During the time, a heretical strain of thought called Arianism was becoming popular. Arius, a popular teacher who fathered this heresy, was wrongly insisting that Jesus was not “consubstantial with the Father,” so Alexander excommunicated him in 321.
As tensions over the spreading heresy grew and pushed the Church to the brink of schism, Alexander responded by organizing the first council of Nicaea in 325, when the Church addressed our understanding of Jesus and articulated it in the Nicene creed that we pray on Sundays today.
In addition to his intellect and faithfulness, his contemporaries admired Alexander as a lover of God who was just and eloquent. He died in 328, and his relics rest in the reliquary chapel of the Basilica.