Maths Times Infinity > Topics > Maths

General tips on maths.

Problem solving strategies:

• Look at small, simple cases. Solve those fully. Try to apply the same techniques to the actual big problem. Try to notice a pattern and then see if you can prove it - why is it true?

• Try putting a question into your own words. That may help you understand what it means and what it's asking.

Conjectures:

• Generalise it. It's probably not an isolated thing. Find other examples. What happens if you tweak the conditions? How do they affect the result? Therefore, what is their true role/function? Do simple cases. Build from there. Theorise more powerfuly statements.
• Strengthen it. Weak statements are hard to prove. Be more specific. Get to the heart of the real relationship/phenomenon. Then it might become clear what it's really saying, where it comes from and why it's true.

It's funny, but it's often easier to prove something much more powerful than the conjecture itself. For example, when they finally proved Fermat's Last Theorem, they also proved a huge amount of other stuff which technically, they didn't have to. It was just the most natural approach.