Outside stimulation is necessary for coming up with good ideas
-Feynman
mathematicians and scientists need a certain level of randomness and inefficiency to come up with new ideas
From “You And Your Research”, Hamming makes the point that whatever you think is the best working environment for you, probably isn’t it. Sitting in a room by yourself is useful at times but it’s likely not ideal for generating new ideas.
From here:
Paraphrasing here to the best of my memory, Alan said, “Reading a couple hundred books a year is the bare minimum. It’s just the baseline. You also need to be embedded in a community of others who have diverse perspectives to bounce these ideas off of.” Alan argued passionately in favor of college and grad school. While he is well aware of its imperfections, he believes it’s still better than an “oral culture” or being an autodidact (just following your nose where your curiosity leads you).
But “in the end, we’re all autodidatic in having to find the motivation to do the learning ourselves. The key for autodidact-types is to set up ways to avoid insularity.” He recommends that autodidacts institute a “learning tax” on themselves: a decent percentage of one’s learning should be in areas other than the ones you are most interested in. But ultimately a university context can be very helpful to force you to learn what you didn’t even realize was worthwhile, and to supply “serendipitous other perspectives”. As for what to study, the key is that it needs to be difficult in ways that reshape your perspectives, like math, physics, or molecular biology.