When faced with a problem that seems insurmountable, I often switch to a different problem or modify the existing one to find a new approach.

Most hard ideas can be simplified into easier concepts by identifying and removing unnecessary complexities.

When something feels too complex, it often indicates that it's not the right solution; sometimes you need to take a step back to find a simpler approach.

Focus on solving one overarching problem at a time to achieve success. Define success concretely and concentrate your energy on that goal.

In mathematics, there are many obstructions to solving problems, and computer scientists have been effective in ruling out certain approaches through no-go theorems, indicating that some problems may be undecidable.

When faced with multiple potential solutions, breaking them down makes the challenges more manageable, but prioritization is essential due to limited resources.

Theoretical math requires a different way of thinking, where you need to sit with a problem for a long time, building intuition and discipline to solve it.

The first step to overcoming challenges is to make the tasks small enough that you can accomplish them, no matter how trivial they may seem.

The Collatz conjecture, which involves iterating a simple process on natural numbers, is easy to state but remains unsolved, illustrating the complexity of seemingly simple mathematical problems.