When was the modern number system invented?

Answer 1

It was invented in prehistoric times and has evolved as our understanding and needs developed.

From natural (counting) numbers to the set of integers, to rational numbers (fractions) to real numbers (incorporate Irrational Numbers), to complex numbers and then quaternions. The last of these, which even many mathematicians will not have come across in their work, were formally introduced to the world of mathematics by Hamilton in 1843.