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Negative numbers had long been useful to algebraists—even Western algebraists.

And that is why the great algebraist, Carl Jacobi, so often said: “invert, always invert.”

Mathematics received an impulse, largely, it is true, from the Arabs of Spain, but also from the East; Leonardo Fibonacci, the first Christian algebraist, had travelled in Syria and Egypt.

The same method applied to a problem given by the ancient Hindu algebraist Brahmagupta, who lived in the seventh century after Christ, might result in placing Brahmagupta in prehistoric times.

We believe in the existence of the ruins of Palmyra and Thebes, and in certain discoveries of algebraists and astronomers.