Mathematics for the Modern Mind

A₁ arbitrary arithmetic axiomatic axioms basic Brouwer calculus called Cantor's cardinal number circle complex numbers concept connection consider construction constructivists David Hilbert defined diagram dimension disk elementary events elements enumerable equal Euclid Euclid's Euclidean geometry example exists expression figure finite Flatland formal formalistic formula Henri Poincaré Hermann Weyl Hilbert ideas imagine important infinite decimal fractions integral numbers intuition John von Neumann Kolmogorov language Lorenzen M₁ M₂ mathe mathematical logic mathematical theory mathematician matician matics means ments method modern mathematics natural numbers negative numbers Nicolas Bourbaki non-Euclidean geometry number pairs objects operation P₁ P₂ parallel postulate Paul Lorenzen philosopher physicist physics play Poincaré possible problem proof proved raining rational numbers real numbers relation rule S₁ S₂ wins sentence sequence set theory simple space sphere square statement form straight line structures subsets symbols theorem things tion triangle truth table valid variable Weyl words