With no explanation, label text_A→text_B with either "DON'T KNOW", "NO" or "YES".
text_A: After the death of his wife in July 1803, Ampère moved to Paris, where he began a tutoring post at the new École Polytechnique in 1804. Despite the absence of formal qualifications, Ampère was appointed a professor of mathematics at the school in 1809. As well as holding positions at this school until 1828, in 1819 and 1820 Ampère offered courses in philosophy and astronomy, respectively, at the University of Paris, and in 1824 he was elected to the prestigious chair in experimental physics at the Collège de France. In 1814 Ampère was invited to join the class of mathematicians in the new "Institut Impérial", the umbrella under which the reformed state Academy of Sciences would sit.
text_B: Is there good reason to believe that in 1809 Ampère was very knowledgeable in the field of mathematics?
YES.