What the Church says about the Pope....from the MY CATHOLIC FAITH catechism

When does the Church teach infallibly through the Pope alone? --The Church teaches infallibly through the Pope alone, when he speaks officially (ex cathedra) as the Supreme Head, for the entire universal Church.
As the Pope has authority over the Church, he could not err in his official teaching without leading the Church into error. As Our Lord said to Peter, the first Pope: "I have prayed for thee, that thy faith may not fail; and do thou, when once thou hast turned again, strengthen thy brethren" (Luke 22:31-32).
In order to speak infallibly, the Pope must speak ex-cathedra, or officially, under the following conditions:


1. He must pronounce himself on a subject of faith or morals. Infallibility is restricted to questions regarding faith and morals. The Church pronounces on natural sciences and on legislation only when the perversity of men makes of them instruments for opposing revealed truths.If the Pope should make judgments on mathematics or civil governments, he is as liable to error as any other man with the same experience. Letters to kings and other rulers are not infallible pronouncements. However, we should hold the Pope's opinions on any subject with great respect, on account of his position and experience.
   
2. He must speak as the Vicar of Christ, in his office as Pope, and to the whole Church, to all the faithful throughout the world. In his capacity as private teacher, for example, in his encyclical letters, he is as any other teacher of the Church.Should the Pope, like Benedict XIV, write a treatise on Canon Law, his book would be written in a private capacity, and liable to error, just as the books of other theologians. We accept, not on faith, but in obedience to his authority, out of respect for his experience and wisdom.
   
3. He must make clear by certain words his intention to speak ex-cathedra. These words are most often used: "We proclaim," "we define," etc.The Pope's infallible decrees are termed "doctrinal," since they involve doctrine. From the earliest days of the Church, the infallibility of the Pope has been acknowledged. In the year 417 the Holy See condemned the Pelagian errors; St. Augustine cried out the famous words, "Rome has spoken; the cause is ended!" The Council of Florence in 1439 called the Pope "the Father and Teacher of Christians."