On the Fermat conjecture (Q5917607)

This note begins with a prehistory of the Fermat problem, and then proceeds to briefly explain that in studying rational points on curves the interesting case is that of elliptic curves. The article provides a succinct summary of facts about elliptic curves and modular functions relevant to explaining the content of the modularity conjecture (here attributed to all of Eichler, Shimura, Taniyama and Weil), thence of Ribet's Theorem, and finally its connection with Fermat's Last Theorem.