Einstein's personalityLet's get this out of the way. Einstein didn't fail math. He was always a very smart and hardworking student. In primary school, he was at the top of his class and "far above the school requirements" in math. And before he was 15 he had mastered differential and integral calculus.
What may have helped propagate the myth was Einstein's unruly and defiant personality. Einstein would do great at the things he likes, and not good at the things he doesn't like. He had excelled in his university classes that he liked, and did average in the ones he disliked (such as physics experiments classes). Einstein was certainly a black sheep and kept clashing with authority. He was an outspoken peace activist and social democrat. He was brave, and not afraid to speak his mind even when he was getting dead threats and the wars were brewing in Europe. This defiant/black-sheep personality also helped him formulate novel theories that revolutionized the prevalent physics views/understanding at the time.
True to the stereotype, Einstein was goofy and forgot stuff all the time. He had spent a lot of time in this brain, thinking about physics all the time. "I can already imagine the fun we will have," he wrote to Maric about a prospective vacation. "And then we'll start in on Helmholtz's electromagnetic theory of light." He was immersed with physics/ideas all the time, and his daily life almost came as interludes to his physics thinking. This has also been a prevalent pattern in Richard Feynman's life.
Contrary to the nerd professor stereotype, Einstein was also very outdoorsy, sailed, hiked, and liked to live a good life. He was a very good violin player and enjoyed giving concerts to friends. Teaching was initially hard and awkward for Einstein, but he gradually got accustomed to it, and found his own unique style and voice for teaching.
Einstein enjoyed company and attention of his friends. He founded the Olympia Academy with group of friends in Bern, Switzerland, who met in his apartment in order to discuss philosophy and physics. Einstein used this group to bounce off his ideas, and study and learn new things very much like Benjamin Franklin's Junto group. (I also recommend the Benjamin Franklin's biography written by Walter Isaacson.)
Einstein's researchEinstein was a very intuitive and creative person. He famously said "Imagination is more important than knowledge." Einstein was a big ideas person. He was a deep thinker, but not a brute force technical/math/hardwork physicist type. His papers are not tour-de-force papers, rather they were simple, and more like position papers. He was a theorist. He read a lot of papers, including many experimental papers, and thought a lot and suggested elegant theories to explain the phenomena reported in those papers. The way he developed those theories is mainly by running thought experiments (gedankenexperiment).
The chapter about Einstein's miracle year (1905) is a very good read. This was where Einstein caught his first breakthrough. Einstein, then 26, published 4 groundbreaking papers (short position papers), on the photoelectric effect, Brownian motion, special relativity, and the equivalence of mass and energy. Einstein kept this momentum and kept publishing interesting papers at a good rate, including his new theory of general relativity in 1911.
What factors led to his breakthrough miracle year? Einstein had been churning some ideas and gestating theories starting from his college years. He had also been bouncing ideas off his friends in Olympia Academy. And finally, he was employed at the patent office which stimulated Einstein's thinking. Working at the patent office was like listening to high-tech startup pitches everyday, except the topics were mostly on electric/magnetic waves and clock synchronization, which instigated his thinking on photoelectric effect and relativity.
Einstein's relentless focusIt was very interesting to read about the promising young Einstein trying to get a job, but failing to get even a small teaching job. His attempts at PhD dissertations were also turned down. Unappreciated genius indeed. In addition to those difficulties, Einstein also lived through very turbulent times in Europe. His marriage and personal life also went through very tough periods. Throughout all this, he was always focused on his research and found solace in his studies. He was a man with a mission. He was afraid he would die before he could build his relativity theory, and was OK with dying afterwards.
On page 162, the book talks about how deep Einstein could concentrate. When his students dropped by his apartment, they found that Einstein was finishing work on a complicated problem, while he had his small son in his lap crying. Not exactly an ideal work environment, but Einstein was so focused, he wasn't bothered by the son crying, and solved the problem. A couple page later, there was a heartwarming description of Einstein and Lorentz doing research together. Two passionate physics geeks discussing ideas and bouncing questions back and forth.