This is probably the reason why there are so many more autodidact programmers than mathematicians. When programming, you know if you made an error as soon as you try to run your code. The program, by definition, must be "correct" in order to execute. The "source of correction" is the error detection built into any programming language runtime or compiler.
No such "source of correction" exists for mathematics, and that makes it an inherently more difficult subject to teach yourself, because any errors you make will "fail silently" unless you are capable of detecting them yourself, which by definition you cannot do without experience. This is why a mentor/professor makes learning mathematics so much easier; he/she plays the role of mathematical compiler.
Good point and great analogy, though I think EWD might be turning over in his grave. While the error detection built into compilers and the testing process are, in general, indispensable tools for developing stable software, a program that executes without any evidence of error is a great distance from a program that has been shown to be correct.
It's still easier to build up an understanding of computers under that environment. You may not be proving your programs correct, but you are probably proving them useful.
"The program, by definition, must be "correct" in order to execute"
This definition of 'correct' is why software may have a poor user interface and many security holes.
Your observation also assumes that the language is completely specified. In C, for example, certain constructs lead to undefined behavior. As a modification of the old warning, running your program may unexpectedly cause demons to fly out of your nose tomorrow. Execution therefore does not imply correctness.
I find that after doing some proofs work you start to get a sort of sixth sense feeling for when something isn't rigorously correct. In the words of one of my professors, "something smells wrong".
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This is probably the reason why there are so many more autodidact programmers than mathematicians. When programming, you know if you made an error as soon as you try to run your code. The program, by definition, must be "correct" in order to execute. The "source of correction" is the error detection built into any programming language runtime or compiler.
No such "source of correction" exists for mathematics, and that makes it an inherently more difficult subject to teach yourself, because any errors you make will "fail silently" unless you are capable of detecting them yourself, which by definition you cannot do without experience. This is why a mentor/professor makes learning mathematics so much easier; he/she plays the role of mathematical compiler.
Good point and great analogy, though I think EWD might be turning over in his grave. While the error detection built into compilers and the testing process are, in general, indispensable tools for developing stable software, a program that executes without any evidence of error is a great distance from a program that has been shown to be correct.
It's still easier to build up an understanding of computers under that environment. You may not be proving your programs correct, but you are probably proving them useful.
This definition of 'correct' is why software may have a poor user interface and many security holes.
Your observation also assumes that the language is completely specified. In C, for example, certain constructs lead to undefined behavior. As a modification of the old warning, running your program may unexpectedly cause demons to fly out of your nose tomorrow. Execution therefore does not imply correctness.
Proof verification, btw, offer a "source of correction" for mathematics -https://en.wikipedia.org/wiki/Automated_theorem_proving#Rela... .
I find that after doing some proofs work you start to get a sort of sixth sense feeling for when something isn't rigorously correct. In the words of one of my professors, "something smells wrong".