Richard Feynman taught himself advanced mathematics from books without the aid of a teacher. Here's how he mastered calculus by the age of 15:
He started with a series of self-instruction books called Calculus for the Practical Man, which explained the principles of differential and integral calculus in a clear and simple way.
He followed the book closely and took meticulous notes in his own notebook, copying diagrams and formulas carefully. He also compiled a table of contents for his notes, which helped him find the relevant sections later. He found the book fascinating and challenging, and it was the first time he realized that he could understand something that his father could not.
He developed his own mathematical notations and symbols before he entered college, and experimented with topics such as the half-derivative using his own logic.
Feynman’s calculus notes show his insatiable curiosity and his determination to learn by himself. He later became one of the most influential physicists of the 20th century, known for his contributions to quantum mechanics, particle physics, and many other fields.