The discoveries in modern mathematics begin with Cardano, complex numbers, Galileo who found that even numbers were one-to-one with all integers, Cantor who discovered new numbers, infinities with infinite subsets, Hamilton who discovered quaternions leading to new non commutative algebras, Goedel who showed the axioms of arithmetic were inherently incomplete, Cohen who showed that neither the atom of choice nor the continuum hypotheses would help

and Turing, the inventor of the modern computer who prove it has limits.