Gauss's quadratic reciprocity can be viewed as an origin of Abelian class field theory.

On the orther hand ,Gauss's integral formula of Linking number was studied by E.Witten in connection with Physics.

However,the seemingly disjoint fields can be joint together. I will introduce the basic idea of linking number ,topology of torus, and explain basic analogies between knots and primes,3-manifolds and number rings,which is fundamental.