How to solve math problems

Jan Mandel

• Keep in mind what the problem is to make sure you are not doing something else. Many problems are solved and proofs done simply by understanding what is what.
• Visualize the problem and the background material from memory, with your eyes closed. If you are just a little unsure of something, look it up. It never hurts to return to the basics - even many times.
• Keep returning to the problem and the material and keep it all in the back of your mind as much as possible. Think about it every time when you have a quiet moment.
• When you have done the above, your brain will have something to work on in the background, and eventually an idea will come to you. Execute the idea.
• When you think you are done, examine your solution in detail and justify every step for yourself very carefully. Look up and clarify for yourself everything you are just a little unsure of. Try really hard to prove your solution wrong. Attack it from every angle.
• Repeat until you solve the problem.
• If you solve many problems this way, you will get good at it and get faster. But you must start slow.