Math can do a lot of things, including "proving" logical impossibilities. For example:

Let a = b.
Then a^2 = a*b.
Then 2a^2 = a^2 + a*b.
Then 2a^2 - 2ab = a^2 + ab - 2ab.
Consequently 2a^2 - 2ab = a^2 - ab.
Factoring, 2(a^2 - ab) = 1(a^2 - ab).
Divide by (a^2 - ab), and...
2 = 1

(There is (sort of) an error in the above, but most people miss it. See if you can guess it!)