PlacesPlaces
Arizona, 1979 by Tetman Callis
Day: February 12, 2013
Sometimes it all adds upSometimes it all adds up
“Mathematics is not a body of facts arranged and justified by a stringent logical structure. To give a dynamic metaphor that stems from the related field of fluid flow, it is like a turbulent river. The flow of the water is extremely complex, but every now and again you see the appearance of stable structures, eddies and whirlpools. These stable structures correspond to the propositions and theorems of mathematics. It is the logical structure of mathematics that gives these theorems their stability, but when we look at things in this way we see that the stability is not absolute. The data can be structured in many different ways corresponding to what we are interested in and in the mathematical ideas that arise to do the structuring. These ideas arise in response to the question, ‘What is going on here?’—that is, from the attempt to make sense of the phenomena in question.” – William Byers, How Mathematicians Think