Introduction

These three aspects of mathematics could be presented in any order. Which is the best order? Professional mathematical papers are frequently criticised for only presenting the game-like aspects of mathematics while saying nothing about scientific or perceptual aspects, as well as omitting every sign of how their results were discovered in the first place. Very occasional exceptions, such as Euler, are famous for being exceptional. Henri Poincaré asked:

‘Ideas were tried out and discarded…ideas were tried out and retained?’ Yes, indeed! The process of trying out ideas, of experimenting with this approach then that approach, of abandoning ideas that don't work, is a process of play, of experiment, of conjecturing, testing, and then, very likely, rejecting: ‘Aha! Of course, it's an analogue of the Laplace transform, let's see [CHECKS BY CALCULATION]. Oh, it isn't. What a pity! Back to the drawing board!’