and a few months later to Pavia. In Pavia, the Einsteins settled in Palazzo Cornazzani, a medieval building where, at different times, Ugo Foscolo, Contardo Ferrini and Ada Negri lived. When the family moved to Pavia, Einstein, then 15, stayed in Munich to finish his studies at the Luitpold Gymnasium. His father intended for him to pursue electrical engineering, but Einstein clashed with the authorities and resented the school's regimen and teaching method. He later wrote that the spirit of learning and creative thought was lost in strict rote learning. At the end of December 1894, he traveled to Italy to join his family in Pavia, convincing the school to let him go by using a doctor's note. During his time in Italy, he wrote a short essay with the title "On the Investigation of the State of the Ether in a Magnetic Field". Einstein excelled at math and physics from a young age, reaching a mathematical level years ahead of his peers. The 12-year-old Einstein taught himself algebra and Euclidean geometry over a single summer. Einstein also independently discovered his own original proof of the Pythagorean theorem aged 12. A family tutor Max Talmud says that after he had given the 12-year-old Einstein a geometry textbook, after a short time "[Einstein] had worked through the whole book. He thereupon devoted himself to higher mathematics ... Soon the flight of his mathematical genius was so high I could not follow." His passion for geometry and algebra led the 12-year-old to become convinced that nature could be understood as a "mathematical structure". Einstein started teaching himself calculus at 12, and as a 14-year-old he says he had "mastered integral and differential calculus". At the age of 13, when he had become more seriously interested in philosophy (and music), Einstein was introduced to Kant's Critique of Pure Reason. Kant became his favorite philosopher, his tutor stating: "At the time he was still a child, only thirteen years old, yet Kant's works, incomprehensible to ordinary mortals, seemed to be clear to him." In 1895, at the age of 16, Einstein took the entrance examinations for the Swiss Federal polytechnic school in Zürich (later the Eidgenössische Technische Hochschule, ETH). He failed to reach the required standard in the general part of the examination, but obtained exceptional grades in physics and mathematics. On the advice of the principal of the polytechnic school, he attended the