Number Theory Before Fermat

This chapter outlines very briefly the development of Counting, Number Theory and Arithmetic before Fermat’s time, so that it is easier to understand the importance of Fermat’s contribution. Here we also discuss other linked branches of mathematics and explain the views of mathematicians in general at that time.
This will underline how special Fermat’s contribution was.
 

Fermat’s Life Outside of Mathematics

Here we discuss the little that is known of Fermat’s private life. Although Fermat devoted his spare time to mathematics, he was aware that this was not his profession. Therefore, to better understand the person behind the great mind, it is necessary also to consider his professional life in parliament. As for his personal life, we do not really know much, as he carefully shielded his life from the public world.
 

Fermat and Mathematics

Fermat was not only one of the greatest number theorists, but he also did important and foundational work on optics, probability and general calculus. Here we point out the diversity of his mathematical interests and the multiple problems which he worked on before we turn our eyes on his most important contributions.
 

Fermat and Mathematicians

Since Fermat did not take it directly into his own hands to publish his works, his only way to communicate was through other mathematicians, with whom he shared his love for mathematics and with whom he was in constant correspondence throughout his mathematical life. Here we also show how the great controvery between Fermat and Descartes started.
 

Fermat and Number Theory

In this chapter we explain some of Fermat’s more important theorems, based on examples,
and give many of the proofs.
 

Fermat’s Last Theorem

Here the emphasis is laid on Fermat’s famous last theorem. This was remarkably simple in its content, but its proof was so complex that for 350 years mathematicians all over the world tried and failed to prove it. Only recently, in 1994, did Andrew Wiles from Princeton give a proof which most of the experts now believe is true. The chase for this proof motivated both skilled mathematicians and amateurs, and was one of the ‘most wanted’ in the mathematical world. Since I do not claim to even understand the simplest parts of the proof except in very rough outline, no summary of the proof will be found here. However, we do present the story of its discovery, and the dramatic and finally successful search for a proof. The chronological table will outline the more important steps towards its final solution.
 

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