Algebra · a Light

Algebra had no symbols for four hundred years

Abu Kamil, an Egyptian calculator working a generation or so after al-Khwarizmi, wrote everything out in words. An equation was a sentence: a square and ten roots equal thirty nine dirhams. There was no x, no equals sign, no notation for a power, and the proofs were geometrical, drawn as actual squares and rectangles. Inside that constraint he did serious work. He allowed irrational quantities as coefficients and as answers, which al-Khwarizmi had not, handled powers up to the eighth, and solved systems in several unknowns. One of his puzzles about buying birds has 2,676 whole number solutions, and he counted every one of them and recorded that he was pleased with himself. Fibonacci took problems from him into the book that brought algebra to Latin Europe.

Abu Kamil · Egypt, c. 850-930 CE