Einstein’s Theory of Irreducible Algebraic Polynomials

This paper discusses Einstein’s theory of irreducible polynomials in algebra. (6+ pages; 4 sources; MLA citation style)

I           Introduction

            Mathematicians like Einstein seek to explain how the world works; their tools for doing so are the laws of mathematics.

            Einstein is probably best known for his work on relativity, and the Unified Field Theory, but he did significant work in other areas of mathematics as well.

            This paper will discuss his theory with regard to polynomials used in algebra, and why they are irreducible. As a non-mathematician, the only way I can hope to approach this is to reproduce the theory itself, and then define the terms used to formulate it. By restating the terms in my own words, I can then work toward a better understanding of the theory.

II          Einstein’s Irreducible Criterion

            This is the criterion Einstein demanded for irreducible polynomials in algebra:

“A sufficient condition assuring that an integer polynomial p(x) is irreducible in the polynomial ring. 

The polynomial 

where for all and (which means that the degree of p(x) is n) is irreducible if some prime number p divides all coefficients, but not the leading coefficient and, moreover, does not divide the constant