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

>>11
Because the mathematicians OBVIOUSLY get all the chicks.

I must say, beyond dirac delta functions and fourier transforms, mathematics are fucking useless, as non-integer numbers have no objective existence and mathematics is an axiomatic science.

Philosophy >> Physics >>>>>>> Maths.