ABSTRACT
It is concerned with the study of the properties of the integers: After working with these numbers long enough one can begin to see patterns emerge and it is the study of these patterns that evolved into number theory. These were what author would call work books: concrete problems and only one solution given with no attempt to generalize. The Arabs and especially the Hindus kept up the study, but on the whole their work continued along the Diophantine line: doing specific cases rather than a general theory, whether they were doing original work or not. He began his work in number theory trying to prove many of Fermat's statements, went on to generalize some of these results and finally began to produce original results of his own. He also used analysis in the study of arithmetic questions, primarily the use of elliptic functions and at the age of fourteen conjectured the prime number theorem.
