd class
. is the cup product
[X] is the fundamental class of X
<a,b> is the Kronecker pairing

Science == productive endeavour that has given us the modern world.

Philosophy == mental masturbation that after three thousand years has still failed to give definitive final answers to the questions Plato was asking.  What's the point, other than "oo er I'm so clever, look at me, oo?"