Final answer:
Filippo Brunelleschi's greatest rival in the 1401 baptistery door competition was Lorenzo Ghiberti, who was awarded the commission.
Step-by-step explanation:
Filippo Brunelleschi, a noted architect and engineer of the Italian Renaissance, faced competition for the design of the bronze doors for the Florence Baptistery. His greatest rival in the 1401 competition was Lorenzo Ghiberti, who eventually won the contract. Brunelleschi's innovative works, especially his expertise in mathematical perspective and engineering, allowed him to design the magnificent dome of the Florence Cathedral, which is still admired today as a masterpiece of Renaissance architecture.
Ghiberti won the competition by a narrow margin and went on to create the famous bronze doors depicting scenes from the Old Testament, known as the "Gates of Paradise".