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 at age 12. A family tutor Max Talmud says that after he had given the 12-year-old Einstein a geometry textbook, after a short time " 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".