In order to solve this differential equation you look at it until a solution occurs to you.

There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it may be difficult. Von Neumann didn't say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof. After that I was afraid of von Neumann.

What is the difference between method and device? A method is a device which you use twice.

If there is a problem you can't solve, then there is an easier problem you can't solve: find it.

Epitaph on Newton: Nature and Nature's law lay hid in night: God said, "Let Newton be!," and all was light. [added by Sir John Collings Squire: It did not last: the Devil shouting "Ho. Let Einstein be," restored the status quo] [Aaron Hill's version: O'er Nature's laws God cast the veil of night, Out blaz'd a Newton's soul and all was light.

It may be more important in the mathematics class how you teach than what you teach.

Look around when you have got your first mushroom or made your first discovery: they grow in clusters.