Böhm-Jacopini theorem I had a discussion with a friend developer and teacher. He told me about the Structured program theorem arguing that this theorem is one of the most important to know about. However, I have never heard about it and I don't understand how it may have deeply contributed to the computer theory. It seems quite cited in academic papers though.
I had never heard about it before, but taking a quick look at it I can understand why it is considered so important.

Basically, being able to prove that any program can be implemented via three basic operations (sequence, seletion, iteration) allows for simpler formalization when designing a new programming language.

It's basically a one-to-one correspondance to a Turing machine programme, therefore you can easily prove your programming language to be Turing complete.