is this really an (urgent) homework question?!!

well, the conjecture is related to many problems in algebraic geometry and ring theory. i've even heard that it has attracted number theorists as well. as someone whose interest is ring theory,

i give you one example: if Jacobian conjecture is true, then every endomorphism of a Weyl algebra is an automorphism! the disappointing thing is that some mathematicians are almost confident

that the conjecture is basically false!