The Unreasonable Effectiveness of Mathematics – R.W. Hamming

I always liked his book on Numerical Methods, and his idea about knowledge as compounding interest. The part of this essay I enjoy is the second explanation:

> 2. We select the kind of mathematics to use. Mathematics does not always work. When we found that scalars did not work for forces, we invented a new mathematics, vectors. And going further we have invented tensors. In a book I have recently written [10] conventional integers are used for labels, and real numbers are used for probabilities; but otherwise all the arithmetic and algebra that occurs in the book, and there is a lot of both, has the rule that

> 1 + 1 = 0.

> Thus my second explanation is that we select the mathematics to fit the situation, and it is simply not true that the same mathematics works every place.