Maier's Ph.D. thesis was an extension of his paper "H. Maier, Chains of large gaps between consecutive primes, Advances in Mathematics, 39 (1981), 257–269". In this paper Maier applied for the first time what is now known as Maier's matrix method. This method later on led him and other mathematicians to the discovery of unexpected irregularities in the distribution of prime numbers. There have been various other applications of Maier's Matrix Method, such as on irreducible polynomials and on strings of consecutive primes in the same residue class.