Thread by @FactsOfMath

Steps to Solving a Math Problem:

1. Reread the problem statement, taking care not to miss any important adjectives which may make proving your statement easier.

2. Determine a simple example which illustrates the concept and attempt to prove your statement for that simple case.

3. Get discouraged as the simple example turns out to be harder than originally anticipated.

4. Determine there must have been some sort of simple point you were missing and continue working on your simple example.

5. Get discouraged as the simple example turns out to be harder than originally anticipated.

6. Reread the problem statement, noting that your simple example does not fit the hypotheses of what you are trying to prove.

7. Get discouraged and start thinking about how much more money you could be making in the industry doing much simpler math.

8. Remind yourself that no one in industry is happy either.

9. Realize that the assumptions of your simple example make the statement trivial.

10. Determine a slightly less simple example which illustrates the concept and attempt to prove your statement for that simple case.

11. Get discouraged when you realize that solving the slightly less simple example essentially equates to solving the entire problem, which is very hard.

12. Spend time thinking about the progress of your peers, how they are doing so much better than you, and how your job prospects are hopeless in comparison to theirs.

13. Remind yourself that comparing yourself to peers can only serve to make you more discouraged and continue trying to prove your statement.

14. Recall a theorem you learned six months ago which may help in proving your statement.

15. Determine an outline of a potential proof which incorporates that theorem. Become slightly hopeful that you are making progress in your proof.

16. Fill in details of your outline. Become more hopeful that this may turn out to become a solution.

17. Look up Theorem that you were planning to use. Realize it does not apply. Become discouraged.

18. Ask for help from a professor or peer. Receive an explanation which seems like bullshit, but then realize that you don’t know enough to call it out.

19. Attempt to sort through the explanation using the fragments you remember after the discussion. Be too stubborn to ask your friend to repeat their explanation.

20. Get discouraged and start thinking about how much more money you could be making in the industry doing much simpler math.

21. Remind yourself that money does not buy happiness.

22. Realize that the answer to your problem may lie in a computation involving matrices. Delay this computation for as long as possible.

23.Become discouraged and attempt to prove an unrelated statement. Become discouraged at that statement and return to attempting to prove your original statement.

24. Drag yourself through the matrix computation. Arrive at an answer which cannot be correct.

25. Do the computation again, and arrive at a different answer which could technically be correct, but seems unlikely.

26. Do the computation again, and arrive at a third different answer which seems more like something you could work with.

27. Check your computation for accuracy and realize that the second computation was actually the correct one.

28. Attempt to take a break from working on the problem.

29. Worry about how little progress you are making and quickly return to work.

31. Note a trivial observation which solves your example.

32. Realize this trivial statement generalizes to prove your statement.

33. Realize the statement you were trying to prove was much more trivial than the hours of work you put into it might suggest.

34. Get discouraged and start thinking about how much more money you could be making in the industry doing much simpler math.

35. Remind yourself that, at least every so often, you are doing something you love.

36. Find another statement to prove and repeat at step one.