The Gudermannian function relates the regular and the hyperbolic trigonometric functions without the use of complex numbers?The Catalan numbers solve a number of problems in such as the number of ways to completely parenthesize an algebraic expression with *n*+1 factors?A sphere can be cut up and reassembled into two spheres the same size as the original?It is impossible to devise a single formula involving only polynomials and radicals for solving an arbitrary quintic equation?Euler found 59 more while for 2000 years, only 3 pairs had been found before him?We cannot knot strings in 4-dimensions? We can, however, knot 2-dimensional like spheres.There are 6 unsolved mathematics problems whose solutions will earn you one million US dollars each?