Introduction

I began the Preface saying: Mathematics and physics have an intimate relationship, albeit on-and-off. Mathematics provides both machinery for calculation and structures for analogy. Primes and Particles describes that relationship in detail in terms of serious mathematics and serious physics. I want to provide detailed examples that evidence and describe that relationship in specific rather than generic terms. Our themes will be: The parallel of primes and particles. Proofs of the stability of matter. The two-dimensional Ising model. The Dedekind-Weber (1882) analogy of arithmetic, algebra, and analysis. A function that packages a set of numbers, that function then has lovely analytic properties and symmetries (so telling us about that set). The analogy between kinship theory and the rules of interaction of particles. Just what is mathematical physics. The second part of the Introduction surveys what we know about Ising, stability of matter, and the Dedekind-Weber analogy.