MathematicsT1
Mahāvīra's Ganita-sara-sangraha I.52 (850 CE) gives the first
explicit recognition that √(negative) is undefined on reals. The
reasoning: every square is non-negative, so no real number squared
yields a negative. Cardano (1545) calls these roots "fictitious";
Bombelli (1572) treats them as imaginary; Gauss (1799) gives the
complex-number foundation. The impossibility acknowledgement is
Mahāvīra's, ~700 years before Cardano.
The Ganita-sara-sangraha of Mahaviracarya · tr. M. Rangacarya, 1912