Euler accepted an invitation from Frederick the Great to join the Berlin Academy of Sciences. Frederick sought to enhance the academy's reputation and attract leading intellectuals.

Euler became the director of the Physics-Mathematics Class at the Berlin Academy. He oversaw the scientific research and direction of the academy during this period.

Euler's time in Berlin was marked by extraordinary productivity. He wrote numerous books and articles on a wide range of subjects, including calculus, number theory, mechanics, optics, and astronomy.

Euler published "Introductio in analysin infinitorum", a groundbreaking work that laid the foundation for modern mathematical analysis. It systematized and expanded upon existing knowledge of calculus and introduced new concepts.

Euler published "Institutiones calculi differentialis", a comprehensive textbook on differential calculus that further solidified his reputation as a leading mathematician.

Euler's relationship with Frederick the Great was sometimes strained. Frederick admired Euler's intellectual abilities but occasionally found him socially awkward and less polished than other members of the court.