Why is writing down mathematical proofs more fault-proof than writing computer code?

I have noticed that I find it far easier to write down mathematical proofs without making any mistakes, than to write down a computer program without bugs. It seems that this is something more widespread than just my experience. Most people make software bugs all the time in their programming, and they have the compiler to tell them what the mistake is all the time. I've never heard of someone who wrote a big computer program with no mistakes in it in one go, and had full confidence that it would be bugless. (In fact, hardly any programs are bugless, even many highly debugged ones). Yet people can write entire papers or books of mathematical proofs without any compiler ever giving them feedback that they made a mistake, and sometimes without even getting feedback from others. Let me be clear. this is not to say that people don't make mistakes in mathematical proofs, but for even mildly experienced mathematicians, the mistakes are usually not that problematic, and can be solved without the help of some "external oracle" like a compiler pointing to your mistake. In fact, if this wasn't the case, then mathematics would scarcely be possible it seems to me. So this led me to ask the question: What is so different about writing faultless mathematical proofs and writing faultless computer code that makes it so that the former is so much more tractable than the latter? One could say that it is simply the fact that people have the "external oracle" of a compiler pointing them to their mistakes that makes programmers lazy, preventing them from doing what's necessary to write code rigorously. This view would mean that if they didn't have a compiler, they would be able to be as faultless as mathematicians. You might find this persuasive, but based on my experience programming and writing down mathematical proofs, it seems intuitively to me that this is really not explanation. There seems to be something more fundamentally different about the two endeavours. My initial thought i