--KRONECKER, L. _Jahresberichte der Deutschen Mathematiker Vereinigung, Bd. 2, p. 19._ =1635.= Plato said “ἀεὶ ὁ θεὸς γεωμέτρε.” Jacobi changed this to “ἀεὶ ὁ θεὸς ἀριθμητίζει.” Then came Kronecker and created the memorable expression “Die ganzen Zahlen hat Gott gemacht, alles andere ist Menschenwerk.”--KLEIN, F. _Jahresbericht der Deutschen Mathematiker Vereinigung, Bd. 6, p. 136._ =1636.= Integral numbers are the fountainhead of all mathematics. --MINKOWSKI, H. _Diophantische Approximationen (Leipzig, 1907), Vorrede._ =1637.= The “Disquisitiones Arithmeticae” that great book with seven seals.--MERZ, J. T. _A History of European Thought in the Nineteenth Century (Edinburgh and London, 1908), p. 721._ =1638.= It may fairly be said that the germs of the modern algebra of linear substitutions and concomitants are to be found in the fifth section of the _Disquisitiones Arithmeticae_; and inversely, every advance in the algebraic theory of forms is an acquisition to the arithmetical theory.--MATHEWS, G. B. _Theory of Numbers (Cambridge, 1892), Part 1, sect. 48._ =1639.= Strictly speaking, the theory of numbers has nothing to do with negative, or fractional, or irrational quantities, _as such._ No theorem which cannot be expressed without reference to these notions is purely arithmetical: and no proof of an arithmetical theorem, can be considered finally satisfactory if it intrinsically depends upon extraneous analytical theories. --MATHEWS, G. B. _Theory of Numbers (Cambridge, 1892), Part 1, sect. 1._