Number Theory 1 Six proofs of the infinity of primes 3 2 Bertrand's postulate 9 3 Binomial coefficients are(almost)never powers 15 4 Representing numbers as sums of two squares 19 5 The law of quadratic reciprocity 25 6 Every finite division ring is a field 33 7 The spectral theorem and Hadamard's determinant problem 37 8 Some irrational numbers 45 9 Three timesπ2/653 “Irrationality and”Number Theory 1 Six proofs of the infinity of primes 3 2 Bertrand’s postulate 9 3 Binomial coefficients are (almost) never powers 15 4 Representing numbers as sums of two squares 19 5 The law of quadratic reciprocity 25 6 Every finite division ring is a field 33 7 The spectral theorem and Hadamard’s determinant problem 37 8 Some irrational numbers 45 9 Three times π2/6 53 “Irrationality and π