How to be a good scientist

How to get better at mathematical and scientific research?

1. Read (or devote time to your craft) everyday: slowly, deliberately… learning compounds. This is the fundamental step, if we are not putting in enough time, no amount of tips will help. Read things which actually help building the skills you want, textbooks, research papers, classic papers (Shannon etc); avoid sugary/pop stuff.
2. Discuss ideas: with a colleague, with an LLM, talk out your thoughts, clarify things, do it on a walk. This helps with recall, building clarity, communication, and learning.
3. Artefacts and Teaching: just plain consumption is not enough, try writing everyday, do proofs, do implementation of almost everything you know, write good blogs, make YouTube videaos. This helps with recall too; and helps us see our blind spots.
4. Reach out and form a community: reach out to professors, go to office hours, reach out to researchers, go to conferences, talks, try to build a community. This helps in getting new ideas, and staying at the forefront.
5. Depth will compund, choose it over breadth: Have a thesis in mind, and with that in mind, keep searching, exploring, going deeper, asking questions, too much breadth might not take you anywhere. Having a general vision will at least take you in one direction; and also provides you a “why” for your research and work.
6. Spaced Repetition and Recall: for new topics, learning syntax, for math areas you’re not working on currently spaced repetition tools like Anki might help.
7. A small problem every day: Of course, you must have some big problem statements always in your mind; but on a day-to-day basis solve the smaller problems, and as you solve them, you prepare yourself for the bigger ones. These can be any problems from you textbooks, programming problems, puzzles, etc. Read one problem, and take it with you before you’re about to sleep and mull over it. This helps build thinking and problem solving skills.
8. Write: I think this is so important, it needed a new point apart from point 3. Keep a personal journal as well, keep writing your thoughts, get good at writing, for yourself, for your work, etc. Everyone is using LLMs to write, but being able to write well with your own personal style will help set apart your work, and will refine your thinking.
9. Being a disciplined professional: Do not romanticize research and learning too much, romanticizing it introduces the ethereal notions of “passion”, “genius” etc, these introduce scope of giving excuses (example: blaming it on luck, privelage etc). Understanding that this (learning math, doing research) is a skill and a job (like plumbing, etc) will help you get through low-motivation and doubt. It is a craft like any other, do it for a few hours everyday. But keep going, and do it well.