Clear Mind
The Second Mind
A Clear Mind: Foundations for Mathematics
Prerequisites
Good mathematics requires a clear mind. Good mathematics requires sustained focus. The foundation of such sustained focus is a level of mental energy furnished by sufficient sleep and good diet. The foundation of clarity is calmness.
Antirequisites
I find that when my mind is filled with many thoughts, it is difficult to hear my mathematical thoughts behind the noise. Even enjoyable activities such as trips with family might make it difficult to continue working at night. Mental energy is used on this, and it somehow is difficult to think after this.
More worrying is social media. I find that social media makes it difficult to concentrate on mathematics. Thoughts drift too easily to videos, comments, threads read on boundless scrolling. Something feels off about social media–like the smell of roaches nested in a cupboard. They’re there, but you can’t put your finger where. But you see them come out at night.
Clear Thinking
I will often run into scenarios where I no longer have traction on any mathematical problems.
At times, I desire to continue, but I try many times to make progress on a problem and no new ideas come to mind. At other times, I feel that I ought to continue, but I simply cannot.
In these scenarios, I have found it more efficient to refocus my energy on other pursuits–such as writing or programming, or light physics or mathematics reading for recreation.