Squaring any real number gives a non-negative result. So the equation x² = −1 has no real solution. Modern quantum mechanics depends on us going through anyway — inventing an imaginary number i and walking it into the workable algebra of complex numbers. In 850 CE, Mahāvīra is the first writer in the surviving mathematical record to state the impossibility cleanly: 'a negative quantity is not a square quantity, it has therefore no square root.' Cardano calls these roots 'fictitious' in 1545; Bombelli walks through them in 1572; Gauss formalises in 1799. The door begins with Mahāvīra closing it.