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“Brahmasphutasiddhanta XVIII.22 (628 CE) gives the four sign-multiplication rules: (−)·(+) = (−), (−)·(−) = (+), (+)·(+) = (+), with the parallel zero rules. The hardest case — negative times negative — was hedged in European mathematics for centuries: Cardano (1545) calls negative roots "fictitious"; Wallis (1685) is the first to argue geometrically for the rule; Hankel (1867) gives the first formal construction. Brahmagupta states all four rules without apology in 628 CE. ”