Math are discovered rather than invented

 Penrose argues that many mathematical phenomena (the numerical value of pi, for example, or the irrationality of the square root of two, or the existence of Mandelbrot figures) are discovered rather than invented. 

Consequently, he proposes that there is a Platonic reality to mathematics: that it exists in an abstract sense, independent of the human mind, and that we must recognise three different kinds of ‘world’ representing three different forms of existence – the physical, the mental and the mathematical