Courant minimax principle

Imagine you have a cup filled with water. You want to move the water from one container to another, but you can only pour out one drop of water at a time. What is the fastest way to move all the water to the new container?

This is a tricky question because you have to balance two things: moving the water quickly and not spilling any. If you try to pour too much water at once, you might spill some and have to start over. But if you pour too little, it will take a very long time to move all the water.

The Courant Minimax Principle is a rule that helps you balance these two things. It says that, in general, the best way to move the water is to make each pour as large as possible without spilling any water. This way, you are moving a lot of water quickly, but you are also being careful not to spill any.

This principle is useful in many areas of math and science where you are trying to optimize something while avoiding risks. For example, if you are designing an airplane wing, you want it to be as aerodynamic as possible (to fly fast), but you also want it to be strong enough to withstand turbulence (to avoid crashing). The Courant Minimax Principle helps you find the best balance between these two requirements.