A short piece of very sound advice this week:
If there is a problem you can’t solve, then there is an easier problem you can solve: find it.
Pólya’s How To Solve It is a classic guide to the messy craft of “heuristics”. It’s also rare among maths books in having a lively sense of humour:
The traditional mathematics professor of the popular legend is absentminded. He usually appears in public with a lost umbrella in each hand. He prefers to face a blackboard and to turn his back on the class. He writes a, he says b, he means c, but it should be d. Some of his sayings are handed down from generation to generation:
“In order to solve this differential equation you look at it till a solution occurs to you.”
“This principle is so perfectly general that no particular application of it is possible.”
“Geometry is the science of correct reasoning on incorrect figures.”
“My method to overcome a difficulty is to go round it.”
“What is the difference between method and device? A method is a device which you used twice.”
No resemblance to living persons is etc. etc.