In principle programmers are supposed to write correct code. But I wonder if in practice it's possible to solve really hard problems without incorrect code as an intermediate step.
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in my experience when you solve a hard problem like a mathematical algorithm, sometimes your code has no bugs. but when you solve a practical problem like adding retry logic when a socket fails, there are always bugs
Yes, I wrote a lot of math code about a year ago, and I was astonished how often things worked the first time.
