Yes. You need spend a lot more time thinking about each line of a math proof than you do about each line of code you write, and you need to develop skills and t

Yes. You need spend a lot more time thinking about each line of a math proof than you do about each line of code you write, and you need to develop skills and techniques for catching and correcting errors. Your ability to catch errors tends to be closely linked to the amount of time you've spent working in a particular area - because you build up a mental suite of test cases to check every claim against. One mistake I see occasionally is jumping into a brand new area of math and moving just as quickly as you would in the old area where you had more expertise, making huge blunders every step of the way. When you enter a new area, you have to go really excruciatingly slowly as you build up the intuition and suite of examples. Almost every math paper contains an error or two - they are usually easy for an expert to fix (the equivalent of leaving out a semicolon at the end of a line in C++, takes only a moment to fix if you have familiarity with the language - but incredibly frustrating to a user who doesn't know how to make the easy fix).