This post is inspired by Think from first principles before you Google (or ask ChatGPT) by Paras Chopra.

The central point is that you should always start by thinking from first principles and trying to solve a problem yourself. Only after you have invested time in thinking with your own brain, should you reach out for external solutions. Doing otherwise is lazy thinking, and you will just blindly use the hammer provided by somebody else.

If you ask another person for help, they will be more ready to help you because you’ve put in some work. If you search on Google or ask ChatGPT, it will help you understand and judge the provided answers better. Maybe the answers provided don’t apply in your context, and by doing the prework you will notice that more quickly.

Besides thinking beforehand about the problem, I also want to emphasize looking back after solving a problem. George Polya (a famous Hungarian mathematician, author of “How to solve it”) emphasized that for a future mathematician, the most important part of problem solving is the looking back step.

Some questions for looking back are:

• Is there any other ways of doing the problem that are simpler?
• What are the key insights that make the found solution work?
• Could we modify the problem so that the solution still works?
• Are there similar problems which could also be solved with the same solution?
• Are there other solutions that we could use?

If you think that you will never encounter a problem of that type again, then looking back is not so important. You solved the problem that you had, and now you can move on. But, if you think that you will encounter that kind of problem again, use this chance when your memory of the problem is fresh to extract even more lessons. Similar to first-principles thinking, it is an investment of time into learning.