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1 History of Classical Algebra
1.8 Symbolical algebra 記号代数学
負の数と複素数、18世紀（FTAはそれらを不可避にした）において頻繁に使われるけれども、ほとんど理解されなかった。例えば、ニュートンは負の数を、「無より小さい」量と説明し、ライプニッツは、複素数を“存在と不存在の間の両生類”であると言った。オイラーは“ +の記号がついていたら正の量、−の記号がついていたら負の量、と呼ぶ”と主張した。
（−1）（−1）= 1のような負の数の取り扱い規則は、古代から知られていた。けれども過去にはいかなる証明も与えらなかった。18世紀の後半と19世紀始めの間に、数学者たちは、なぜそのような規則が成り立つのかということに疑問を持ち始めた。
この話題についての最も包括的な仕事は、1830年のピーコック（解析協会のリーダー）のTreatise of Algebra（代数学論）であった。ピーコックのthe Principle of Permanence of Equivalent Forms(等値形式の恒久普遍原理)は、本質的に記号代数学の法則が算術的代数学の法則になると言っている。
次の数十年に、イギリス数学者たちが、ピーコックが予言したことを、通常の算術の法則とは何通りもの仕方で異なっている性質を持った代数（多元環）を導入することによって、実際に具体化した。
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