David Brown wrote:
Simply, the fixed point functions allow you to write recursion of anonymous functions. But, I couldn't explain it. I got to where I could understand it enough to grok some simple code, but it doesn't appear to have stuck.
The Little Schemer teaches the fixed point functions and Y combinator as one of the fundamental pieces of functional programming. I figured that somehow a lot was dependent on them. Paul Graham named his VC company "Y Combinator" so it seems he thinks it is pretty important as well.
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