BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY
نویسنده
چکیده
We begin with a short (obviously incomplete) historical summary related to the book being reviewed. A complex number α is said to be “algebraic” if there is a polynomial 0 6= p(x) with integer coefficients such that p(α) = 0; otherwise α is said to be “transcendental”. The first recorded instance of mathematicians encountering an “irrational” algebraic number appears to be the ancient Greeks. Indeed, if one considers a square with unit sides, then, of course, by the Pythagorean Theorem a diagonal must have length √ 2. To Pythagoras (and his followers) is also due the result that √ 2 cannot be expressed as the quotient of integers. One story has it that Hippasus, the person who revealed this irrationality, died at sea in a shipwreck, “struck by the wrath of the gods.” As history evolved, so did mathematicians’ views about numbers. During the sixteenth century cubic equations were discussed by the Italian algebraists G. Cardano and R. Bombelli ([v1], Part C §2). In particular a very curious phenomenon appeared with equations like x = 15x+ 4 . Here one readily finds that x = 4 is a root and, after division by x−4, that the other two roots are also real. However, the Italian school had developed methods to handle such an equation directly. These methods do give the correct real roots but only through the use of quantities like
منابع مشابه
BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY
Representations of semisimple Lie algebras in the BGG category í µí²ª, by James E.
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