1.Summing n k=1 k using Gauss' triangle trick.2.Irrationality of 2 by proof without words.3.Niven's proof of the irrationality of p .4.Uncountability of the Reals by Cantor's Diagonal Argument.5.Denumerability of the Algebraics by Heights and Counting Roots.6.Infinitude of rimes by both Euclid's roof and Euler's roof.7.Constructibility of the Regular 17-gon by Gauss' exlicit construction.8.Binomial Theorem by Induction.9.FLT n=4 by Fermat's Infinite Descent.10.Every PID is a UFD.11.The lim n (1+1 n ) n =e by L'Hital's Rule.12.Pick's Theorem by reduction to triangles and squares.13.Fibonacci numbers in terms of the Golden Ratio by recurrence relations.14.R n is a metric sace in more than one way.15.Euler's Formula e iq =cosq+isinq by differentiation.16.Summing k1 1 k 2by Fourier series.17.Quadratic reciprocity by Eisenstein's proof (counting lattice points).18.(Z/nZ) is a group (of units) for nN , and Z/pZ is a field for prime p .19.Euler's formula v-e+f=2 for planar graphs.20.Fundamental Theorem of Algebra by Liouville's Theorem.