1MATH 338: History and Philosophy of MathematicsPractice final examFill in the blanks1.TheHindumathematicians were responsible for introducingplace valuesandthe number zero.2.The Babylonians used base60arithmetic.3.Thaleswas the first to emphasize the importance ofproof.4.Euclid wrote five axioms forgeometry.5.Apolloniuswrote the classic bookConic Sectionsin 200 BC.6.A conic section with eccentricity 1.0001 is ahyperbola.7.A conic section with eccentricity less than 1 is anellipse.8.Fermat thought the formula22𝑛+ 1always gave a prime number.9.Descartes unifiedgeometryandalgebraby inventinggraphs.10.An integral is asumof infinitely manyinfinitesimals, while a derivative is aquotientof two infinitesimals.11.Gauss, Lobachevsky, and Bolyai discoverednon-Euclidean geometries.12.A set withℵ0elements is calledcountablyinfinite.13.Frege and Russell tried to base all of mathematics onlogic.14.G. H. Hardy’s wrote “There is no permanent place in the world foruglymathematics.”15.The Continuum Hypothesis isindependentof the Z-F axioms of set theory.16.Umar Al-Khayyamistudiedcubicequations, but his work was completed byCardano.17.Modern algebra was driven by two problems: The solution of the quinticequation andFermat’s Last Theorem.18.Andrew Wiles provedFermat’s Last Theorem.19.Peano wrote five axioms fornatural numbers.20.Euler proved that the sum of the reciprocals of the squares is𝜋26.21.NewtonandLeibnizdiscovered Calculus independently.22.Although we can prove there are infinitely many of them, there is no formula forprime numbers.23.The Egyptians only (almost) used fractions with numerator1.