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

>>29
Quantum mechanics provides mathematical models that work and give usable concrete results in the real world.  Transistors, for instance, could not have been created without solid state physics requiring the ground work laid out by people like Niels Bohr.

Your unwillingness to accept this fact is your problem, not science's.